Analytical solution for a suspension bridge by applying HPM and VIM

Abstract

In this paper, homotopy perturbation method (HPM) and variational iteration method (VIM) are used to solve the large amplitude torsional oscillations equations in a nonlinearly suspension bridge. This paper compares the HPM and VIM in order to solve the equations of nonlinearly suspension bridge. A comparative study between the HPM and VIM is presented in this work. The achieved results reveal that the HPM and VIM are very effective, convenient and quite accurate to nonlinear partial differential equations. These methods can be easily extended to other strongly nonlinear oscillations and can be found widely applicable in engineering and science. The Laplace transform method is applied to obtaining the Lagrange multiplier in the VIM solution.

Keywords:

• torsional oscillations equations
• homotopy perturbation method
• variational iteration method
• nonlinear equations
• Laplace transform method

1999 AMS Mathematics Subject Classifications::

• 34C15
• 74Q10
• 34A34
• 34G20
• 44A10