Hello, I am taking a vibrations course and we are currently talking about using PDEs to find responses of beams. In the book, there is an equation to find the natural frequencies of a simply supported beam under an axial load:(adsbygoogle = window.adsbygoogle || []).push({});

omega = (pi^2/l^2)*sqrt(EI/roA)*sqrt(n^4 + (n^2*P*l^2)/(pi^2*EI))

However, what if the load (P) is not axial but sinusoidal. For example, P = sin(t). How would we find the natural frequencies then. There are other equations to find the natural frequency but none of them talk about beams subjected to sin or cos loads.

Thanks!

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# Natural frequency of beam exposed to sinusoidal force

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