The scaled boundary finite element method(SBFEM)was extended to calculate the natural frequen-cies of laminated composite beams.With this method,the beam was simplified as a 1D model.Only the dis-placement components along the x and z directions were selected as the fundamental unknowns.Based on the fundamental equations of elasticity and the scaled boundary coordinates,under the principle of virtual work and with the dual vector technique,the 1st-order ordinary differential scaled boundary finite element dynamic equa-tion for composite beams was obtained,with its general solution in the form of the analytical matrix exponen-tial function.The Padé expansion was utilized to solve the matrix exponential function and the dynamic stiffness matrix for each beam layer was acquired.According to the principle of matching degrees of freedom,the global stiffness and mass matrices of the laminated beam were gained.The eigenvalue equation was solved to give the natural vibration frequencies of the laminated composite beam.The results show that,the proposed method is widely applicable without limitation on the layer number and boundary conditions.Comparisons between the numerical natural frequencies and the experiment results of 3-,4-and 10-layered step-shaped cantilever beams,validate the accuracy,high efficiency and fast convergence of the SBFEM.
关键词
复合梁/自由振动频率/比例边界有限元/Padé级数
Key words
laminate composite beam/natural frequency/scaled boundary finite element method(SBFEM)/Padé expansion
维普
万方数据