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Complex strain energy in frequency domain study?

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After doing a frequency domain study at a frequency \omega, COMSOL computes the integrated strain energy in my vibrating plate as a complex quantity: U0=(-1.65e-4 + 8.319e-6 i). What does this mean?

One thought I had is that the physical strain energy as a function of time U(t) is just equal to the real part of |U0|*exp(i \omega t). But that can't be true because strain energy is always positive. Taking U(t) = Re[ U0 exp(i \omega t) ] means it would go negative.

Also, if the displacement is oscillating at \omega, then the strain energy should be oscillating at 2*\omega. For example, for a 1D spring, x=x0*cos(\omega*t) => U ~ k x^2 ~ cos(\omega*t)^2 ~ (1 + cos(2\omega*t))/2.

What is implied when COMSOL returns a complex derived quantity in a frequency domain study.

0 Replies Last Post 3 nov. 2011, 12:52 UTC−4
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Hello phys314

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