Md. Sazzad Hossien Chowdhury, Md. Alal Hosen, Kartini Ahmad, Mohammad Yeakub Ali et al.
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 algebra...
Md. Alal Hosen, M. Saifur Rahman, Md. Shamsul Alam, Md. Ruhul Amin
Md. Alal Hosen, Md. Sazzad Hossien Chowdhury
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 t...
Md. Alal Hosen, Md. Sazzad Hossien Chowdhury
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 e...
Md. Alal Hosen, Md. Sazzad Hossien Chowdhury, Gamal M. Ismail, Ahmet Yıldırım
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 su...
Md. Alal Hosen
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 nonline...
Md. Shamsul Alam, Md. Abdur Razzak, Md. Alal Hosen, Md. Riaz Parvez
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 ...
Md. Alal Hosen, Gamal M. Ismail, Ahmet Yıldırım, Md Abdus Samad Kamal
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 co...
Md. Alal Hosen, Md. Sazzad Hossien Chowdhury, Mohammad Yeakub Ali, Ahmad Faris Ismail
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 us...
Gamal M. Ismail, Md. Alal Hosen, Mostafa Mohammadian, Maha M. El-Moshneb et al.
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 accu...
Md. Alal Hosen, MSH Chowdhury
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...
M. Z. Alam, Md. Alal Hosen, Md. Shamsul Alam
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; ...
Md. Alal Hosen, Md. Sazzad Hossien Chowdhury, Mohammad Yeakub Ali, Ahmad Faris Ismail
Md. Alal Hosen
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 w...
Md. Alal Hosen
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...
Md. Alal Hosen, M Shahjahan Chowdhury, Mohammad Yeakub Ali, Ahmad Faris Ismail
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 Metho...
Md. Zahangir Alam, Md. Alal Hosen, Md. Shamsul Alam
An analytical technique based on the certain odd polynomial functions is introduced for solving nonlinear oscillatory problems, applicable to both autonomous and non-autonomous cases. A set of algebraic equations are found when the proposed technique is applied. The algebraic equations are linear an...
Md. Mohaiminul Islam, Md. Zahangir Alam, Md. Alal Hosen
In the recent past, a simplified solution was obtained by using a modified Krylov-Bogoliubov-Mitropolskii method for a cubic Duffing oscillator in the presence of a linear damped force. However, a similar solution is not always possible for another class of nonlinear oscillators where the inertia ty...
Md. Sazzad Hossien Chowdhury, Md. Alal Hosen, Mohammad Yeakub Ali, Ahmad Faris Ismail
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 initi...