Free vibration analysis of nonlinear axially loaded beams using a modified harmonic balance method - M. Wali Ullah; M. Saifur Rahman; M. Alhaz Uddin (Partial Differential Equations in Applied Mathematics, 2022)
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.