Steady, Forced Vibration of Unsymmetrical Piecewise-linear System : 1st Report, Explanation of Analytical Procedure

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In this paper, steady, forced vibrations in an unsymmetrical piecewise-linear system with one degree of freedom, whose characteristics of the restoring and damping force are composed of two distinct linear regions, are analysed by means of a new method utilizing appropriate perfect Fourier series expansion. Main features of this method consist in the following procedures : 1) Linearizing the original nonlinear equation of motion by presumedly expanding the nonlinear part of the restoring and damping force into a Fourier series with the same period as of the given exciting force. 2) Obtaining the formal solution of the thus linearized equation by deeming the above-mentioned nonlinear part as if it were an exciting force from without. This solution contains certain unknown coefficients of the Fourier expansion above assumed. 3) Determining these unknown coefficients from the conditions that the above obtained formal solution satisfies the given piecewise-linear characteristics of the system. A certain process of convergency improvement by means of series transformation may prove highly effective in this step.
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