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The force integration method (FIM) and the methods based on the mode transfer principle are the frequently used choices for solving the vibro-impact problem of continuum. Notably, there are different solving options such as numerical and semianalytical procedures. In this paper, a new modeling method based on the mode transfer principle, called the relative mode transfer method (RMTM), is proposed, and its semianalytical solution is obtained. A typical vibro-impact problem of continuum beam is studied. The time-history response under periodic excitation is obtained using the FIM, mode transfer method (MTM) through numerical procedure, and the RMTM through numerical procedure and semianalytical procedure. The effects of the method on the system steady-state response, amplitude-frequency response, and sticking motion are discussed. The impact type is divided into “hard impact” and “soft impact” when obtaining the results.

Effect of Method Type on the Response of Continuum Vibro-Impact