The classical problem of the deflection a cantilever beam linear elastic material, under action an external vertical concentrated load at free end, is analysed. We present differential equation governing behaviour this physical system and show that equation, although straightforward in appearance, fact rather difficult to solve due presence non-linear term. In sense, similar another well known system: simple pendulum. An approximation for small deflections was obtained from large...

Article Application of He's Homotopy Perturbation Method to the Duffing-Harmonic Oscillator was published on March 1, 2007 in journal International Journal Nonlinear Sciences and Numerical Simulation (volume 8, issue 1).

This paper deals with the nonlinear oscillation of a simple pendulum and presents not only exact formula for period but also expression angular displacement as function time, amplitude oscillations frequency small oscillations. is written in terms Jacobi elliptic sn(u;m) using following initial conditions: different from zero while velocity zero. The displacements are plotted Mathematica, an available symbolic computer program that allows us to plot easily obtained. As we will see, even...

This paper deals with the non-linear oscillation of a simple pendulum and presents an approach for solving differential equation that governs its movement by using harmonic balance method.With this technique it is possible to easily obtain analytical approximate formulas period pendulum.As we shall see, these show excellent agreement exact calculated use elliptical integrals, they are valid both small large amplitudes oscillation.The most significant feature treatment presented simplicity...

The homotopy perturbation method is used to solve the nonlinear differential equation that governs oscillations of a simple pendulum, and an approximate expression for its period obtained.Only one iteration leads high accuracy solutions relative error less than 2% amplitudes as 130°.Another important point this provides analytical angular displacement function time sum infinite number harmonics, although practical purposes it sufficient consider only finite harmonics.We believe present study...

The current study shows a novel singular perturbed delay third order model (NSPD-TOM) with its two categories using the conventional Lane-Emden mathematical model. comprehensive detail of perturbed, shape/delay and terms are also provided for both NSPD-TOM. numerical performances NSPD-TOM presented through procedures artificial neural networks optimizations global swarming procedure local refinements active set method. is numerically performed based on accuracy, substantiation, authenticity...

An approximation scheme to obtain the period for large amplitude oscillations of a simple pendulum is analysed and discussed. The analytical approximate formula same as that suggested by Hite (2005 Phys. Teach. 43 290), but it now obtained analytically means term-by-term comparison power-series expansion with corresponding series exact period.

Article An Improved 'Heuristic' Approximation for the Period of a Nonlinear Pendulum: Linear Analysis Classical Problem was published on September 1, 2007 in journal International Journal Sciences and Numerical Simulation (volume 8, issue 3).

A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions the relativistic and Duffing-harmonic oscillators.The by truncating infinite series corresponding first order solution before introducing this in second linear differential equation, so on.We find works very well for whole range of initial amplitudes, excellent agreement frequencies periodic with exact ones has been demonstrated discussed.The formulas obtained show solutions, are...

Accurate approximate closed‐form solutions for the cubic‐quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use previous results using a cubication method which restoring force is expanded Chebyshev polynomials and original nonlinear differential equation approximated by cubic equation. Explicit then expressed as function complete elliptic integral first kind Jacobi cn. Then obtain other expressions these solutions, relationship between...

Article An Equivalent Linearization Method for Conservative Nonlinear Oscillators was published on March 1, 2008 in the journal International Journal of Sciences and Numerical Simulation (volume 9, issue 1).

Closed-form exact solutions for the periodic motion of one-dimensional, undamped, quintic oscillator are derived from first integral nonlinear differential equation which governs behaviour this oscillator. Two parameters characterize oscillator: one is coefficient linear term and other term. Not only common case in both coefficients positive but also all possible combinations negative values these provide motions considered. The set signs provides four different cases three pairs...