Dynamic analysis of prestressed Timoshenko beam by using wavelet-based spectral finite element method

In this article, wavelet-based spectral finite element (WSFE) is formulated for time domain and wave domain dynamic analysis of Timoshenko beam subjected to a uniform axial tensile or compressive force (prestressed). Daubechies wavelet basis functions transform the time and space-dependent governing partial differential equations into a set of coupled space-dependent ordinary differential equations (ODE). The resulting ODEs are decoupled through an eigenvalue analysis and then solved exactly to obtain the shape functions and dynamic stiffness matrix. In the WSFE model, a beam can be divided into only a single element, but larger number of elements may be used in a finite element (FE) model. The accuracy of present WSFE model is validated by comparing its results with those of FE method. The results display advantages of WSFE model compared to FE one in reducing number of elements as well as increasing numerical accuracy. These advantages are more visible in higher frequency content excitations. In addition, the effects of axial tensile or compressive force on time domain analysis and system natural frequencies are investigated. Divergence instability of beam subjected to critical axial compressive force is investigated.