Variational and projectional approaches based on the method of integro‐differential relations is applied to derive finite‐dimensional systems of ODEs approximating the natural vibrations of rectilinear elastic beams with the rectangular cross‐section. This technique involves special semi‐discrete integral projections of constitutive equations relating the stress and strain tensors as well as the velocity and momentum vectors. The spectral properties of a homogeneous isotropic beam with the square cross section are analyzed by taking into account the problem symmetry. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Proceedings in Applied Mathematics & Mechanics – Wiley
Published: Jan 1, 2017
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