28 Replies Latest reply on Apr 10, 2014 4:52 PM by Shaun Densberger

    Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass

    Nathan Obermiller

      What are our options in Solidworks to account for the missing mass effect on a response spectrum analysis?

       

      Suppose I have an assembly with only one significant vibration mode (lets assume its a 1DOF for this discussion) with a mass participation of 50% at 30Hz and one other mode at 150Hz with mass participation of the remaining 50%.  However, lets assume our response spectrum analysis cutoff frequency is 33Hz as typical.  I am I correct in believing common practice would be to apply an equivalent static load using the remaining 50% mass on the assembly, possibly simply by modeling a 0.5g gravity load?  If we were to do this, what are our options to superimpose this load on the response spectrum results?  Is that even valid?

       

      Thank you.

        • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
          Jared Conway

          "our response spectrum cutoff is at 33hz"

           

          are you thinking that means that the software won't use the 150Hz response?

            • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
              Nathan Obermiller

              " 'our response spectrum cutoff is at 33hz'

               

              are you thinking that means that the software won't use the 150Hz response?"

               

               

              Yes, that is what I'm thinking.  If my base excitation is limited to say 33Hz, the analysis stops at 33Hz from my understanding, regardless of what you set the solver properties.  If you look at the mass participation analysis results for the response spectrum analysis study, it will only show the modes below 33Hz. 

               

              I may be wrong, but the evidence in the results output seems to show those frequencies above the cutoff are not solved.

               

              I'm not entirely sure if there is a way to similate those higher modes without solving for them.  For instance, it would be inappropriate to extend the simulation to 150Hz to account for the missing mass in the mass participation because the equipment will not see load in this frequency range.  The missing mass load must be some fraction of the normal load, but I am uncertain how to apply it to the results of the response spectrum analysis.

               

              I believe the old COSMOS/M package had a coefficient method available.  From the old ASTAR manual:

              " The Missing Mass Correction

              technique is incorporated in the ASTAR program for Response Spectrum

              analysis in order to estimate the error introduced by the ignored higher modes and

              to improve the results. This correction is presented as a factor in the output file

              immediately after the printed accelerations. The user may apply this factor to

              improve the accuracy for the results obtained for accelerations or stresses."

            • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
              Shaun Densberger

              If you modal analysis doesn't capture the 150 Hz mode, then it will not be included in your dynamic analysis. That being said, if you do capture the 150 Hz mode in your modal analysis, but yout RSC only goes to 33 Hz, then my assumption would be that SW will set the response at 150 Hz to 0 (since the curve doesn't contain a value at that frequency).

               

              You are correct that there are methods for accounting for the remaining mass, but I don't this Dassult incorperated this into SW from COSMOS.

                • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                  Nathan Obermiller

                  I just tried changing the settings with a higher upper limit (above my input spectrum) and I get an error.

                    • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                      Shaun Densberger

                      Do you mean you modified your modal analysis such that the highest mode found is greater than the highest frequency on your RSC?

                        • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                          Nathan Obermiller

                          If I go to the study properties, frequency options, and change the upper cutoff frequency.  Error is "Additional points are required in definition of the excitation curve..."

                           

                          Also, one of my requirements is to evaluate the frequencies with a specific resolution.  I know you can set up the frequency step in the harmonic analysis, but I see no options in the response spectrum analysis to do this.  Is there a way to set up the solver to provide frequency resolution such as the following?

                           

                          Frequency Range (Hz)

                          Frequency Step (Hz)

                          0.2-3.0

                          3.0-3.6

                          6.5-5.0

                          5.0-8.0

                          8.0-15.0

                          15.0-18.0

                          18.0-22.0

                          22.0-33.0

                          0.10

                          0.15

                          0.20

                          0.25

                          0.50

                          1.00

                          2.00

                          3.00

                           

                            • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                              Shaun Densberger

                              If I go to the study properties, frequency options, and change the upper cutoff frequency.  Error is "Additional points are required in definition of the excitation curve..."

                               

                              Hmmm, looks like your RSC must have a range that matches the frequencies from your modal analysis.

                               

                              Also, one of my requirements is to evaluate the frequencies with a specific resolution.  I know you can set up the frequency step in the harmonic analysis, but I see no options in the response spectrum analysis to do this.  Is there a way to set up the solver to provide frequency resolution such as the following?

                               

                              Where is this requirement from? I ask because there isn't really a frequency resolution with the response spectrum method.

                               

                              In a harmonic analysis, you're exciting your system with given frequencies and magnitudes and calculating the response (hence being able to control the frequency step size). For example, you might have an excitation curve with a magnitude of 1 m/s^2 for a frequency range of 1 Hz to 300 Hz. You can then ask the solver to calculate the response at 1 Hz increments (1 Hz, 2 Hz, 3 Hz, ...,300 Hz) or 0.5 Hz increments (1 Hz, 1.5 Hz, 2 Hz, ...,300 Hz).

                               

                              With the response spectrum method, your input curve is the response of the system at given frequency (hence the damping being included in the curve). For example, say you have the following RSC:

                               

                              Frequency (Hz)Acceleration (m/s^2)
                              0.30.2
                              0.62
                              2.05
                              5.05
                              151.6
                              501.6

                               

                              And you system has two modes: 5 Hz and 12 Hz. What happens is that SW takes the modal analysis solution for the 8 Hz mode and applies a 5 m/s^2 acceleration to the system (since the RSC defines that as the response of the system at 8 Hz) and calculates the resulting displacements and stresses. SW then takes the modal analysis solution for 12 Hz and applies either ~2 m/s^2 or ~2.85 m/s^2 (which it uses depends on whether you have linear or logarithmic interpolation) and calculates the resulting displacements and stresses.

                               

                              You have have two sets of displacement and stress results, but at the end of the day you want just one set. This is where the modal combination algorithm comes in, of which SW has four (Absolute Sum, SRSS, CQC, and NRL). Which you use depends on the specifics of your model.

                                • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                  Nathan Obermiller

                                  This resolution requirement comes from our customer's design specification.  Really this applies to the frequency solver of the RSA module for analyzing the resonance modes.  If the resolution is not high enough then the solver may not identify a resonance, or inaccurately identify it's response.  For instance, the solver may identify 8Hz as a peak with a resolution of 0.2Hz, but really the peak is a 8.1, and the amplification at that peak may be much higher than at 8Hz.  I'm not sure how the Response Spectrum module solves the problem, but I do notice significant differences when I perform a harmonic study using the same excitation curves.  Does the response spectrum solver not include amplification behavoir?

                                   

                                  Perhaps this more accurately represents a seismic multi-frequency test with a RRS where harmonic modes are not excited like it would be on a sine sweep or sine beat test?

                                   

                                  Also, you mentioned at 8Hz it would pick up 5m/s^2.  Does the solver not interpolate between points so that the acceleration at 8Hz would be more like 4g, or was this a typo?

                                   

                                  Frequency (Hz)Acceleration (m/s^2)
                                  0.30.2
                                  0.62
                                  2.05
                                  5.05
                                  151.6
                                  501.6
                                    • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                      Shaun Densberger

                                      This resolution requirement comes from our customer's design specification.

                                       

                                      Your customer might be mistaken then; as I understand the RSM, this isn't a valid request.

                                       

                                      Really this applies to the frequency solver of the RSA module for analyzing the resonance modes.  If the resolution is not high enough then the solver may not identify a resonance, or inaccurately identify it's response.

                                       

                                      I'm not too sure how SW handles it (I use another package), but a linear dynamic analysis is really two analyses: a modal analysis (finding your eigenvalues and vectors) and a dynamic analysis (whether response spectrum, frequency sweep, time history, etc). The dynamic analysis uses the results from the modal analysis as an input.

                                       

                                      For instance, the solver may identify 8Hz as a peak with a resolution of 0.2Hz, but really the peak is a 8.1, and the amplification at that peak may be much higher than at 8Hz.

                                       

                                      You'd only need to worry about this if your RSC showed this (a large jump from 8 Hz to 8.1 Hz). That being said, an accurate dynamic analysis starts with an accurate modal analysis.

                                       

                                      I'm not sure how the Response Spectrum module solves the problem, but I do notice significant differences when I perform a harmonic study using the same excitation curves.  Does the response spectrum solver not include amplification behavoir?

                                       

                                      That's because the curve means two different things between a response spectrum analysis and a harmonic analysis. In a harmonic analysis, the curve defines your forcing function (whether base excitation or a force); you can think of it as describing the base of a shaker table with respect to the frequency. In a response spectrum analysis, the curve defines the system's response as a function of frequency; the system's dynamic amplification characteristics are captured in a response spectrum curve. The curves are typically created by plotting the response of n number of mass-spring-dampener systems, where each has it's own unique resonance frequency. This is why you'll see a damping value included with the RS curve. For example, the values I gave previously include 2% damping. Check out this link for more information.

                                       

                                      Also, you mentioned at 8Hz it would pick up 5m/s^2.  Does the solver not interpolate between points so that the acceleration at 8Hz would be more like 4g, or was this a typo?

                                       

                                      Ack! I fat-fingered that; should be 5 Hz (I've edited my post). You'll need to check this for SW, but there should be a method for defining how the software interpolates between two values.

                                        • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                          Nathan Obermiller

                                          This seems just like my miscommunication or misunderstanding of what you are saying.

                                           

                                          Is there any way to correlate a harmonic study and response spectrum study through analysis of the component response?  I'm still unsure how the harmonic response is incorporated into the response spectrum study.

                                           

                                          You stated,

                                          In a response spectrum analysis, the curve defines the system's response as a function of frequency; the system's dynamic amplification characteristics are captured in a response spectrum curve.

                                          I know this as the input.  This happens in order to create a required response spectrum.  But all this happens in the black box that is the base exitation for my fixture.  My question is: what is the response of my component to this base excitation and how that is included in the results?  If I have a resonance at 5Hz with an amplification of 10 at a particular point in the harmonic study, why do I not see this amplification in the response spectrum?  The amplification factor in the harmonic study should be independent of the input acceleration (for linear problems).  So why is this amplification non-existent in the response spectrum study.

                                           

                                          If I solve for a single frequency, my acceleration plots should have the same amplifications relative to the base excitation, no?

                                           

                                          I'm asking because I have vibration aging testing on a component.  The test is a sine sweep, 1g from 10-500Hz.  If I do a harmonic study to analyze this I get outrageous results for accelerations, displacements, and stresses.  But my RRS model with a 10g peak is several orders of magnitude below the harmonic study.  Is harmonic only to resolve the significant resonance modes?  Should it not be used for stresses and displacements and other values like the frequency solver?

                                            • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                              Jared Conway

                                              I Think we need to take a step back.

                                               

                                              Do you need harmonic or response spectrum? They are different types of studies.

                                               

                                              If you need harmonic and are using response spectrum cause it doesn't look right, is go back and find our why harmonic isn't working rather than trying to find workarounds to something to you may not need.

                                               

                                              Post the spec you are trying to follow.

                                              • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                                Shaun Densberger

                                                Is there any way to correlate a harmonic study and response spectrum study through analysis of the component response?  I'm still unsure how the harmonic response is incorporated into the response spectrum study.

                                                 

                                                I'd have to think about this a little more. When you say harmonic response, you're talking about dynamic amplification, correct?

                                                 

                                                My question is: what is the response of my component to this base excitation and how that is included in the results?

                                                 

                                                The response is define by your modal analysis results, the RSC, and your mode combination method.

                                                 

                                                If I have a resonance at 5Hz with an amplification of 10 at a particular point in the harmonic study, why do I not see this amplification in the response spectrum?

                                                 

                                                You do; it's captured in the y-axis value on the RSC.

                                                 

                                                The amplification factor in the harmonic study should be independent of the input acceleration (for linear problems).

                                                 

                                                Correct; the amplification is a function mass, stiffness, and dampening.

                                                 

                                                So why is this amplification non-existent in the response spectrum study.

                                                 

                                                It is, but unlike a frequency sweep (harmonic analysis), the dynamic amplification in captured within the RSC. Remember, a RSC is the response of n number of mass-spring-dampener systems to a pre-defined input. In the example I gave, a Zone 4 seismic event was used to excite n number of masses, and their responses (dynamic amplification included) is the plot shown in the RSC. The frequency axis on a RSC is not the frequency of some sort of focing function, but rather the resonance frequency of your system.

                                                 

                                                If I solve for a single frequency, my acceleration plots should have the same amplifications relative to the base excitation, no?

                                                 

                                                I'm not sure what you mean; can you clarify this for me?

                                                 

                                                 

                                                I'm asking because I have vibration aging testing on a component.  The test is a sine sweep, 1g from 10-500Hz.

                                                 

                                                You should be doing a harmonic analysis then, not a response spectrum analysis.

                                                 

                                                If I do a harmonic study to analyze this I get outrageous results for accelerations, displacements, and stresses.

                                                 

                                                It's hard to say why this is without looking at the model. Just keep in mind that a harmonic analysis is time independent (it's not going to capture how long it takes to get to the peak amplification point).

                                                 

                                                But my RRS model with a 10g peak is several orders of magnitude below the harmonic study.

                                                 

                                                RRS? Is this your response spectrum analysis? If so, did you use the same input curve for this study as you did for your harmonic study? If so, then the reason why there is such a big differences is because the curve means two different things between the two analysis types.

                                                 

                                                Is harmonic only to resolve the significant resonance modes?  Should it not be used for stresses and displacements and other values like the frequency solver?

                                                 

                                                No. In SW, a frequency analysis is used to calculate your resonance frequencies and the mode shape associated with them (this is why I've been referring to it as a modal analysis). A frequency analysis is the foundation of any linear dynamic analysis. A harmonic analysis uses the results of a frequency analysis and sinusoidal input (defined by you) to excite a constraint or a force, and solves for the steady-state response of the system as a function of frequency. It can accurately capture displacements, stresses, accelerations, etc. provided that you have done a good frequency analysis and that you're looking for the steady-state response of the system.

                                                  • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                                    Nathan Obermiller

                                                    Thanks for the response.

                                                     

                                                     

                                                    Shaun Densberger wrote:

                                                     

                                                    Is there any way to correlate a harmonic study and response spectrum study through analysis of the component response?  I'm still unsure how the harmonic response is incorporated into the response spectrum study.

                                                     

                                                    I'd have to think about this a little more. When you say harmonic response, you're talking about dynamic amplification, correct?



                                                          Yes.  The amplification in each node in the RSC study and in the harmonic study.

                                                     

                                                    My question is: what is the response of my component to this base excitation and how that is included in the results?

                                                     

                                                    The response is define by your modal analysis results, the RSC, and your mode combination method.

                                                     

                                                    If I have a resonance at 5Hz with an amplification of 10 at a particular point in the harmonic study, why do I not see this amplification in the response spectrum?

                                                     

                                                    You do; it's captured in the y-axis value on the RSC.
                                                         

                                                     

                                                    The amplification factor in the harmonic study should be independent of the input acceleration (for linear problems).

                                                     

                                                    Correct; the amplification is a function mass, stiffness, and dampening.

                                                     

                                                    So why is this amplification non-existent in the response spectrum study.

                                                     

                                                    It is, but unlike a frequency sweep (harmonic analysis), the dynamic amplification in captured within the RSC. Remember, a RSC is the response of n number of mass-spring-dampener systems to a pre-defined input. In the example I gave, a Zone 4 seismic event was used to excite n number of masses, and their responses (dynamic amplification included) is the plot shown in the RSC. The frequency axis on a RSC is not the frequency of some sort of focing function, but rather the resonance frequency of your system.



                                                          Right, so if I have a single harmonic ocillator at 5Hz, why is my amplification not the same as if I did a harmonic study and looked at a single frequency at 5Hz?  I understand why the combined results are different, but if I look at a single frequency value, I should be able to correlate the amplifications, no?  Same question below.

                                                         

                                                     

                                                    If I solve for a single frequency, my acceleration plots should have the same amplifications relative to the base excitation, no?

                                                     

                                                    I'm not sure what you mean; can you clarify this for me?



                                                           See above.

                                                     

                                                    I'm asking because I have vibration aging testing on a component.  The test is a sine sweep, 1g from 10-500Hz.

                                                     

                                                    You should be doing a harmonic analysis then, not a response spectrum analysis.



                                                      I have sine sweep and random multifrequency testing.  Both with different input spectrums.  My sine sweep mimics aging at 1g.  My RSC mimics an earthquake at 10g.  My sine sweep has response that is 10 times higher with 10 times the stresses.  Its hard to believe that is correct.  The study properties are copied so there were no different in the model setup.  This initiated my whole question on comparing the harmonic and the RSC results.  My model is over 20mb with dozens of subcomponents so I'm not going to share it.  And since this a conceptual question I don't want to go through the process of making up dummy blocks to discuss.

                                                     

                                                    If I do a harmonic study to analyze this I get outrageous results for accelerations, displacements, and stresses.

                                                     

                                                    It's hard to say why this is without looking at the model. Just keep in mind that a harmonic analysis is time independent (it's not going to capture how long it takes to get to the peak amplification point).

                                                     

                                                    But my RRS model with a 10g peak is several orders of magnitude below the harmonic study.

                                                     

                                                    RRS? Is this your response spectrum analysis? If so, did you use the same input curve for this study as you did for your harmonic study? If so, then the reason why there is such a big differences is because the curve means two different things between the two analysis types.

                                                     

                                                    Is harmonic only to resolve the significant resonance modes?  Should it not be used for stresses and displacements and other values like the frequency solver?

                                                     

                                                    No. In SW, a frequency analysis is used to calculate your resonance frequencies and the mode shape associated with them (this is why I've been referring to it as a modal analysis). A frequency analysis is the foundation of any linear dynamic analysis. A harmonic analysis uses the results of a frequency analysis and sinusoidal input (defined by you) to excite a constraint or a force, and solves for the steady-state response of the system as a function of frequency. It can accurately capture displacements, stresses, accelerations, etc. provided that you have done a good frequency analysis and that you're looking for the steady-state response of the system.

                                                     

                                                    That being said.  I define the options of the RSC to give relative results compared to the base excitation, use a single frequency in the RSC, why would the results of a single harmonic study plot step not be the same?  In theory, my forcing function at a single frequency should not be any different than my harmonic function?

                                            • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                              Nathan Obermiller

                                              So if I wanted a resolution as in the following:

                                               

                                               

                                              Frequency Range (Hz)

                                              Frequency Step (Hz)

                                              0.2-3.0

                                              3.0-3.6

                                              6.5-5.0

                                              5.0-8.0

                                              8.0-15.0

                                              15.0-18.0

                                              18.0-22.0

                                              22.0-33.0

                                              0.10

                                              0.15

                                              0.20

                                              0.25

                                              0.50

                                              1.00

                                              2.00

                                              3.00

                                              do I have to change my base excitation spectrum to have a resolution with the frequency steps above and interpolate the accelerations myself between my require response spectrum (RRS) plot?  You said the RSC interprets the input as individual harmonic ocillators.  So is this how I tell solidworks I want an ocillator every 0.1Hz from 0.2-3.0 Hz and then every 0.15Hz between 3-3.6Hz...and so on?

                                                • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                                  Shaun Densberger

                                                  I'm going to respond to both of your messages here.

                                                   

                                                  After thinking about it, the output of a harmonic analysis is the input to a response spectrum analysis (or close to it).

                                                   

                                                  Right, so if I have a single harmonic ocillator at 5Hz, why is my amplification not the same as if I did a harmonic study and looked at a single frequency at 5Hz?  I understand why the combined results are different, but if I look at a single frequency value, I should be able to correlate the amplifications, no?  Same question below.

                                                   

                                                  You should, provided that your input for your RS analysis is based on the output of your harmonic analysis.

                                                   

                                                  For example, say you have a mass-spring-dampener system (like the one below) that is excited via base motion. The base motion follows the function y(t) and the output at the mass follows x(t). If you were to plot both x and y as a function of time, you'd get the Time Plot graph; here we can see the transient and steady-state response. After some time, the mass (x) would reach it's maximum stead-state value (x_max_ss).

                                                   

                                                  If you would to plot the response of the mass (x) as a function of the input frequency, then you'd get the Frequency Plot graph. Here the y-axis is the magnification factor (M). We can see that x_max_ss occurs at the damped natural frequency; this is the plot you'd get from a harmonic analysis in SW (or something close, depending on what your y-axis represented). For a harmonic analysis, your input would be the magnitude of the sine sweep (in this case, A), the frequency step size (delta_omega), and the dampening (zeta).

                                                   

                                                  Now, if you were to take the second time derivative of the mass's position function (x) and plug in a time value when x(t) = x_max_ss, then you'd get the maximum steady-state acceleration (a_max_ss). The maximum steady-state acceleration for the mass could also be found using a harmonic analysis in SW.

                                                   

                                                  Now, for a response spectrum analysis is SW (or any FEA package), you're input is a response spectrum curve. A response spectrum curve can either be in terms of displacement, velocity, or acceleration; for this example we'll use a RSC for acceleration. To generate your response spectrum curve, you'd need to plot the maximum steady-state acceleration for your mass (a_max_ss) at your un-damped natural frequency. Since we have only one mass-spring-dampener system, we'll only have one point and our response spectrum curve will look like the Dirca-Delta function.

                                                  Dynamics.png

                                                   

                                                  I have sine sweep and random multifrequency testing.  Both with different input spectrums.  My sine sweep mimics aging at 1g.  My RSC mimics an earthquake at 10g.  My sine sweep has response that is 10 times higher with 10 times the stresses.  Its hard to believe that is correct.  The study properties are copied so there were no different in the model setup.  This initiated my whole question on comparing the harmonic and the RSC results.  My model is over 20mb with dozens of subcomponents so I'm not going to share it.  And since this a conceptual question I don't want to go through the process of making up dummy blocks to discuss.

                                                   

                                                  For your sine sweep, what value of dampening are you using? What type of material is your model made out of? How are components connected in the physical system (welding, fasteners, etc)? When you did the RSA, what did you use for your mode combination method? SRSS? How far apart were the mode frequencies spaced?

                                                   

                                                  That being said.  I define the options of the RSC to give relative results compared to the base excitation, use a single frequency in the RSC, why would the results of a single harmonic study plot step not be the same?

                                                   

                                                  Are you using the exact same curve as an input for both the harmonic analysis and the RSA?

                                                   

                                                  In theory, my forcing function at a single frequency should not be any different than my harmonic function?

                                                   

                                                  Yes, for a harmonic analysis, but not a RSA.

                                                   

                                                  So if I wanted a resolution as in the following...do I have to change my base excitation spectrum to have a resolution with the frequency steps above and interpolate the accelerations myself between my require response spectrum (RRS) plot?  You said the RSC interprets the input as individual harmonic ocillators.  So is this how I tell solidworks I want an ocillator every 0.1Hz from 0.2-3.0 Hz and then every 0.15Hz between 3-3.6Hz...and so on?

                                                   

                                                  A piece wise continuous response spectrum curve with some sort of interpolation has infinite resolution for the range of the curve. If your RSC is a linear linear from 0-500 Hz (and then nothing after), then you have all response values for any frequency between 0 Hz and 500 Hz. A response spectrum curve is a plot of the response of n number of mass-spring-dampener systems that each have a unique fundamental mode.

                                                    • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                                      Nathan Obermiller

                                                       

                                                      You should, provided that your input for your RS analysis is based on the output of your harmonic analysis.

                                                       

                                                      For example, say you have a mass-spring-dampener system (like the one below) that is excited via base motion. The base motion follows the function y(t) and the output at the mass follows x(t). If you were to plot both x and y as a function of time, you'd get the Time Plot graph; here we can see the transient and steady-state response. After some time, the mass (x) would reach it's maximum stead-state value (x_max_ss).

                                                       

                                                      If you would to plot the response of the mass (x) as a function of the input frequency, then you'd get the Frequency Plot graph. Here the y-axis is the magnification factor (M). We can see that x_max_ss occurs at the damped natural frequency; this is the plot you'd get from a harmonic analysis in SW (or something close, depending on what your y-axis represented). For a harmonic analysis, your input would be the magnitude of the sine sweep (in this case, A), the frequency step size (delta_omega), and the dampening (zeta).

                                                       

                                                      Now, if you were to take the second time derivative of the mass's position function (x) and plug in a time value when x(t) = x_max_ss, then you'd get the maximum steady-state acceleration (a_max_ss). The maximum steady-state acceleration for the mass could also be found using a harmonic analysis in SW.

                                                       

                                                      Now, for a response spectrum analysis is SW (or any FEA package), you're input is a response spectrum curve. A response spectrum curve can either be in terms of displacement, velocity, or acceleration; for this example we'll use a RSC for acceleration. To generate your response spectrum curve, you'd need to plot the maximum steady-state acceleration for your mass (a_max_ss) at your un-damped natural frequency. Since we have only one mass-spring-dampener system, we'll only have one point and our response spectrum curve will look like the Dirca-Delta function.

                                                       

                                                       

                                                      For this to work i need to use absolute response values and look at my fixture response?

                                          • Re: Solidworks 2012 Simulation Response Spectrum Analysis - Missing Mass
                                            Nathan Obermiller

                                            Yes.  Taking a step back to the thread question.  Is there a way to apply the missing mass load?  Can I add a static load analysis using the missing mass factor to the response spectrum analysis results using the pressure vessel design portion?  Looks like the 2012 version of the pressure vessel only allows us to combine static results.

                                             

                                            I am surprised SW removed this missing mass functionality from ASTAR.  Is there any way to adjust the input outside the GUI to allow the solver to define this missing mass coefficient and add it to the nodal stress values?