THREE APPROACHES FOR THE AXIAL VIBRATIONS OF BARS ON MODIFIED WINKLER SOIL WITH 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 so-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 approach reduces the structure to an holonomic n -degree-of-freedom mechanism, the energies of which are easily written, and the resulting equations of motion can be deduced by using the Lagrange equations for discrete systems.