Discussion Forum

Posted: 9 years ago Nov 16, 2015, 9:45 a.m. EST

Hi, Since the problem is nonlinear, the response to the harmonic load is not harmonic and the frequency domain analysis types cannot be used. The only possibility is to run a time dependent solution (including geometric nonlinearity) until a a stable cycle is found. This will, unless the model is rather small or has high damping, be quite time consuming. Using good initial conditions (e.g. based on the linear solution) helps somewhat. Regards, Henrik

Posted: 9 years ago Nov 16, 2015, 12:41 p.m. EST

Hi Henrik, thank you for replying, Well I want to get a frequency response curve at large actuating force. The curve should be of hardening nature. I did for small force using "perturbed frequency domain" and it shiws resonance at the natural frequency. Since geometric non-linearity is activated by default i was expecting a hardening curveg at large actuating force. What I understand from frequency domain is that it keep changing frequency and captures the response. Wether it is linaer or nonlinear, is not it like this? You said that I should run a time dependent study to capture the nonlinear response, ok so how can I get the responses over a range of frequencies? Moreover how to introduce damping to get a steady state sooner ( is there other way of introducing damping other than material damping alpha and beta values). You thorough response would be highly appreciated.

Posted: 9 years ago Nov 16, 2015, 4:28 p.m. EST

[QUOTE] Well I want to get a frequency response curve at large actuating force. The curve should be of hardening nature. I did for small force using "perturbed frequency domain" and it shiws resonance at the natural frequency. Since geometric non-linearity is activated by default i was expecting a hardening curveg at large actuating force. [/QUOTE] Geometric nonlinearity is only activated by default in a few special cases, like when using a hyperelastic material. Using geometric nonlinearity together with frequency response is meaningful only for establishing a linearization point for the perturbation. [QUOTE] What I understand from frequency domain is that it keep changing frequency and captures the response. Wether it is linaer or nonlinear, is not it like this? [/QUOTE] The underlying theory of the frequency response methods assume that both the input and the output are proportional to cos(omega*t). This is the case only for a linear system. Compare solving the two one DOF problems [MATH] \frac {d^2 x}{dt^2}+x=Acos(\omega t) [/MATH] and [MATH] \frac {d^2 x}{dt^2}+x^3=Acos(\omega t) [/MATH] The first equation represents a standard spring-mass system, whereas the spring is progressive in the latter case. The solutions are completely different. In the second case, 1. the solution is not harmonic 2. the solution is not proportional to A 3. there is no well defined natural frequency [QUOTE] You said that I should run a time dependent study to capture the nonlinear response, ok so how can I get the responses over a range of frequencies? Moreover how to introduce damping to get a steady state sooner ( is there other way of introducing damping other than material damping alpha and beta values). [/QUOTE] A frequency sweep would be very demanding indeed. You would have to run a long time dependent analysis for each frequency in the sweep, and then collect the peak values. This would best be done by scripting using Matlab, Java, or the Application Builder. In addition to Rayleigh damping, you can use viscous damping for time domain analyses. Regards, Henrik

Posted: 9 years ago Nov 17, 2015, 3:38 a.m. EST

Thanks again for this thorough reply. So how can I add the viscous damping while doing time dependent analysis?

Posted: 9 years ago Nov 18, 2015, 7:39 a.m. EST

Hi, Viscous damping is not yet available in all physics interfaces. If you model using Solid Mechanics, you will find it under in the list of damping models (since version 5.1), but it is not yet available in the Beam interface. Using pure 'beta' damping in the Rayleigh damping feature will however give something essentially equivalent to viscous damping. The conversion (within a factor of two or so, it is not exactly equivalent for general cases) is beta = eta/E where E is the modulus of elasticity and eta is the viscosity (unit Pa*s). Regards, Henrik

Posted: 9 years ago Nov 18, 2015, 8:31 a.m. EST

Dear Henrik, I'm highly thankful for your detailed kind reply. I have other quick question, can we solve von-Karman nonlinear equations using the equation modeling appraoch in COMSOL? kind regards Shahid

Posted: 9 years ago Nov 18, 2015, 9:14 a.m. EST

[QUOTE] I have other quick question, can we solve von-Karman nonlinear equations using the equation modeling appraoch in COMSOL? [/QUOTE] http://www.comsol.com/community/forums/general/thread/47029

Posted: 9 years ago Nov 18, 2015, 9:20 a.m. EST

Hi Henrik, I already checked these threads, well I understand that a thin plate model in COMSOL is equivalent to von-Karman equations. but I was wondering if I can solve the equations directly using the equations based modeling apperoach?