Vibration and stability of non-uniform beams with abrupt changes of cross-sequin by using C~1 modified beam vibration functions

摘要

A unified method is presented for the analysis of vibration and stability of axially loaded non-uniform beams with abrupt changes of cross-section. The beam may also be supported on Winkler elastic foundation, and both the axial force and the foundation stiffness can be varied arbitrarily. The method is based on the Euler-Lagrangian approach using a family of C~1 admissible funcions as the assumed modes. The assumed modes comprise essentially the vibration modes a of a single span hypothetical prismatic beak with the samke end supports but without the intermediate supports, modified by piecewise C~1 cubic polynomials. The chosen admissible functions therefore possess both the advents of fast convergence of he eigenfuncions and the appropriate order of continuity at the location of abrupt change of cross secion. The method allows extensive use of matrix notations and programming is rather straightforward. Numerical results also show that he method is versatile, efficient and accurate.