Journal of Applied and Computational Mechanics
A Dual Lagrange Multiplier Approach for the Dynamics of the Mechanical Systems
Document Type : Research Paper
Authors
1 Department of Mathematics, Government College University, Faisalabad, Pakistan
2 National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, Suzhou, China
Abstract
The variational iteration method, a powerful tool for solving nonlinear oscillators with initial conditions, has been expanded to accommodate two-point boundary conditions. In this modification, two Lagrange multipliers are introduced, and their identification process mirrors that of the conventional approach. A generalized equation is provided for a category of highly nonlinear mechanical systems, followed by three illustrative examples derived from this generalized equation. These examples serve to demonstrate the effectiveness of the method. The solutions produced by this modified approach not only show remarkable agreement with numerical results but also exhibit superior accuracy when compared to outcomes obtained through other established methods.
Keywords
- Amplitude-frequency relationship
- Lagrange multiplier
- variational principle
- nonlinear conservative oscillator
Main Subjects
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