Vibrations of multi-span non-symmetric composite beams

Abstract

In the present study the exact vibration frequencies of multi-span laminated beams are found using the exact element method, including the effect of rotary inertia and shear deformations. The effect of shear in laminated beams is more significant than in homogeneous beams, due to the fact that the ratio of extensional stiffness to transverse shear stiffness is high. The exact dynamic stiffness matrix is derived, and then any set of boundary conditions including elastic connections, number and length of spans, can be solved as in the classical direct stiffness method for framed structures. The natural frequencies of vibration of a structure are those values of frequency that cause the dynamic stiffness matrix to become singular, and one can find as many frequencies as needed from the same matrix. In the paper several examples are given, and compared with results from the literature.