Oscillations of weakly nonlinear autonomous multiple-degree-of-freedom dynamical systems are studied. The analysis includes nonlinear effects arising from the potential as well as the kinetic energies of the systems and the systems include elements that produce nonlinear dissipative forces. The method of averaging is applied to a suitably transformed set of equations. In several important cases nonperiodic solutions for arbitrary initial conditions are obtained by quadratures.
Transients in Certain Autonomous Multiple-Degree-of-Freedom Nonlinear Vibrating Systems
P. R. Sethna
Department of Aeronautics and Engineering Mechanics, University of Minnesota, Minneapolis, Minn.
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Sethna, P. R. (March 1, 1963). "Transients in Certain Autonomous Multiple-Degree-of-Freedom Nonlinear Vibrating Systems." ASME. J. Appl. Mech. March 1963; 30(1): 44–50. https://doi.org/10.1115/1.3630104
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