Simulating Nonlinear Oscillations of Viscoelastically Damped Mechanical Systems
Journal Title: Engineering, Technology & Applied Science Research - Year 2014, Vol 4, Issue 6
Abstract
The aim of this work is to propose a mathematical model in terms of an exact analytical solution that may be used in numerical simulation and prediction of oscillatory dynamics of a one-dimensional viscoelastic system experiencing large deformations response. The model is represented with the use of a mechanical oscillator consisting of an inertial body attached to a nonlinear viscoelastic spring. As a result, a second-order first-degree Painlevé equation has been obtained as a law, governing the nonlinear oscillatory dynamics of the viscoelastic system. Analytical resolution of the evolution equation predicts the existence of three solutions and hence three damping modes of free vibration well known in dynamics of viscoelastically damped oscillating systems. Following the specific values of damping strength, over-damped, critically-damped and under-damped solutions have been obtained. It is observed that the rate of decay is not only governed by the damping degree but, also by the magnitude of the stiffness nonlinearity controlling parameter. Computational simulations demonstrated that numerical solutions match analytical results very well. It is found that the developed mathematical model includes a nonlinear extension of the classical damped linear harmonic oscillator and incorporates the Lambert nonlinear oscillatory equation with well-known solutions as special case. Finally, the three damped responses of the current mathematical model devoted for representing mechanical systems undergoing large deformations and viscoelastic behavior are found to be asymptotically stable.
Authors and Affiliations
M. D. Monsia, Y. J. F. Kpomahou
Keywords
Related Articles
- EP ID EP91059
- DOI -
- Views 277
- Downloads 0
Simulating Nonlinear Oscillations of Viscoelastically Damped Mechanical Systems
The aim of this work is to propose a mathematical model in terms of an exact analytical solution that may be used in numerical simulation and prediction of oscillatory dynamics of a one-dimensional viscoelastic system ex...
A Five-Level Current-Source Inverter for Grid-Connected or High-Power Three-Phase Wound-Field Synchronous Motor Drives
Simple converter structure, inherent short-circuit protection and regenerative capability are the most important advantages of current-source inverters (CSI’s) which have made them suitable for medium-voltage high-power...
Implementation of Building Information Modeling (BIM) in Pakistan Construction Industry
This paper examines the implementation of building information modeling (BIM) in construction industry. Various initiatives and approaches are used in different countries to promote the BIM implementation in their constr...
Analysis and Fabrication of an Active Cooling System for Reducing Photovoltaic Module Temperature
The purpose of this study is to fabricate and analyze an active cooling system for reducing photovoltaic (PV) module temperature and increasing its efficiency. An active cooling system was devised to cool the PV module....
Numerical Analysis of SHB Effects in Laterally-Coupled Distributed Feedback (LC-DFB) Lasers
In this paper the stability of Laterally-Coupled Distributed Feedback (LC-DFB) Lasers against the Spatial Hole Burning (SHB) effect is analyzed theoretically. The stability of the laser structure is evaluated using the f...