Three approaches for the axial vibrations of bars on modified winkler soilwith nonclassical boundary conditions

In this paper three approximate numerical approaches are compared, for the title problem. The first method is a variational one,and it is known as an optimized Rayleigh or Rayleigh-Schmidt method. As such, it belongs to the s o-called "energy approaches". On the contrary, the second method solves the differential equation of motion according to a recent quadrature procedure , and is known as the "differential quadrature method", or DQM. The last ap proach reduces the structure to an holonomic n-degree-of-freedom mechanism, the energies of which are easily written, and the resulting equations of m otion can be deduced by using the Lagrange equations for discrete systems. (C) 2000 Academic Press.