Coupled free vibration of composite beams with asymmetric cross-sections

A set of linear differential equations of motion for coupled free vibrations of composite beams with asymmetric cross-sections is obtained in this paper based on Euler–Bernoulli beam theory. More coupling terms are included in the governing equations; and hence, both even and odd order spatial derivatives are included. All these features lead to much difficulty in solving the resultant equations. The axially unloaded condition of F1 = 0, instead of e = 0, is adopted to simplify the equations of motion for the case of inextensional beams. An algorithm is developed for solving the resultant equations to obtain natural frequencies and modes of the beams. Numerical examples for validation show that the equations of motion obtained in this paper are correct and the corresponding algorithm is effective and easy to use.