The stability analysis of a slider-crank mechanism due to the existence of two-component parametric resonance

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Abstract

The objective of this paper is an analytical and numerical study of the dynamics and dynamic instability of a slider-crank mechanism with an inextensible elastic coupler. Special attention is given to the phenomena arising due to modal interactions produced by the existence of multi-component, specifically two-component, parametric resonance. Such modal couplings are very common in the bending-bending motions of fixed/ rotating beams. The two-component parametric resonance occurs when one of the natural frequencies of flexible parts of the mechanism is one-half or twice of the excitation frequency and simultaneously the sums or the differences among the internal frequencies are the same, or neighboring, as the frequency of excitation. The effects of two-component parametric resonance post on instability condition are also investigated. Resonance generated by more than two component modes are neglected due to its remote probability of occurrence in nature. The mechanics of the problem is Newtonian. Methods of analysis will consist of the dynamics of small deformations superimposed on the undeformed state. Without loss of generality and based on the Euler-Bernoulli beam theory, the coupled nonlinear equations of motion of a slider-crank mechanism with an inextensible flexible linkage are derived. The Newtons second law is used to obtain the boundary constraints at the piston end. Galerkins procedure was used to remove the dependence of spatial coordinates in the partial differential equations. The method of multiple time scales is applied to consider the steady state solutions and the occurrence of dynamic instability of the resulting multidegree-of-freedom dynamical system with time-periodic coefficients.

Original languageEnglish
Pages (from-to)4225-4250
Number of pages26
JournalInternational Journal of Solids and Structures
Volume36
Issue number28
DOIs
Publication statusPublished - 1999 Oct 1

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Parametric Resonance
eccentrics
chutes
Stability Analysis
Inextensible
Excitation
Multiple Time Scales
Euler-Bernoulli Beam
Newton second law
Periodic Coefficients
occurrences
Coupler
Euler-Bernoulli beams
Steady-state Solution
Natural Frequency
Nonlinear equations
Pistons
Linkage
Partial differential equations
Equations of motion

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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abstract = "The objective of this paper is an analytical and numerical study of the dynamics and dynamic instability of a slider-crank mechanism with an inextensible elastic coupler. Special attention is given to the phenomena arising due to modal interactions produced by the existence of multi-component, specifically two-component, parametric resonance. Such modal couplings are very common in the bending-bending motions of fixed/ rotating beams. The two-component parametric resonance occurs when one of the natural frequencies of flexible parts of the mechanism is one-half or twice of the excitation frequency and simultaneously the sums or the differences among the internal frequencies are the same, or neighboring, as the frequency of excitation. The effects of two-component parametric resonance post on instability condition are also investigated. Resonance generated by more than two component modes are neglected due to its remote probability of occurrence in nature. The mechanics of the problem is Newtonian. Methods of analysis will consist of the dynamics of small deformations superimposed on the undeformed state. Without loss of generality and based on the Euler-Bernoulli beam theory, the coupled nonlinear equations of motion of a slider-crank mechanism with an inextensible flexible linkage are derived. The Newtons second law is used to obtain the boundary constraints at the piston end. Galerkins procedure was used to remove the dependence of spatial coordinates in the partial differential equations. The method of multiple time scales is applied to consider the steady state solutions and the occurrence of dynamic instability of the resulting multidegree-of-freedom dynamical system with time-periodic coefficients.",
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AB - The objective of this paper is an analytical and numerical study of the dynamics and dynamic instability of a slider-crank mechanism with an inextensible elastic coupler. Special attention is given to the phenomena arising due to modal interactions produced by the existence of multi-component, specifically two-component, parametric resonance. Such modal couplings are very common in the bending-bending motions of fixed/ rotating beams. The two-component parametric resonance occurs when one of the natural frequencies of flexible parts of the mechanism is one-half or twice of the excitation frequency and simultaneously the sums or the differences among the internal frequencies are the same, or neighboring, as the frequency of excitation. The effects of two-component parametric resonance post on instability condition are also investigated. Resonance generated by more than two component modes are neglected due to its remote probability of occurrence in nature. The mechanics of the problem is Newtonian. Methods of analysis will consist of the dynamics of small deformations superimposed on the undeformed state. Without loss of generality and based on the Euler-Bernoulli beam theory, the coupled nonlinear equations of motion of a slider-crank mechanism with an inextensible flexible linkage are derived. The Newtons second law is used to obtain the boundary constraints at the piston end. Galerkins procedure was used to remove the dependence of spatial coordinates in the partial differential equations. The method of multiple time scales is applied to consider the steady state solutions and the occurrence of dynamic instability of the resulting multidegree-of-freedom dynamical system with time-periodic coefficients.

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