The Extended Galerkin Method for Approximate Solutions of Nonlinear Vibration Equations

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