Semi-analytical treatment of complex nonlinear oscillations arising in the slider-crank mechanism

The model for the free nonlinear oscillation of the slider-crank mechanism is very complicated and difficult to solve accurately using most of the existing approximate analytical schemes. However, the continuous piecewise linearization method (CPLM), which is a recently proposed semi-analytical algorithm, is capable of producing simple and accurate periodic solutions for conservative systems irrespective of the complexity of the nonlinear restoring force. Hence, this study applied the CPLM to solve and analyze the complex nonlinear oscillations arising in the slider-crank mechanism. The CPLM results were verified using numerical solutions and it was found that the CPLM solution was accurate to less than 1.0% for angular amplitudes up to 165°. Analysis of the frequency-amplitude response revealed the existence of asymptotic behaviour as the ratio of the crank radius to the connecting rod length approaches zero or unity. Hence, oscillation models for the observed asymptotic responses were derived and found to be significantly simpler compared to the original oscillation model. Finally, analysis of the large-amplitude oscillations of the slider-crank mechanism revealed the presence of strong anharmonic response.