A NUMERICALLY EFFICIENT ALGORITHM FOR STEADY-STATE RESPONSE OF FLEXIBLE MECHANISM SYSTEMS

Presented in this work is a numerically efficient algorithm for treati ng the periodic steady-state response of flexible mechanisms as the so lution to separated two-point boundary value problems. The finite elem ent method is applied to discretize continuous elastic mechanism syste ms and a set of second-order ordinary differential equations is obtain ed with periodically time-varying coefficient matrices and forcing vec tors. Modal analysis techniques are employed to decouple these equatio ns into a number of single scalar ordinary differential equations in m odal basis. The periodic time-boundary conditions at both ends of a fu ndamental period equal to a cycle of input motion are mathematically s eparated by introducing auxiliary variables, thus resulting in a so-ca lled almost-block-diagonal matrix for linear algebraic systems of equa tions. Solving such a system is computationally less expensive than so lving a general linear algebraic system. Examples are included to illu strate the procedures applied to a four-bar linkage through which comp uting time is compared with other approaches.