Suppose we have a plate under sinusoidal excitation in the centre of opposite clamped edge. We use Rayleigh damping. how we can calculate damping energy?
If we use ANSYS as FEM solver, which results should be extracted to compute damping energy for every element. i know ANSYS gives strain energy and kinetic energy for every element for every time.
ANSYS is used for modelling.
thanks in advance for your answers.
After a Finite Element Analysis it is Possible to Calculate the Following Damping Energy = (1/2)*{dot Phi}^T *[C]*{dot Phi} with your {Phi} Eigenvectors. Where [C] is the Damping Matrix. If you are Programming (Batch Mode), The Corresponding Speeds can be Obtained with a Simple Finite Difference Formula for Each Iteration.
more information is needed, how is the excitation applied? and is the behavior elastic or inelastic? Generally if the excitation is a single force at single point, the area under hysteresis loop for that force (force-displacement loop curves) gives you the energy. If the excitation is delivered to the entire body or is a result of inertial effect (transient, free vibration..etc) you need to calculate the hysteresis loop for all Gaussian points in the plate's elements and add them up.
I want to explain that the formula which I have cited calculates the energy for each mode corresponding to each frequency. The energy of your real time dependent displacements needs to be computed with the same formula by using the displacement vector (instead of the eigenvector) which is a combination of the eigenvectors.
The damping forces are -[C] {dot displacement}.
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