A generalized approach to coupled nonlinear vibrations of continuous systems
Summary: We propose a mathematical model which covers many practical vibration problems for continuous systems. The equations of motion consist of two nonlinearly coupled partial differential equations. The quadratic and cubic nonlinearities as well as the linear part of the equations are represented by arbitrary operators. A perturbation approach (method of multiple time scales) has been applied directly to partial differential equations. The responses as well as the amplitude and phase modulation equations are found for the primary resonances of the external excitation and for the one-to-one internal resonances between the natural frequencies of the equations. The coefficients of amplitude and phase modulation equations are calculated in their most general form. Results are then applied to nonlinear cable vibrations for small sag-to-span ratios.
scientific article; zbMATH DE number 1229957