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Lucas Polynomial Solution of the Single Degree of Freedom System
Scientific Research Communications, 2023Free vibration of a single degree of freedom system is a fundamental topic in mechanical vibrations. The present study introduces a novel and simple numerical method for the solution of this system in terms of Lucas polynomials in the matrix form.
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Single–Degree–of–Freedom Systems
2009The theory of vibro–impact dynamics has been applied to classical lumped discrete systems represented by single–, two–, and multi–degree of freedom against one– or two–sided barriers. One freedom systems in the form of mass–spring–dashpot with one–sided barrier have been extensively studied in the literature. Other systems such as a ball bouncing on an
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Vibrations of Single-degree-of-freedom Systems
1975A mechanical system is said to be vibrating when its component parts are undergoing periodic (that is cyclically repeated) oscillations about a central configuration (usually the statical equilibrium position). It can be shown that any system, by virtue of its inherent mass and elasticity, can be caused to vibrate by externally applied forces.
G. H. Ryder, M. D. Bennett
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Single Degree of Freedom (SDOF) Systems
2021We review briefly the second law of Newton and its impulse-momentum and work-energy versions and use them to write equations of motion for single degree of freedom systems. These equations are solved by analysis in the time and frequency domains. Analytical and numerical methods are used for solution.
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RESONANCE CONTROL FOR A FORCED SINGLE-DEGREE-OF-FREEDOM NONLINEAR SYSTEM
International Journal of Bifurcation and Chaos, 2004The main characteristic of a forced single-degree-of-freedom weakly nonlinear system is determined by its primary, super- and sub-harmonic resonances. A nonlinear parametric feedback control is proposed to modify the steady-state resonance responses, thus to reduce the amplitude of the response and to eliminate the saddle-node bifurcations that take ...
Andrew Y. T. Leung +2 more
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Force Vibration of Single Degree of Freedom System
2020The harmonic excitation or force vibration can be described by means of sine function or by means of cosine function.
Farzad Hejazi, Tan Kar Chun
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Single‐Degree‐of‐Freedom Nonlinear Homogeneous Systems
Journal of Engineering Mechanics, 1994A class of nonlinear oscillator that scales input-output relations is identified and studied in this paper. This type of system shows variable stiffness, variable damping, or both, and is piecewise linear in conical regions of the state space. The following passive and semi-active mechanical systems, which exhibit this variable structure, are used to ...
José A. Inaudi +2 more
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Free Vibration of Single Degree of Freedom System
2020A single degree of freedom (SDOF) system describes structural motion with only one degree of freedom. This simplifies the analysis procedure because it is a system with only one displacement coordinate. SDOF system is often used for approximation during the early engineering stage, rather than during the detailed engineering stage.
Farzad Hejazi, Tan Kar Chun
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Optimum dynamic dampers for single‐degree‐of‐freedom systems
Communications in Applied Numerical Methods, 1987AbstractReducing the vibration amplitude of mechanical systems is an on‐going problem for engineers. This paper, which focuses on one aspect of the problem, discusses the design of optimum vibration absorbers for linear damped systems. After the optimum design problem is introduced, a numerical optimization strategy is implemented for the solution. The
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