abstract
- © 2021, The Author(s), under exclusive licence to Springer Nature B.V.This paper aims to apply a transformation method that replaces the elastic forces of the original equation of motion with a power-form elastic term. The accuracy obtained from the derived equivalent equations of motion is evaluated by studying the finite-amplitude damped, forced vibration of a vertically suspended load body supported by incompressible, homogeneous, and isotropic viscohyperelastic elastomer materials. Numerical integrations of the original equations of two oscillators described by neo-Hookean and Mooney¿Rivlin viscohyperelastic elastomer material models, and their equivalent equations of motion, are compared to the frequency¿amplitude steady-state solutions obtained from the harmonic balance and the averaging methods. It is shown from numerical integrations and approximate steady-state solutions that the equivalent equations predict well the original system dynamic response despite having higher system nonlinearities.