Large-amplitude vibration analysis of a strong nonlinear tapered beam using continuous piecewise linearization method

Abstract

The large-amplitude free vibrations of an inextensible tapered beam with inertia and static nonlinearities were investigated using the continuous piecewise linearization method (CPLM). The CPLM solution was found to be in excellent agreement with exact numerical solutions and more accurate than other published approximate solutions. The study focuses on the large-amplitude vibrations where the nonlinear effects are strong and the response is characterized by anharmonicity. The present investigation showed that the CPLM solution predicted the anharmonic response due to strong nonlinearity whereas the other published solutions showed large errors. The effects of inertia and static nonlinearities were investigated and it was observed that an increase in the static nonlinear stiffness increases the vibration frequency whereas an increase in inertia nonlinearity reduces vibration frequency. Also, the combined effect of the inertia and static nonlinearities on the large-amplitude vibration response was investigated. It was observed that an increase in the ratio of the static to inertia nonlinearity increases the vibration frequency and vice versa.