Flexural and torsional free vibrations of horizontally curved beams on Pasternak foundations

This study investigates the out-of-plane free vibrations of curved beams with variable curvature on a Pasternak foundation. The governing differential equations of motion are derived based on Timoshenko beam theory, and the Runge-Kutta method and the determinant search method combined with the Regula-Falsi method are used to solve the problem. The natural frequencies and mode shapes of selected cases are presented with various end constraints, which are analyzed to highlight the effects of the parameters related to curve shape, section geometry, rotatory and torsional inertias, and foundation stiffness. Experiments are conducted to verify the proposed model.