scholarly journals Analytical and Dynamic study of Pulled Mass Nonlinear Vibration by Two Cables using Newton's Harmonic Balance Method

2020 ◽  
Vol 2 (2) ◽  
pp. 79-86
Author(s):  
Masoud Rahmani ◽  
Ionut Cristian Scurtu ◽  
Amin Moslemi Petrudi
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Nonlinear Vibrations ◽  
Nonlinear Differential Equations ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Good Match ◽  
Engineering Research ◽  
Solution Methods ◽  
Vibration Problems

In recent years, much research has been done on nonlinear vibrations, and analytical and numerical methods have been used to solve complex nonlinear equations. The behavior of nonlinear oscillating equations is discussed until the second order is approximated. Harmonic balance method, which itself has limitations in application. This method continues to be able to study a wider range of nonlinear differential equations. In general, nonlinear vibration problems are of great importance in physics, mechanical structures, and other engineering research. First, the equation of nonlinear vibrations governing the mass of the particle mass connect to the drawn cable is calculated and then the Newton Harmonic Balance Method is used to study the nonlinear vibrations of the set and obtain the answer and its frequency. The method (NHBM) is done with Maple software and a comparison between the results of this method with the solution methods used by other researchers is shown to be a good match.  

scholarly journals The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Y. H. Qian ◽  
J. L. Pan ◽  
S. P. Chen ◽  
M. H. Yao
Keyword(s):  
Exact Solutions ◽  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Nonlinear Dynamical Systems ◽  
Harmonic Balance Method ◽  
Time History ◽  
Approximate Solutions ◽  
Balance Method ◽  
Lumped Mass ◽  
Strongly Nonlinear

The exact solutions of the nonlinear vibration systems are extremely complicated to be received, so it is crucial to analyze their approximate solutions. This paper employs the spreading residue harmonic balance method (SRHBM) to derive analytical approximate solutions for the fifth-order nonlinear problem, which corresponds to the strongly nonlinear vibration of an elastically restrained beam with a lumped mass. When the SRHBM is used, the residual terms are added to improve the accuracy of approximate solutions. Illustrative examples are provided along with verifying the accuracy of the present method and are compared with the HAM solutions, the EBM solutions, and exact solutions in tables. At the same time, the phase diagrams and time history curves are drawn by the mathematical software. Through analysis and discussion, the results obtained here demonstrate that the SRHBM is an effective and robust technique for nonlinear dynamical systems. In addition, the SRHBM can be widely applied to a variety of nonlinear dynamic systems.

An Approximated Harmonic Balance Method for Nonlinear Vibration of Viscoelastic Structures

2006 ◽  
Vol 128 (3) ◽  
pp. 330 ◽  
Author(s):  
El Hassan Boutyour ◽  
El Mostafa Daya ◽  
Lahcen Azrar ◽  
Michel Potier-Ferry
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method

scholarly journals A modified harmonic balance method for solving forced vibration problems with strong nonlinearity

2020 ◽  
pp. 146134842092343 ◽  
Author(s):  
M W Ullah ◽  
M S Rahman ◽  
M A Uddin
Keyword(s):  
Forced Vibration ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Strong Nonlinearity ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Vibration Problems ◽  
Nonlinear Forced Vibration

In this paper, a modified harmonic balance method is presented to solve nonlinear forced vibration problems. A set of nonlinear algebraic equations appears among the unknown coefficients of harmonic terms and the frequency of the forcing term. Usually a numerical method is used to solve them. In this article, a set of linear algebraic equations is solved together with a nonlinear one. The solution obtained by the proposed method has been compared to those obtained by variational and numerical methods. The results show good agreement with the results obtained by both methods mentioned above.

scholarly journals Multi-level residue harmonic balance method for nonlinear vibration of the beam

2021 ◽  
pp. 146134842110384
Author(s):  
Abu SMZ Hasan ◽  
M S Rahman
Keyword(s):  
Dynamic System ◽  
Nonlinear Vibration ◽  
Nonlinear Dynamic ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Nonlinear Dynamic System ◽  
Balance Method ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Multi Level

This study presents the nonlinear vibration and chaotic response of a beam subjected to harmonic excitation. The multi-level residue harmonic balance method is applied to solve the geometrically cubic nonlinear vibration of the simply supported beam. The obtained results agree well with those of the numerical integration method. The amplitude frequency response curves are presented to illustrate the nonlinear dynamic system response both for a damping and without damping model. Also, the chaotic response is examined for a simply supported beam with a nonlinear dynamic system.

scholarly journals Analytical Study of Nonlinear Vibrations of the Tympanic Membrane by Homotopy Perturbation Method

2020 ◽  
Vol 2 (5) ◽  
pp. 187-192
Author(s):  
Masoud Rahmani ◽  
Amin Moslemi Petrudi ◽  
Ionut Cristian Scurtu
Keyword(s):  
Perturbation Method ◽  
Tympanic Membrane ◽  
Harmonic Balance ◽  
Homotopy Perturbation Method ◽  
Harmonic Balance Method ◽  
Engineering Research ◽  
Homotopy Perturbation ◽  
The Common ◽  
Vibration Problems ◽  
Human Tympanic Membrane

Nonlinear vibration problems are generally of great importance in physics, mechanical structures, and other engineering research. This type of equation is very difficult and time-consuming. Researchers, therefore, focus on analytical and numerical methods; In this paper, using the new Newton-Harmonic Balance analytical method, which includes a combination of Newton methods and the harmonic balance method, the common Homotopy Perturbation method is used to solve the nonlinear equation of human tympanic membrane vibration and are compared and validated.

scholarly journals AN ANALYSIS OF NONLINEAR VIBRATIONS OF CABLES BY HARMONIC BALANCE METHOD

1983 ◽  
Vol 1983 (338) ◽  
pp. 59-68
Author(s):  
Kazuo TAKAHASHI ◽  
Kazuto FUJIMOTO ◽  
Koji MURANAKA ◽  
Masaru TAGAWA
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Vibrations ◽  
Harmonic Balance Method ◽  
Balance Method
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