Natural frequencies for flexural and torsional vibrations of beams on Pasternak foundation

This paper studies the free vibrations of prismatic beams resting on Pasternak foundation. Special attention is given to the consideration of the bending–twist deformations of the beams. The governing differential equations of the motion are derived by imposing the dynamic equilibrium of a Timoshenko beam element. Differential equations are solved numerically using the combination of the Runge–Kutta and Regula–Falsi methods. The results of some cases are presented, and are analyzed to highlight the effects of the end constraint, rotatory and torsional inertias, aspect ratio, thickness ratio, beam stiffness, and foundation stiffness on the natural frequencies of the beams. The natural frequencies of the present model are validated by comparing to those from model tests.