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Can COMSOL prestressed Eigenfrequency Analysis Provide Valid Elastic Energy Estimates for Mode Shapes?

Posted 22 apr 2025, 03:40 CEST Results & Visualization, Studies & Solvers, Uncertainty Quantification Version 6.2 0 Replies

Nelson Leon

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Hello,

I'm working on a cryogenic suspension design for a gravitational wave detector and using COMSOL Multiphysics to study internal vibration modes. I'm trying to determine whether the elastic strain energy reported in an Prestress Eigenfrequency Study can be reliably used to estimate the thermal motion of modes at cryogenic temperatures using energy scaling — for example, by scaling mode shapes such that the total energy equals

A senior collaborator raised this concern:

“Eigenvalue analysis is a frequency-domain calculation, and energy is not properly defined because initial conditions are not included. Therefore, the energy returned by COMSOL may not be meaningful.”

I understand that eigenfrequency mode shapes in COMSOL are arbitrarily normalized. However, COMSOL does internally compute the strain energy density and integrates it over the domain to report a total elastic energy per mode. I have already exported this using a volume integral of:

My questions:

Does this computed strain energy in COMSOL prestress eigenfrequency studies represent the actual mechanical energy stored in the mode shape (up to normalization)?
Is it valid to rescale the eigenmode displacements using:

If not, what is the rigorous way to obtain mechanical energy or displacement amplitudes from eigenmode simulations?
Are there COMSOL resources, papers, or documentation that clarify the assumptions and limits of using eigenmode strain energy for physical interpretations?

I understand that damping, Q-factor, and time-domain dynamics are not included in the eigenfrequency solver, but I’m only interested in using the elastic energy to scale the displacement fields to match thermal energy at 4 K.

Thank you for any help or guidance!

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