Abstract
An efficient analytical method for vibration analysis of a Euler-Bernoulli beam on elastic foundation with elastically restrained ends has been reported. A Fourier sine series with Stoke’s transformation is used to obtain the vibration response. The general frequency determinant is developed on the basis of the analytical solution of the governing differential equation for all potential solution cases with rigid or restrained boundary conditions. Numerical analyses are performed to investigate the effects of various parameters, such as the springs at the boundaries to examine how the elastic foundation parameters affect the vibration frequencies.
Highlights
Beams resting on elastic foundations have wide application in engineering practice
A number of studies have been performed to predict the dynamic response of beams on elastic foundations with different boundary conditions
Free vibration and stability behavior of uniform beams and columns with nonlinear elastic end rotational restraints has been considered by Rao and Naidu [6]
Summary
Beams resting on elastic foundations have wide application in engineering practice. The vibration analysis of beams is investigated using various elastic foundation models, such as, Vlasov, Pasternak, and Winkler models. Maurizi et al [2] have considered the vibration frequencies for a beam with different boundary conditions. S. Kim [9] have considered vibration of beams with generally restrained boundary conditions. A number of studies have been reported investigating the free vibration of beams on elastic foundation [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. An efficient method is introduced for the analysis of the free vibration behavior of Euler-Bernoulli beams on an elastic foundation with elastic restraints. Free vibration analyses of elastically supported beam on an elastic foundation are carried out and comparisons are made between with and without elastic foundation
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