NATURAL TRANSVERSE VIBRATION ANALYSIS OF EULER-BERNOULLI BEAMS RESTING ON FILONENKO-BORODICH ELASTIC FOUNDATIONS USING GENERALIZED INTEGRAL TRANSFORM METHOD
DOI:
https://doi.org/10.4314/njt.2026.4314Keywords:
Euler-Bernoulli beam theory, Filonenko-Borodich foundation, Natural frequency, Generalized integral transform method,Abstract
This study presents an analysis of natural transverse vibrations of an Euler-Bernoulli beam resting on a Filonenko-Borodich elastic foundation (EBBoFBEF) using Generalized Integral Transform Method (GITM). The study is important in design of foundation beams against resonance failures. Such failures occur when the excitation frequency coincides with the natural frequency. The governing equation for free harmonic vibrations of the EBBoFBEF is a homogeneous equation. GITM uses eigenfunctions for similar dynamic thin beam that correspond to the boundary conditions as mode shapes and integral kernels. Thus, no prior determination of the shape functions is needed. The orthogonality properties of the eigenfunctions simplify the resulting integration. The equation is reduced to an algebraic problem. Solutions for natural frequencies are obtained for three cases of cantilever, clamped-clamped, and simply supported ends. The solutions are obtained for the boundary conditions at each vibration mode. The natural frequencies in this study for the dimensionless foundation structure parameters ranging from 1 to 10,000 for the first parameter and representing the vertical modulus 0 to 2.5 for the second parameter representing the tension in the coupling membrane for the first five modes were identical with previous exact solutions. For clamped-clamped and cantilever EBBoFBEF, the frequency parameters obtained by GITM were identical to previous results. The study showed that elastic foundations increase the natural vibration frequencies. These findings offer valuable insights into the dynamic response and vibration characteristics of EBBoFBEF with implications for design safety against resonance.
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