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Elastic Strain energy in prestressed eigenfrequency study-inclusion of static prestress?

Posted 2026/02/11 13:03 GMT-5 Results & Visualization, Structural Mechanics, Physics Interfaces Version 6.2 1 Reply

Nelson Leon
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Hello,

I am performing an eigenfrequency analysis of a suspended mechanical structure using the Structural Mechanics Module. The model includes gravity, leading to a significant static prestress in some components.

I extract elastic strain energy using the built-in volume integral

I observe the following behavior:

For gravity-loaded (prestressed) eigenfrequency studies, the elastic strain energy differs significantly from the corresponding eigenfrequency study with gravity removed.

The extracted elastic strain energy does not converge monotonically with mesh refinement, even though eigenfrequencies and mode shapes do.

Directional differences (e.g., longitudinal vs transverse motion) appear in the prestressed case but disappear when gravity is removed.

My questions are:

  • In a prestressed eigenfrequency analysis, does the reported elastic strain energy include contributions from the static prestress field, or only from the linearized modal deformation?

  • Is non-monotonic convergence of elastic strain energy under mesh refinement expected when static prestress is present?

  • When gravity is removed, should the elastic strain energy of low-frequency rigid-body-like modes be expected to become isotropic due to loss of a preferred direction?

  • Is elastic strain energy a reliable quantity for evaluating modal energy in strongly prestressed, gravity-dominated modes?

Thank you in advance for your help!

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1 Reply Last Post 2026/02/12 11:00 GMT-5
Henrik Sönnerlind COMSOL Employee

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Posted: 4 hours ago 2026/02/12 11:00 GMT-5

Some quick remarks here.

There are many ways you can go wrong when looking at strain energy in an eigenfrequency analysis in general, and even more so in a prestressed analysis.

The first thing to note is that the amplitudes of the eigenmodes are arbitrary and depend on the normalization used in the eigenvalue solver. With different choices of normalization scheme, the relative amplitudes of different modes may also differ. Therefore, comparing the energy stored between modes may not be meaningful.

For the same reason, it never makes sense to compare the strain energy of the prestressed state (which has a physical meaning) with the strain energy of an eigenmode.

I presume you are using a built-in variable such as solid.Ws_tot to evaluate the strain energy. That variable gives the cycle average of the strain energy in the vibrating mode, using only the (arbitrary) modal deformations. In other words, the prestress enters only insofar as it may change the mode shape.

Since strain energy is quadratic with respect to deformation, rescaling the modes by a factor of 10 will change the computed total energy by a factor of 100.

As for the mesh-refinement dependence of convergence, it is hard to say. I would guess that in most cases it is convergent, but with quite different behavior (for example, converging from above or below) depending on the chosen normalization.

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Henrik Sönnerlind
COMSOL
Some quick remarks here. There are many ways you can go wrong when looking at strain energy in an eigenfrequency analysis in general, and even more so in a prestressed analysis. The first thing to note is that the amplitudes of the eigenmodes are arbitrary and depend on the normalization used in the eigenvalue solver. With different choices of normalization scheme, the relative amplitudes of different modes may also differ. Therefore, comparing the energy stored between modes may not be meaningful. For the same reason, it never makes sense to compare the strain energy of the prestressed state (which has a physical meaning) with the strain energy of an eigenmode. I presume you are using a built-in variable such as `solid.Ws_tot` to evaluate the strain energy. That variable gives the cycle average of the strain energy in the vibrating mode, using only the (arbitrary) modal deformations. In other words, the prestress enters only insofar as it may change the mode shape. Since strain energy is quadratic with respect to deformation, rescaling the modes by a factor of 10 will change the computed total energy by a factor of 100. As for the mesh-refinement dependence of convergence, it is hard to say. I would guess that in most cases it is convergent, but with quite different behavior (for example, converging from above or below) depending on the chosen normalization.

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