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A new method is proposed to calculate natural frequencies of a rectangular variable cross-section beam with multiple cracks under different temperatures. The temperature module is introduced through the elastic modulus, and cracks are modelled by bending springs without mass. Based on the transfer matrix method, the characteristic equation of the cracked beam is derived by the implementation of different boundary conditions. Examples are presented on cantilever beams having different non-uniformity parameters, and the influence of the temperature, the number and geometric parameters of cracks on natural frequencies is also investigated. Compared with results obtained using the Patran FEM method, good agreements are obtained and this analytical method is demonstrated to be feasible.

Modal analysis of a rectangular variable cross-section beam with multiple cracks under different temperatures