Free vibration of complex cable/mass systems: theory and experiment

Lin, Hai; Perkins, Noel C.

doi:10.1006/jsvi.1995.0008

Cited by 23 publications

(17 citation statements)

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“…The cable model follows that of cable-mass systems developed in reference [10] with #uid forces considered in reference [11]. The #uid forces on the buoy and cable are approximated by using Morison's equation and do not include possible #uctuating lift and drag components due to vortex shedding.…”

Section: Equations Of Motionmentioning

confidence: 99%

Linear Vibration Characteristics of Cable–buoy Systems

Kim¹,

Perkins²

2002

Journal of Sound and Vibration

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Section: Equations Of Motionmentioning

confidence: 99%

Linear Vibration Characteristics of Cable–buoy Systems

Kim¹,

Perkins²

2002

Journal of Sound and Vibration

Self Cite

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“…First frequency(Hz) Second frequency(Hz) Third frequency(Hz) Numerical results from [6] 173.88 988.45 3211 Experiment results from [3] 171 987 3034 Theoretical method [5] by This study is to obtain transverse vibration responses via natural frequencies of un-cracked and cracked beams obtained in accordance with aforementioned conditions of beams, and then the proportion control scheme will be applied to carry out beam control based on different K values of controller with K=10000ˣ20000ˣ50000, 100000, 500000 and 5000000. The percentage reductions of the maximum amplitude before and after the control are obtained for the comparison between the transverse vibration response relationship diagrams of cracked and un-cracked beams before and after the control.…”

Section: Methodsmentioning

confidence: 99%

“…Every section of beam can be connected by employing transfer matrix method [5] for calculation of eigenvalue of the entire system. The general solution of equation (5), for each segment is as shown below:…”

Section: Calculation Of Eigenvaluesmentioning

confidence: 99%

“…The cracks are simulated as rotational springs and the beam is divided into two sections, while the proposed theoretical method is verified by finite element method. Lin et al [5] proposed a theoretic model to describe the non-linear, three-dimensional response of a suspended cable supporting an array of discrete masses. It is applied to obtain the eigenvalues of that complicated system, and the transfer matrix of this method can be applied to the free vibration of complex mass system.…”

Section: Introductionmentioning

confidence: 99%

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Suppression of the dynamic response of cracked beams with active control

2017

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Abstract.Recently, studies on the dynamic responses of cracked beams are quite worthy of being conferred. The theoretical dynamic properties of cracked beams previously obtained by La-DQM method were utilized to evaluate the maximum amplitudes of cracked beams. A comparatively new concept which utilized the controller gain to suppress the transverse vibration response of cracked beams in the perspective of proportional control scheme was proposed. A simulation study which applied an active control strategy to suppress the amplitude of vibration on the cracked beams with MATLAB SIMULINK software has been successfully accomplished. The maximum dynamic response of cracked beams is found to be inversely proportional to controller gain. Increasing the controller gain properly to control the vibration of the cracked beams is suggested in this study.

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“…For instance, eigenvalue problems in linear structural dynamics can lead to non-smooth eigensolutions (in space) as a result of forces/moments produced by discrete elements such as springs (linear or rotational) [10], attached masses [11], cracks [12], etc. For example, the slow convergence of a Ritz series was noted in Ref.…”

Section: Introductionmentioning

confidence: 99%

Harmonic balance/Galerkin method for non-smooth dynamic systems

Kim

Perkins

2003

Journal of Sound and Vibration

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Models of non-li near systems frequently introduce forces with bounded continuity resulting in nonsmooth (even discontinuous) flow. Examples include systems with clearances, backlash, friction, and impulses. Asymptotic methods require smooth (differentiable) flow and are therefore ill-suited for analyzing non-smooth systems. In these cases, the traditional harmonic balance method may be used to obtain approximate periodic solutions, but the method suffers from extremely slow convergence in general. Generalizations of the traditional harmonic balance method are introduced in this paper that result in superior convergence rates and superior modes of convergence. These improvements derive from the introduction of one or more expansion functions that possesses the same degree of continuity as the exact solution. In particular, forming an infinite series of such functions results in an expansion in the same function space of the exact solution. This expansion converges pointwise to the exact solution and to all derivatives thereof. These improvements are illustrated by example upon re-evaluating a classical single degree-of-freedom model for friction-induced vibration.

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Free vibration of complex cable/mass systems: theory and experiment

Cited by 23 publications

References 1 publication

Linear Vibration Characteristics of Cable–buoy Systems

Linear Vibration Characteristics of Cable–buoy Systems

Suppression of the dynamic response of cracked beams with active control

Harmonic balance/Galerkin method for non-smooth dynamic systems

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