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Internal Vibration and Synchronization of Four Coupled Self-Excited Elastic Beams  [PDF]
Miguel A. Barron
Open Journal of Applied Sciences (OJAppS) , 2016, DOI: 10.4236/ojapps.2016.68050
Abstract: The vibration behavior and the synchronization between some internal points of four coupled self-excited beams are numerically studied. Coupling through the root of the beams is considered. The transverse displacements of the internal points and the beam tips are monitored, and the power spectra of the resulting time series are employed to determine the oscillation frequencies. The synchronization between beams is analyzed using phase portraits and correlation coefficients. Numerical results show multiple frequencies in the vibration pattern, and complex patterns of synchronization between pairs of beams.
Numerical Analysis of Oscillation Death in Coupled Self-Excited Elastic Beams  [PDF]
Miguel A. Barron,Isaias Hilerio,Gabriel Plascencia
Advances in Mechanical Engineering , 2012, DOI: 10.1155/2012/746537
Abstract: The emergence of the oscillation death phenomenon in a ring of four coupled self-excited elastic beams is numerically explored in this work. The beams are mathematically represented through partial differential equations which are solved by means of the finite differences method. A coupling scheme based on shared boundary conditions at the roots of the beams is assumed, and as initial conditions, zero velocity of the first beam and three normal vibration modes of a linear elastic beam are employed. The influence of the self-exciting constant on the ring dynamics is analyzed. It is observed that oscillation death arises as result of the singularity of the coupling matrix. 1. Introduction In the past years the collective behavior of coupled nonlinear oscillators has been widely studied in many disciplines, for example, physics [1], biology [2], ecology [3], chemistry [4], and mechanics [5]. A wide diversity of nonlinear dynamic phenomena such as locking [1], partial synchronization [6], full synchronization [7], antiphase synchronization [8], and clustering [9] have been reported in coupled oscillators. Many coupling schemes have also been tested: local [10], nearest [11], global [12], diffusive [13], adaptive [14], delayed [15], hierarchical [16], and so on. An interesting behavior of coupled oscillators is amplitude death and oscillation death, which are steady states where the coupled oscillators stop their oscillation in a permanent way and become frozen in time [17–19]. Sometimes this cessation of oscillations in time is named quenching [20]. Amplitude death arises through a Hopf bifurcation mechanism in coupled oscillators with an important parameter mismatch or in identical oscillators with time delays [21]. An already existing unstable steady state with zero amplitude is transformed by the coupling into a stable one allowing its observation; that is, the coupling induces stability at the origin of the phase space. On the other hand, oscillation death occurs through a saddle-node bifurcation mechanism allowing the emergence of new fixed points: a new stable steady state with nonzero amplitude is created by the coupling [19, 21]. Frequently, in the literature amplitude death is confused with oscillation death [22–27]. Even the famous finding of Lord Rayleigh [28] related to the quenching of two organ pipes standing side by side is indistinctly considered as amplitude death or oscillation death [29]. To date, in spite of the significant conceptual and technical differences between amplitude death and oscillation death, there is not yet a clear
An Efficient Analytical Method for Vibration Analysis of a Beam on Elastic Foundation with Elastically Restrained Ends  [PDF]
Mustafa ?zgür Yayli,Murat Aras,Süleyman Aksoy
Shock and Vibration , 2014, DOI: 10.1155/2014/159213
Abstract: An efficient analytical method for vibration analysis of a Euler-Bernoulli beam on elastic foundation with elastically restrained ends has been reported. A Fourier sine series with Stoke’s transformation is used to obtain the vibration response. The general frequency determinant is developed on the basis of the analytical solution of the governing differential equation for all potential solution cases with rigid or restrained boundary conditions. Numerical analyses are performed to investigate the effects of various parameters, such as the springs at the boundaries to examine how the elastic foundation parameters affect the vibration frequencies. 1. Introduction Beams resting on elastic foundations have wide application in engineering practice. The vibration analysis of beams is investigated using various elastic foundation models, such as, Vlasov, Pasternak, and Winkler models. A number of studies have been performed to predict the dynamic response of beams on elastic foundations with different boundary conditions. Numerous works have been performed to explore the static deflection and vibration response of the beams resting on various elastic foundations. Chun [1] has investigated free vibration of hinged beam. Maurizi et al. [2] have considered the vibration frequencies for a beam with different boundary conditions. Vibration of beams on partial elastic foundations has been studied by Doyle and Pavlovic [3]. Laura et al. [4] have investigated beams which carry concentrated masses subject to an axial force. Abbas [5] has investigated vibration of Timoshenko beams with elastically restrained ends. Free vibration and stability behavior of uniform beams and columns with nonlinear elastic end rotational restraints has been considered by Rao and Naidu [6]. Free vibration behaviour of an Euler-Bernoulli beam resting on a variable Winkler foundation has been considered by Kacar et al. [7]. Civalek [8] has implemented differential quadrature and harmonic differential quadrature methods for buckling analysis of thin isotropic plates and elastic columns. H. K. Kim and M. S. Kim [9] have considered vibration of beams with generally restrained boundary conditions. A number of studies have been reported investigating the free vibration of beams on elastic foundation [10–25]. Although vibration analysis of beams on elastic foundation is a widely studied topic, there are only few papers that exist in the literature pertaining to the analysis of beams with elastically restrained ends. In this study, an efficient method is introduced for the analysis of the free
Parametric Study of Nonlinear Beam Vibration Resting on Linear Elastic Foundation
Journal of Mechanical Engineering and Automation , 2012, DOI: 10.5923/j.jmea.20120206.02
Abstract: Nonlinear beam resting on linear elastic foundation and subjected to harmonic excitation is investigated. The beam is simply supported at both ends. Both linear and nonlinear analyses are carried out. Hamilton’s principle is utilized in deriving the governing equations. Well known forced duffing oscillator equation is obtained. The equation is analyzed numerically using Runk-Kutta technique. Three main parameters are investigated: the damping coefficient, the natural frequency, and the coefficient of the nonlinearity. Stability regions for first mode analyses are unveiled. Comparison between the linear and the nonlinear model is presented. It is shown that first mode shape the natural frequency could be approximated as square root of the sum of squares of both natural frequency of the beam and the foundation. The stretching potential energy is proved to be responsible for generating the cubic nonlinearity in the system.
Effects of Structural Parameters on the Dynamics of a Beam Structure with a Beam-Type Vibration Absorber  [PDF]
Mothanna Y. Abd,Azma Putra,Nawal A. A. Jalil,Jamaludin Noorzaei
Advances in Acoustics and Vibration , 2012, DOI: 10.1155/2012/268964
Abstract: A beam-type absorber has been known as one of the dynamic vibration absorbers used to suppress excessive vibration of an engineering structure. This paper studies an absorbing beam which is attached through a visco-elastic layer on a primary beam structure. Solutions of the dynamic response are presented at the midspan of the primary and absorbing beams in simply supported edges subjected to a stationary harmonic load. The effect of structural parameters, namely, rigidity ratio, mass ratio, and damping of the layer and the structure as well as the layer stiffness on the response is investigated to reduce the vibration amplitude at the fundamental frequency of the original single primary beam. It is found that this can considerably reduce the amplitude at the corresponding troublesome frequency, but compromised situation should be noted by controlling the structural parameters. The model is also validated with measured data with reasonable agreement. 1. Introduction A beam-type absorber is one of the techniques to reduce undesirable vibration of many vibrating systems, such as a synchronous machine, mounting structure for a sensitive instrument, and other continuous structure in engineering. The absorber system usually consists of a beam attached to the host structure using an elastic element. The natural frequency of the absorber is then tuned to be the same as the troublesome operating frequency of the host structure to create counter force, which in return reduces the vibration of the structure. As beams are important structures in civil or mechanical engineering, several works have also been established to investigate the performance of the absorbing beam which is attached also to a beam structure. Among the earliest studies of the double-beam system is one proposed by Yamaguchi [1], which investigated the effectiveness of the dynamic vibration absorber consisting of double-cantilever visco-elastic beam connected by spring and viscous damper. The auxiliary beam is attached to the center of the main beam excited at its end by a sinusoidal force. It is found that the amplitude at resonances of the main beam is sensitive to the stiffness and mass of the absorbing beam. The damping ratio was formulated as a function of mass and layer stiffness of the absorber. Vu et al. [2] studied the distributed vibration absorber under stationary distributed force. A closed form was developed by utilizing change of variables and modal analysis to decouple and solve differential equations. Oniszczuk [3] studied the free vibrations of two identical parallel simply
Analytical study of self-excited vibration on single degree of freedom vibratory-tillage
Soeharsono,Radite PA Setiawan
Journal of Engineering and Applied Sciences , 2010,
Abstract: Analytical and experimental study on vibratory tillage by adding external energy to the tillage tool has been widely conducted. Though this method has been shown to significantly reduce soil resistance, it will, unfortunately, increase the energy consumption excessively. Experimental study on vibratory tillage by self-excited vibration method has also been performed. This method can also reduce soil resistance though not as much as the former. No analytical study of the latter, however, can be found. This paper discusses analytical study of self-excited vibration of tillage-tool on vibratory tillage due to natural excitation of varying cutting forces. The objective of this discussion is to find dynamics parameter of vibratory tillage so the vibration of tillage-tool will be able to reduced draft force required for loosening soil density during tillage operation The Vibration of vibratory tillage was modeled as a vibration with Single Degree of Freedom (SDOF) system. The tillage-tool was connected to an implement by an elliptic spring while the natural excitation of the varying cutting force was modeled as a periodic function, which can be expressed as a Fourier series. The elasticity of elliptic spring and the inertia of tillage tool were optimized such that the tillage-tool vibrates violently around its resonant frequency. This condition decreases both the soils resistance and the draft force required to loosen soil density due to self-exited vibration during tillage operation. The possibility of draft force reduction was investigated further by analyzing time response of the displacement and by analyzing the oscillating pathway of the tine tip.
Locally resonant elastic wave band gaps in flexural vibration of multi-oscillators beam
多振子梁弯曲振动中的局域共振带隙

Wen Qi-Hu,Zuo Shu-Guang,Wei Huan,
文岐华
,左曙光,魏欢

物理学报 , 2012,
Abstract: The flexural vibration behavior of elastic wave across a slender beam with locally resonant multi-oscillators structure is studied by using the transfer-matrix method and the finite element method. A simplified model is proposed, and the formulas of start and end frequencies of band gap are deduced. The more abundant and wider flexural elastic wave band gaps are found in this locally resonant multi-oscillator beam than in one oscillator beam, which can be used in the reduction of multiple-frequency vibration and noise. The frequency response of vibration in the band gap frequency range has obvious attenuation. The results of simplified model are in good agreement with results from the theory model. The research project will provide a new way for vibration reduction of beam structure.
Control Application of Piezoelectric Materials to Aeroelastic Self-Excited Vibrations  [PDF]
Mohammad Amin Rashidifar,Darvish Ahmadi
Shock and Vibration , 2014, DOI: 10.1155/2014/509024
Abstract: A method for application of piezoelectric materials to aeroelasticity of turbomachinery blades is presented. The governing differential equations of an overhung beam are established. The induced voltage in attached piezoelectric sensors due to the strain of the beam is calculated. In aeroelastic self-excited vibrations, the aerodynamic generalized force of a specified mode can be described as a linear function of the generalized coordinate and its derivatives. This simplifies the closed loop system designed for vibration control of the corresponding structure. On the other hand, there is an industrial interest in measurement of displacement, velocity, acceleration, or a contribution of them for machinery condition monitoring. Considering this criterion in quadratic optimal control systems, a special style of performance index is configured. Utilizing the current relations in an aeroelastic case with proper attachment of piezoelectric elements can provide higher margin of instability and lead to lower vibration magnitude. 1. Introduction The dependence of mechanical and electrical properties of piezoelectric materials on their application in various materials as patches or layers makes them an appropriate sensor or actuator for vibration control of structures. In sensing situation, the mechanical and creep deformations of structures can be determined by measuring the electrical potential produced in piezoelectric materials. This property is termed the direct property of the piezoelectric material. Then an effective feedback mechanism sends an electric signal to an actuator to keep the vibration of the mechanical system to a minimum. In actuator applications, the inverse piezoelectric effect is used. Recently, this technique is widely used in the active control of vibrations, deformation control of structures, and aerospace industries. This technique has been investigated by research in solid and aeroelastic areas. In solid, Gaudenzi et al. [1] investigated the vibration control of an overhung beam by means of finite element approach based on Euler-Bernoulli beams. They studied state feedback and velocity feedback control of vibration. Moreover, Q. Wang and C. M. Wang [2] implemented vibration control of a beam with piezoelectric patches by taking finite element method into account. They determined an optimized position for an appropriate actuator and the subsequent vibration amplitude of a hinged-hinged beam by applying a feedback control procedure and converting the finite element model into its state space form. Narayanan and Balamurugan [3] studied
EXPERIMENTAL STUDY ON TURBULENT DRAG REDUCTION AND SELF-EXCITED VIBRATION OF FLEXIBLE TUBES
柔管自激振动特性与减阻效果的实验研究

CAI Shupeng,TANG Chuanlin,LI Damei,
蔡书鹏
,唐川林,李大美

力学与实践 , 2006,
Abstract: To clarify the relation between turbulent drag reduction and self-excited vibration of flexible tubes, experiments were performed on the effects of turbulent drag reduction and the characters of self-excited vibration, by comparing the turbulent drag with, that in a rigid tube and by using a double-sleeve structure and a laser displacement sensor. The results are as the follows: the thinner the flexible tubes, the larger the root mean square of the fluctuating displacement at the outer wall of the tubes, and the larger the decreasing rate of the friction coefficient of the self-excited vibration, while applying a pressure-balanced air on the outer wall, with the rates of drag reduction of the flexible tubes with thickness of 2mm, 3mm, 4mm, being about 12%, 10%, 9% at the Reynolds number of 17500. This would provide a reference for efficient fluid transportation.
Approximate Analytical Solution Of The Piecewise-Smooth Nonlinear Systems Of Multi-Degrees-Of-Freedom ------The Self-Excited Vibration Of The Chinese Cultural Relic Dragon Washbasin
多自由度分段光滑非线性系统的近似解——-中华文物龙洗的自激振动

Jia Qifen Yu Wen Liu Xijun Wang,
贾启芬
,于雯,刘习军,王大钧

力学学报 , 2004,
Abstract: Piecewise-smooth nonlinear dynamics system caused by dry friction is becoming hot problems in mechanics with the development of science and technology. The study of nonlinear dynamics including dry friction systems has made many progresses. Because of the complexity of equations, many researches were based on phase-plane orbit analysis and numerical analysis and experimental research. In this paper, a mathematical model of self-excited vibration caused by dry friction between two elastic structures was established using the Chinese cultural relic dragon washbasin as an example. An approximate analytical solution of the piecewise-smooth nonlinear dynamics systems of multi-degrees-of-freedom induced by dry friction was derived by means of averaging method. According to the approximate analytical solution, the curves of relation between swing and rubbing velocity of hands, the relation between swing and natural frequency of hands and the relation between phase angle and rubbing velocity of hands were obtained. The vibration mechanism of the water droplets spurting phenomenon of the Chinese cultural relic dragon washbasin is further explained. The results not only enhanced the precision but also explained qualitatively the whole kinematic process. If the parameters of the system in the design were changed, the design could be optimized according to the related curves, which supplied the theoretical basis for identifying parameter and analysis and research of steady region of this kind of nonlinear vibration systems. Furthermore, the results are in excellent agreement with that of the numerical solution, so that an efficient and credible analytical method to investigate piecewise-smooth nonlinear systems of multi-degrees-of-freedom was given in this paper.
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