A Semianalytical Method for Nonlinear  Vibration of Euler‐Bernoulli Beams with  General Boundary Conditions

Jian-she, Peng; Liu, Yan; Yang, Jie

doi:10.1155/2010/591786

Cited by 8 publications

(6 citation statements)

References 30 publications

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“…This paper [10] presents a new semi analytical approach for geometrically nonlinear vibration analysis of Euler-Bernoulli beams with different boundary conditions. The method makes use of Linstedt-Poincar'e perturbation technique to transform the nonlinear governing equations into a linear differential equation system, whose solutions are then sought through the use of differential quadrature approximation in space domain and an analytical series expansion in time domain.…”

Section: Literature Reviewmentioning

confidence: 99%

Study of forced vibrations transition processes of vibration protection devices with rolling-contact bearings

Bissembayev

Sultanova

2020

JMMCS

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Many seismic isolation and vibration protection devices use asan essential element the various types of rolling-contact bearings. The rolling-contact bearing is used for creation of moving base of body protected against vibration. The most dynamic disturbances acting in the constructions and structures have highly complex and irregular nature. This article considers the oscillation of a solid body on kinematic foundations, the main elements of which are rolling bearers bounded by the high order surfaces of rotation at horizontal displacement of the foundation. It is ascertained that the equations of motion are highly nonlinear differential equations. Stationary and transitional modes of the oscillatory process of the system have been investigated. It is determined that several stationary regimes of the oscillatory process exist. Equations of motion have been investigated also by quantitative methods. In this paper the cumulative curves in the phase plane are plotted, a qualitative analysis for singular points and study of them for stability is performed. In the Hayashi plane a cumulative curve of body protected against vibration forms a closed path which does not tend to the stability of singular point. This means that the vibration amplitude of body protected against vibration is not remain constant in steady-state, but changes periodically.

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Section: Literature Reviewmentioning

confidence: 99%

Study of forced vibrations transition processes of vibration protection devices with rolling-contact bearings

Bissembayev

Sultanova

2020

JMMCS

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“…Since the DETF is clamped at its two ends, the middle line of the tuning fork beam must be stretched during vibration. For a clamped beam, if the stretching of the middle plane is considered, the axial displacement must be taken into account; the equations of vibration motion for the axial and transverse displacements are coupled and nonlinear [21][22][23]. For the case of largeamplitude vibration, the axial force increases the frequency of vibration according to the increase of the amplitude.…”

Section: General Solution Of the Slender Beammentioning

confidence: 99%

Analysis of the natural frequency of a quartz double-end tuning fork with a new deformation model

Huang

Chang-Chien

Hsieh

et al. 2016

J. Micromech. Microeng.

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The quartz double-end tuning fork is composed of two parallel slender beams with their ends fixed to the proof masses, both ends of which are clamped. The structure is made of a quartz wafer which is anisotropic in stiffness. In anti-phase mode the two slender parallel beams vibrate in opposite directions and can be modelled as an Euler beam. The twist moments caused by the slender beams on the proof mass make the cross-section of the proof mass deform into a warped surface. The objective of this research is to establish the warping deformation model so that we can build up the equation of motion for anisotropic stiffness by using Hamilton’s principle and then perform theoretical analysis. The more realistic warping displacement leads the natural frequency closer to the true one. The purpose of the proof mass is to modulate the frequencies and mode shape of tuning fork beams. The advantage of anti-phase mode is that the centre of mass in unchanged during motion so that the system has a higher signal-to-noise ratio. The theoretically obtained frequency is compared with the experimental one and that obtained by the finite element method.

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“…Abe [5] proposed an accuracy improvement to the multiple scales method for nonlinear vibration analyses of continuous systems with quadratic and cubic nonlinearities. Based on differential quadrature method, Peng et al [6] proposed a new semianalytic method for the geometrically nonlinear vibration of Euler-Bernoulli beams with different boundary conditions. The supercritical equilibrium solutions of an axially moving beam supported by sleeves with torsion springs are analyzed by Ding et al [7].…”

Section: Introductionmentioning

confidence: 99%

An Approximate Analytical Solution of Transversal Oscillations with Quintic Nonlinearities

Herişanu

Marinca

Chilibaru-Opritescu

2020

Springer Proceedings in Physics

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Free damped vibrations of a hinged-hinged Euler-Bernoulli beam subject to a constant axial force at its free end is investigated. The quintic nonlinear equation of motion is derived from Hamilton's principle and then solved using the optimal auxiliary function method (OAFM). Our proposed procedure is highly efficient and controls the convergence of the solutions, ensuring an excellent accuracy after the first iteration. Numerical values are also obtained in order to validate the analytical results.

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A Semianalytical Method for Nonlinear Vibration of Euler‐Bernoulli Beams with General Boundary Conditions

Cited by 8 publications

References 30 publications

Study of forced vibrations transition processes of vibration protection devices with rolling-contact bearings

Study of forced vibrations transition processes of vibration protection devices with rolling-contact bearings

Analysis of the natural frequency of a quartz double-end tuning fork with a new deformation model

An Approximate Analytical Solution of Transversal Oscillations with Quintic Nonlinearities

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