Cheng, Ching-Chuan2014-03-142014-03-141990-12-07etd-04142009-040604http://hdl.handle.net/10919/42077A method is developed to predict the critical harmonic excitation of systems undergoing nonlinear oscillations. The method is based on the total energy approach which limits the system responses within a region bounded by a critical total energy in the phase space. Three one-degree-of-freedom nonlinear systems are investigated. Their governing ordinary differential equations are associated with a quadratic nonlinearity and/or a cubic nonlinearity. The study also is extended to a two-degree-of-freedom nonlinear system. The harmonic balance method is the analytical technique used in solving the nonlinear ordinary differential equations. In comparison with the approximate analytical solutions, numerical approaches are implemented.viii, 58 leavesBTDapplication/pdfenIn CopyrightLD5655.V855 1990.C447Harmonic oscillatorsThesishttp://scholar.lib.vt.edu/theses/available/etd-04142009-040604/