Dynamic Analysis of Nonuniform Beams With Time-Dependent Elastic Boundary Conditions

Abstract

The dynamic response of a nonuniform beam with time-dependent elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained nonuniform beams given by Lee and Kuo. The time-dependent elastic boundary conditions for the beam are formulated. A general form of change of dependent variable is introduced and the shifting polynomials of the third-order degree, instead of the fifth-order degree polynomials taken by Mindlin-Goodman, are selected. The physical meaning of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and several examples are given to illustrate the analysis.