A NEW DYNAMIC FEM OF FRAMES DEVELOPED FROM TIMOSHENKO BEAM MODEL

摘要

Based on the Timoshenko beam model a new dynamic FEM of frames considering the effects of shearing deformation and rotatory inertia of the beam is developed in this paper. The ith dynamic constraint mode functions in an element is derived from the governing equations of Timoshenko beam recurrently. Then the corresponding ith stiffness and mass matrices of elements are derived from the ith element shape function matrices which consist of the ith dynamic mode functions. The assembling of the element matrices to the global ones is similar to current FEM. The eigen-problem obtained finally for free vibration of a structure is a linear one. The new dynamic FEM can be applied to find the higher eigenpair. Compared with J. S. Przemieniecki's dynamic FEM in the same accuracy, the new method is simpler and the size of the elements can be much bigger. Therefore the degree of freedom of the discretilized model can be greatly reduced. Numerical examples show that this method is effective and convenient for solving the higher eigenproblem of free vibration of a structure. The CPU time and the storage of the calculation will be reduced greatly.