Nonlinear forced response of circular cylindrical shells

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Virginia Polytechnic Institute and State University


A combination of the Galerkin procedure and the method of multiple scales is used to analyze the nonlinear forced response of circular cylindrical shells in the presence of internal (autoparametric) resonances. If ωf and af denote the frequency and amplitude of a flexural mode and ωb and ab denote the frequency and amplitude of the breathing mode, the steady-state response exhibits a saturation phenomenon when ωb ≈ 2wf if the shell is excited by a harmonic load having a frequency Ω near ωb. As the amplitude f of the excitation increases from zero, ab increases linearly whereas af remains zero until a threshold is reached. This threshold is a function of the damping coefficients and ωb -2wf. Beyond this threshold, ab remains constant (i.e., the breathing mode saturates) and the extra energy spills over into the flexural mode. In other words, although the breathing mode is directly excited by the load, it absorbs a small amount of the input energy (responds with a small amplitude) and passes the rest of the input energy into the flexural mode (responds with a large amplitude).