Vibration and Bifurcation Analysis of a Nonlinear Damped Mass Grounded System
Authors
Abstract:
In this paper, vibrations and bifurcation of a damped system consists of a mass grounded by linear and nonlinear springs and a nonlinear damper is studied. Nonlinear equation of motion is derived using Newton’s equations. Approximate analytical solutions are obtained using multiple time scales (MTS) method. For free vibration, the approximate analytical results are compared with the numerical integration results. Forced vibrations of the system in primary and secondary resonant cases are studied and the effects of different parameters on the frequency-responses are investigated. Moreover, bifurcation of the system is studied considering different control parameters.
similar resources
Analysis of the Coupled Nonlinear Vibration of a Two-Mass System
This paper presents a fixed-end two-mass system (TMS) with end constraints that permits uncoupled solutions for different masses. The coupled nonlinear models for the present fixed-end TMS were solved using the continuous piecewise linearization method (CPLM) and detailed investigation on the effect of mass-ratio on the TMS response was conducted. The investigations showed that increased mass-r...
full textBifurcation analysis and dynamics of a Lorenz –type dynamical system
./files/site1/files/0Abstract1.pdfIn this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerically. In particular we derived sufficient conditions for existence of Hopf and Pitchfork bifurcati...
full textDesign Procedure of a Nonlinear Vibration Absorber Using Bifurcation Analysis
A nonlinear energy sink (NES) is characterized by its ability to passively realize targeted energy transfer as well as multimodal damping. This latter feature seems to make this device very well suited for reducing the vibration level of MDOF linear structures. The perspective of dealing with MDOF linear primary structures requires the development of an efficient NES design procedure. This pape...
full textVibration Analysis of a Nonlinear System with a Nonlinear Absorber under the Primary and Super-harmonic Resonances (TECHNICAL NOTE)
Abstract In vibratory systems, linear and nonlinear vibration absorbers can be used to suppress the primary and super-harmonic resonance responses. In this paper, the behavior of a nonlinear system with a nonlinear absorber, under the primary and super-harmonic resonances is investigated. The stiffnesses of the main system and the absorber are cubically nonlinear and the dampers are linear. M...
full textNonlinear Vibration Analysis of the Beam Carrying a Moving Mass Using Modified Homotopy
In the present study, the analysis of nonlinear vibration for a simply-supported flexible beam with a constant velocity carrying a moving mass is studied. The amplitude of vibration assumed high and its deformation rate is assumed slow. Due to the high amplitude of vibrations, stretching is created in mid-plane, resulting in, the nonlinear strain-displacement relations is obtained, Thus, Nonlin...
full textNonlinear Vibration Analysis of a cantilever beam with nonlinear geometry
Analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. According to this, an impressive analytical method which is called Modified Iteration Perturbation Method (MIPM) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. This new method is combined by the Mickens and Iteration methods. Moreover, this method don...
full textMy Resources
Journal title
volume 6 issue 1
pages 1- 18
publication date 2014-03-30
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023