An extension has been made with the popular Galerkin/Rayleigh-Ritz method by integrating the weighted equation of motion or Lagrangian functional over the time of one period of vibrations to eliminate the harmonics from the deformation function.  A set of successive equations of coupled higher-order vibration amplitudes is obtained, and a nonlinear eigenvalue problem is solved for the frequency-amplitude dependence of nonlinear vibrations of successive displacements.  The subsequent solutions of vibration frequencies and deformation are actually consistent with other successive approximate methods such as the traditional harmonics balance method.  This is a novel extension to Galerkin/Rayleigh-Ritz method which has wide applications in approximate solutions particularly for vibration problems in solid mechanics.  This extended Galerkin/Rayleigh-Ritz method can also be utilized for the analysis of free and forced nonlinear vibrations of structures as a new technique with significant advantages.

Professor Ji Wang is the founding director of the Piezoelectric Device Laboratory, Ningbo University.  Professor Ji Wang also held visiting positions at Chiba University, University of Nebraska-Lincoln, and Argonne National Laboratory.  He received his PhD and Master degrees from Princeton University in 1996 and 1993 and bachelor from Gansu University of Technology in 1983.