Free vibration analysis of nonlinear axially loaded beams using a modified harmonic balance method

Partial Differential Equations in Applied Mathematics

M. Alhaz Uddin¹  M. Saifur Rahman²  M. Wali Ullah³ 

[1] Department of Computer Science &Technology, Khulna 9203, Bangladesh;;Department of Mathematics, Khulna University of Engineering &

关键词: Harmonic balance method;    Free vibration;    Axially loaded beam;    Nonlinear beams;   

DOI  :  

来源: DOAJ

【 摘 要 】

The conventional harmonic balance method utilizes a numerical approach for solving a set of nonlinear algebraic equations to identify the unknown coefficients. In this research, a modified harmonic balance method has been represented to study a free vibration problem with an axial load. The success of this research is that it requires the solution of a single nonlinear algebraic equation and a system of linear algebraic equations to obtain the desired results. As a result, it takes less effort to compute than the traditional harmonic balance technique. To validate and justify the accuracy of the proposed approach, the acquired outcomes are compared to those obtained using the fourth-order Runge–Kutta technique. The results acquired from the proposed process nicely agree with the numerical results.

【 授权许可】

Unknown