A unified solution for the in-plane vibration analysis of multi-span curved Timoshenko beams with general elastic boundary and coupling conditions

Abstract

A unified solution for the in-plane vibration analysis of multi-span curved Timoshenko beams with general elastic boundary and coupling conditions by combining with the improved Fourier series method and Rayleigh-Ritz technique is presented in this paper. Under the current framework, regardless of boundary conditions, each of displacements and rotations of the curved Timoshenko beams is represented by the modified Fourier series consisting of a standard Fourier cosine series and several closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series representation. All the expansion coefficients are determined by the Rayleigh-Ritz technique as the generalized coordinates. The convergence and accuracy of the present method are tested and validated by a lot of numerical examples for multi-span curved Timoshenko beams with various boundary restraints and general elastic coupling conditions. In contrast to most existing methods, the current method can be universally applicable to general boundary conditions and elastic coupling conditions without the need of making any change to the solution procedure.