Md. Alal Hosen

• Ph.D.
• Professor at Rajshahi University of Engineering and Technology

Nonlinear damped forced oscillators are very importance in the fields of mechanical, electrical and other dynamical systems. Small oscillations are being investigated by classical perturbations. Earlier Cheung et al. presented a modified Lindstedt–Poincare method for large amplitude of oscillation; but its mathematical manipulation is tremendously...

In this paper, an analytical technique based on the global residue harmonic balance method (GRHBM) is applied in order to obtain higher-order approximate analytical solutions of an electrostatically actuated micro-beam. To illustrate the applicability and accuracy of the method, a high level of accuracy was established for the analytical solutions...

An analytical technique has been developed based on the harmonic balance method to obtain approximate angular frequencies. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, couple-mass-spring system having linear and nonlinear stiffnesses with cubic nonlinearity. Two real-world cases of these syste...

Global Residue Harmonic Balance Method for Obtaining Higher-Order Accurate Solutions to the Strongly Nonlinear Oscillator

We propose a new method, namely, the modified harmonic balance method. This paper also analyses and offers the high-order approximate periodic solutions to the strongly nonlinear oscillator with cubic and harmonic restoring force. The existing harmonic balance method cannot be applied directly to such kind of nonlinear oscillators in the presence o...

Purpose An iteration technique has been developed based on the Mickens iteration method to obtain approximate angular frequencies. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, coupled mass–spring system having linear and nonlinear stiffnesses with cubic nonlinearity. Two real-world cases of th...

This article analyzes a strongly nonlinear oscillator with cubic and harmonic restoring force and proposes an efficient analytical technique based on the modified energy balance method (MEBM). The proposed method incorporates higher-order approximations. After applying the proposed MEBM, a set of complicated higher-order nonlinear algebraic equatio...

This paper presents simulation results of the influence of wide range modulation index values ( ) in carrier-based PWM strategy for application in generating the stepped waveform. The waveform is tested for application in single-phase half-bridge modular multilevel converters (MMCs) topology. The results presented in this paper include a variation...

In this paper, an analytical technique has been proposed to obtain higher-order approximate periods for the nonlinear oscillator with the square of the angular frequency depending quadratically on the velocity which is based on the harmonic balance method (HBM). Analytical investigation of the appeared set of nonlinear algebraic equations is usuall...

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpo...

In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubic-quintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebraic equations. In this technique, the high-order no...

In the present paper, a novel analytical technique to obtain higher-order approximate solutions for the equation of motion of a particle on a rotating parabola has been introduced, which is based on an energy balance method (EBM). The results are valid for small as well as large oscillation of initial amplitude. It is highly remarkable that using t...

In this paper, an analytical approximation technique has been presented of obtaining higher-order approximate solutions for highly nonlinear Duffing oscillator based on the energy balance method (EBM). Higher-order approximate natural frequen- cies have been obtained in a novel analytical way. The accuracy of the solution method is evaluated within...

In this paper, an analytical approximation technique has been presented of obtaining higher-order approximate solutions for highly nonlinear Duffing oscillator based on the energy balance method (EBM). Higher-order approximate natural frequencies have been obtained in a novel analytical way. The accuracy of the solution method is evaluated within a...

Based on the harmonic balance method (HBM), an approximate solution is determined from the integral expression (i.e., first order differential equation) of some strongly nonlinear oscillators. Usually such an approximate solution is obtained from second order differential equation. The advantage of the new approach is that the solution converges si...

In the present paper, a novel analytical approximation technique has been proposed based on the energy balance method (EBM) to obtain approximate periodic solutions for the focus generalized highly nonlinear oscillators. The expressions of the natural frequency-amplitude relationship are obtained using a novel analytical way. The accuracy of the pr...

In this study, Harmonic Balance Method (HBM) is applied to determine approximate analytic solutions of strongly nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. Mainly, a set of nonlinear algebraic equations is solved in this method. The new method avoids the necessity of numerically solving sets of algebraic equations wi...

The Duffing-harmonic oscillator is a common model in nonlinear sciences and engineering. In the present paper, the harmonic balance method and rational harmonic balance method has been introduced to derive the approximate periods of a strongly nonlinear Duffing-harmonic oscillator. The comparison of two methods is made to demonstrate that the ratio...

In the present paper, a complicated strongly nonlinear oscillator with cubic and harmonic restoring force, has been analysed and solved completely by harmonic balance method (HBM). Investigating analytically such kinds of oscillator is very difficult task and cumbersome. In this study, the offered technique gives desired results and to avoid numeri...

In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multistage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic...

The aim of this paper is to use high-order harmonic balance method (HBM) as a novel solution procedure for investigation of the Duffing-relativistic oscillation. Usually, a set of complex nonlinear algebraic equations is appeared when HBM is applied. Investigating analytically for such kind of complex nonlinear algebraic equations is tremendously d...

We introduced an analytical technique based on harmonic balance method (HBM) to determine approximate periods of a nonlinear Duffing-harmonic oscillator. Generally, a set of nonlinear algebraic equations are appeared when HBM is formulated. Investing analytically of such kinds of algebraic equations are a tremendously difficult task and cumbersome....

The Duffing-harmonic oscillator is a common model for nonlinear phenomena in science and engineering. In this paper, a new analytical technique has been presented to determine approximate periods of a strongly nonlinear Duffing-harmonic oscillator. Generally, a set of difficult nonlinear algebraic equations appear when harmonic balance method is im...

In the present paper, a new analytical technique is introduced for obtaining approximate periodic solutions of Helmholtz-Duffing oscillator. Modified Harmonic Balance Method (MHBM) is adopted as the solution method. A classical harmonic balance method does not apply directly for solving Helmholtz-Duffing oscillator. Generally, a set of difficult no...

In this paper, an analytical technique has been developed to determine approximate solutions of nonlinear singular oscillator. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this article th...

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine approximate solutions for a strongly nonlinear oscillator with a discontinuous term which is arising from the motion of rigid rod on the surface without slipping. Usually, a set of nonlinear algebraic equations is solved in this method. H...

In this paper an analytical method has been produced to determine approximate periods for nonlinear oscillator 0) 1 (2    x x x   . Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this...

In this paper, an analytical technique has been developed based on a modified harmonic balance method to determine higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term, is an anti-symmetric and quadratic term. Usually, a set of nonlinear algebraic equations is solved with this me...

In this paper, a simple analytical technique has been developed to determine higher-order approximate periodic solutions of a nonlinear oscillator with discontinuities for which the elastic force term is proportional to sgn(x). The classical harmonic balance method cannot be applied directly for such nonlinear problems. It is very difficult to solv...

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x 1/3. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical so...

Recently, a unified Krylov-Bogoliubov-Mitropolskii method has been presented (by Shamsul \cite{1}) for solving an $n$-th, $n=2$ or $n>2$, order nonlinear differential equation. Instead of amplitude(s) and phase(s), a set of variables is used in \cite{1} to obtain a general formula in which the nonlinear differential equations can be solved. By a si...

Recently, an analytical technique has been developed to determine approximate solutions of strongly nonlinear differential equations containing higher order harmonic terms. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the c...

Following a new harmonic balance method, approximate solutions of van der Pol’s equation have been determined near the limit cycle. The method is extendable to higher order nonlinear differential system having a limit cycle. In this paper a second approximate solution of Mulholland equation (a third order differential equation) is found. The soluti...