A MODIFIED FREQUENCY FORMULATION FOR NONLINEAR MECHANICAL VIBRATIONS
Chun‐Hui He, Ji‐Huan He, Jinfeng Ma, Abdulrahman Ali Alsolami, Xiao‐Jun Yang
Abstract
The paper elucidates the characteristics of nonlinear oscillators that contain quasi-linear terms arising in mechanical engineering. Analytical solutions for this type of nonlinear oscillator are often difficult to obtain; they may involve singular and discontinuous terms, which can make them significantly more difficult to obtain. In this paper, a modified frequency formulation for this type of nonlinear oscillator is presented. While the mathematical proof is not provided, illustrative examples are included to demonstrate the remarkable simplicity and reliability of the approach. This paper challenges the conventional wisdom in analytical methods and offers a promising new direction for further investigation.