Haar wavelet discretization method for free vibration study of laminated composite beam under generalized boundary conditions

Abstract

Investigation on vibration of laminated composite beam (LCB) is an important issue owing to its wide use as fundamental component. In the present work, we study the free vibration of arbitrarily LCB with generalized elastic boundary condition (BC) by using Haar wavelet discretization method (HWDM). Timoshenko beam theory is utilized to model the free vibration of LCB. The LCB is first split into several segments, and then the displacement for each segment is obtained from the Haar wavelet series and their integral. Hamilton's principle is applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and continuity conditions at two ends of LCB. The vibration characteristics of beam with different fiber orientations and lamina numbers is investigated and its displacements are compared with those in previous works. Numerical results are shown graphically and demonstrate the validation of our method.

Keywords

• Laminated beam
• Haar wavelet discretization method
• Elastic boundary condition
• Free vibration
• Artificial spring boundary technique