Nonlinear vibration analysis of mechanical systems with multiple joint clearances using the method of multiple scales

2016 ◽  
Vol 105 ◽  
pp. 495-509 ◽  
Author(s):  
Esmaeil Salahshoor ◽  
Saeed Ebrahimi ◽  
Mohsen Maasoomi
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Mechanical Systems ◽  
Joint Clearances

scholarly journals Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

2021 ◽  
Author(s):  
Reza Mohammadi
Keyword(s):  
Nonlinear Vibration ◽  
Frequency Ratio ◽  
Vibration Analysis ◽  
Multiple Scales ◽  
Numerical Technique ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Nonlinear Frequency

Abstract In this paper, the nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT is studied. Nonlocal elasticity theory is applied to consider the small scale effect. The nonlinear equations of motion are derived using Hamilton’s principle. First, a Galerkin-based numerical technique is applied to reduce the nonlinear governing equation into a set of Duffing-type time-dependent differential equations. Afterward, the analytical solutions are derived based on the method of multiple scales (MMS) and perturbation technique. All of the mechanical properties of the beam are temperature dependent. The impacts of the several variables are investigated on the nonlinear frequency ratio of the nanobeams. The results illustrate that when maximum deflection is smaller/ greater than 0.2, its impact on the nonlinear frequency ratio will decrease/increase.

Generalized oscillator model for nonlinear vibration analysis using quasi-static cubication method

2020 ◽  
pp. 030641901989658
Author(s):  
Akuro Big-Alabo ◽  
Emmanuel Ogheneochuko Ekpruke ◽  
Chinwuba Victor Ossia ◽  
David Oke Jonah ◽  
Collins Onyinyechukwu Ogbodo
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Mechanical Systems ◽  
Approximate Solutions ◽  
Oscillator Model ◽  
Significant Feature ◽  
Graduate Courses ◽  
Oscillatory Systems ◽  
Wide Range ◽  
Generalized Oscillator

A generalized oscillator model for nonlinear vibration analysis of various mechanical systems was proposed and solved using the quasi-static cubication method. The proposed generalized oscillator model is useful for introducing and discussing the nonlinear vibration models of several oscillatory systems. To establish the accuracy of the quasi-static cubication method for the generalized oscillator model, a number of simulations were carried out for the nonlinear vibration models of common mechanical systems derived from the generalized oscillator model. The results obtained were found to be in good agreement with exact solutions and other approximate solutions found in the literature. Furthermore, the quasi-static cubication method was found to be accurate for a wide range of oscillation amplitudes. A significant feature of the quasi-static cubication method is its simplicity and accuracy; hence, it is considered an efficient technique for nonlinear vibration analysis in undergraduate and post-graduate courses on dynamics.

1/3 Subharmonic Resonance of the Electro-Conductive Beam in Thermal-Magneto-Elasticity Field

2012 ◽  
Vol 466-467 ◽  
pp. 814-818 ◽  
Author(s):  
Xiao Yan Xi ◽  
Zhian Yang ◽  
Gao Feng Li
Keyword(s):  
Numerical Analysis ◽  
Nonlinear Vibration ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Subharmonic Resonance ◽  
Bending Vibration ◽  
Approximation Solution ◽  
Vibration Equation ◽  
System Parameters

Based on the electro-magneto-elastic theory and the theory of the bending vibration of the electric beam, nonlinear vibration equation of current-carrying beam in thermal-magneto-elasticity field is studied. The Lorentz force and thermal force on the beam are derived. According to the method of multiple scales for nonlinear vibrations the approximation solution of 1/3 subharmonic resonance of the system is obtained. Numerical analysis results show that the amplitude changed with the system parameters.

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