STEADY-STATE FORCED RESPONSE OF A MECHANICAL OSCILLATOR WITH COMBINEDPARAMETRIC-EXCITATION AND CLEARANCE TYPE NONLINEARITY

A mechanical system exhibiting combined parametric excitation and clea rance type non-linearity is examined analytically and experimentally i n an effort to explain complex behavior that is commonly observed in t he steady state forced response of rotating machines. The specific cas e of a preloaded mechanical oscillator having a periodically time-vary ing stiffness function and subject to a symmetric backlash condition i s considered. A generalized solution methodology is proposed based on the harmonic balance method. The resulting non-linear algebraic equati ons are solved by using a direct Newton-Raphson technique, in which a closed form Jacobian matrix is computed using frequency domain methods . Analytical solutions are validated by comparison with numerical inte gration results and experimental measurements obtained from a gear dyn amics test rig. (C) 1995 Academic Press Limited