Abstract
Abstract A finite element method in time is presented for the periodic solution of vibrating elastic mechanisms with clearances. The solution of motion is made possible by utilizing time finite elements which discretize the forcing time period into a number of time intervals. During each interval, the solution form is derived from a Hamilton’s law of varying action. The periodic response is described in terms of a set of temporal nodes of all spatial degrees of freedom of the system, yielding a block-diagonal nonlinear algebraic system to be solved iteratively. The suggested method is applied to an example problem of cam-driven valve train, demonstrating the effectiveness of the method in dealing with multiple clearance nonlinearities.
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