3 Replies Latest reply on Mar 14, 2012 5:14 PM by Anthony Botting

    How is the classification of resonance frequencies determined?

    Thibault Chabaneix

      Hi,

      I'm using Solidworks (Frequency analysis mode) to define the different modes of vibration of a solid that I drew.

      SW determinates 5 modes, with associated frequences.

      These modes are numbered (Déplacements1 ... Déplacements5 in French).

      My question is : how are they classified? this is certainly not randomly.

       

      Thanks.

      Thibault.


       

       


        • Re: How is the classification of resonance frequencies determined?
          Anthony Botting

          Hi Thibault: They are ordered from lowest frequency, to  highest frequency (i.e., from "softest" to "stiffest") of the modes found. They represent the natural frequencies (or "free vibration frequencies") of the particular structure with your particular material and fixtures.

          As an example, you could clamp one end of a beam and apply a tip displacement perpendicular to the beam axis and let go, the structure would vibrate at is (likely) fundamental frequency and mode shape corresponding to the initial displacement direction - sort of a bent arc or half sine wave shape. If you applied an impact load on the end (again, perpendicular to the beam axis), the beam would vibrate at a higher natural frequency and probably exhibit a wavy shape. On the other hand, if you impacted the tip of the beam in the axial direction, you would observe another natural frequency and mode shape, very much higher frequency value but the shape would correspond to an "in-and-out" vibration direction. Some people do actual experiments like this called "hammer tests" that are done in a laboratory setting, where free vibration frequencies and shapes are captured and recorded after impacting the structure at various locations, with a special hammer.

          The software is "discovering" these free vibration frequencies and mode shapes for you. You can set it to find more frequencies and mode shapes in the Properties panel of the study. 

          Note: the results are highly dependent on the fixtures and locations of fixtures. Keep in mind the software fixtures are rigid, while in real life there is usually some flexibility, or compliance, in fixtures (which will change the results quite a lot).

          Hope this helps, a little.

          -Anthony

            • Re: How is the classification of resonance frequencies determined?
              Thibault Chabaneix

              Thanks a lot Anthony.

               

              I thought it took into account the energy which is necessary to set in motion the solid.

              In fact, it is much simpler.

               

              A last question : for my study, I would like to know what is the "more sensible" frequency for the solid, I explain : the frequency (if it does exist) at which the solid will vibrate the most visibly for a given amplitude. For example, for a building, it would be the most "critical" frequency.

              Is there a way to highlight this aspect with the software?

               

                • Re: How is the classification of resonance frequencies determined?
                  Anthony Botting

                  Hi Thibault:

                  From what I understand, it's a standard "Eigenvalue/Eigenvector" matrix analysis solving Newton's second law, equilibrium equation when external forces = 0. That is, solving; MA + KX = 0. Using matrix notation, you get a bunch of scaled relative displacement vectors and actual associated frequencies. So, with no external forces, the displacements are scaled (by some rule written into the software). When you plot one mode shape, for example, the scaled displacements are accurate relative to other areas on the structure. So if color red = 100 units, and color green = 50 units, then for that mode shape you can state that areas colored red will vibrate twice as far as areas colored green (at that frequency). The amplitude does depend on the loading, damping, etc.

                   

                  To get actual answers, I am fairly certain you will need to run a "Linear Dynamics" study, using the "Simulation Premium" software. In the "Modal" option, it will let you apply a base motion amplitude or other load as a function of frequency (in any direction), and then you can observe actual displacement (amplitude) values all over the structure, as a function of the input. You can input damping, too. From that you can determine which vibration shapes and frequencies are the most "visible" (I am using the building analogy). I'm fairly certain it will plot phase angle, too.

                  The Linear Dynamics module does require the natural vibration frequencies and mode shapes (from "Simulation Professional, Frequency Analysis"), as it does a linear summation of those mode shapes against the input loads to calculate the actual response.

                  I hope that helps - Anthony