Vibratory behavior of Euler-Bernoulli beams on elastic foundation: non-classical boundary conditions, orthogonality and external force
DOI:
https://doi.org/10.5902/2179460X89806Keywords:
Modal analysis, Non-classical boundary conditions, External force, Elastic foundation, Orthogonality, Fundamental solution, Euler-Bernoulli beamAbstract
In this work we present the Euler-Bernoulli beam theory, also known as classical theory, for a beam on an elastic foundation and with non-classical boundary conditions. Our objective is to expand the class of problems that use fundamental solution theory to obtain the characteristic equation, natural frequencies, modes of vibration and the forced response of problems involving vibrations. As the problem considered is non-classical, due to the boundary conditions considered, it is necessary to obtain an orthogonality condition that involves the mass attached to the end of the beam to decouple the equations and write the forced response.
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