Based on the peridynamic (PD) theory introduced by Dr. Stewart A. Silling from Sandia
National Laboratories in 2000, this book presents the nonlocal PD differential operator and …

This paper deals with the nonlinear oscillation of a simple pendulum and presents not only
the exact formula for the period but also the exact expression of the angular displacement as …

The current work focuses on the motion of a simple pendulum connected to a wheel and a
lightweight spring. The fundamental equation of motion is transformed into a complicated …

The homotopy perturbation method is used to solve the Duffing-harmonic oscillator. Only
one iteration leads to high accuracy of the approximate solution, which is valid for the whole …

We apply He's homotopy perturbation method to find improved approximate solutions to
conservative truly nonlinear oscillators. This approach gives us not only a truly periodic …

The homotopy method for the solution of nonlinear equations is revisited in the present
study. An analytic method is proposed for determining the valid region of convergence of …

The first-order harmonic balance method via the first Fourier coefficient is used to construct
two approximate frequency–amplitude relations for a conservative nonlinear oscillatory …

A modified He's homotopy perturbation method (HHPM) is used to calculate the periodic
solutions of a conservative nonlinear oscillator for which the elastic force term is proportional …

We use the arithmetic-geometric mean to derive approximate solutions for the period of the
simple pendulum. The fast convergence of the arithmetic-geometric mean yields accurate …

A modified He's homotopy perturbation method is used to calculate the periodic solutions of
a nonlinear oscillator with discontinuities for which the elastic force term is proportional to …