An accurate solution method for the dynamic characteristics of three-layered partial-interaction composite beams

Abstract

In the dynamic analysis of three-layered partial interaction composite beams (PICBs), it is not clear whether the effects of shear deformation and rotary inertia all need to be considered, and the shear-locking problems often occurs in existing finite element methods. To improve computational efficiency, accuracy and stability, an analytical method is proposed by considering the shear slips at the interface and the independent rotary angles among the sub-elements. In the proposed method, a matrix containing the natural frequencies of the three-layered PICB is appropriately established by using the solutions to differential equations of motion rather than the shape function in finite element methods. The main improvement of the proposed method is the analyticity of solutions, which can effectively avoid shear-locking problems often mentioned in finite element methods and obtain accurate solutions due to no introduction of approximate shape functions. The present results agree well with the analytical and numerical results in the literature, which validates the accuracy of the proposed method. The effects of shear deformation and rotary inertia on the dynamic behaviors of three-layered PICBs are discussed. It reveals that the shear deformation can not be ignored but rotary inertia can be ignored in the dynamic analysis of three-layered PICBs, which can effectively reduce the computation complexity. In general, the proposed method has practical value in natural frequency analysis of the three-layered PICB with high computational efficiency, accuracy and stability.