On the Eigenfrequencies of a Cantilever Beam With Attached Tip Mass and a Spring-Mass System

Gürgöze, M.

doi:10.1006/jsvi.1996.0053

Cited by 98 publications

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“…This ME effect is a complex coupling resulted from the magnetomagnetic coupling, magnetomechanical coupling, and electromechanical coupling. Further, the attached magnets will also serve as a tip mass loading which will further reduce the resonant frequency, 12,13 offering the potential of resonance-enhanced ME coefficients at extremely low frequencies.…”

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confidence: 99%

Giant magnetoelectric effect in Pb(Zr,Ti)O3-bimorph/NdFeB laminate device

Xing

Viehland

2008

Applied Physics Letters

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A Pb(Zr,Ti)O3-bimorph/NdFeB laminate device has a giant magnetoelectric (ME) effect. Our results reveal a giant ME coefficient of 16V∕cmOe or 62nC∕cmOe at a low (subresonant) frequency of 10Hz, and one of 250V∕cmOe or 960nC∕cmOe at a first order resonant bending mode frequency of ∼60Hz. The findings show a simple means by which to achieve magnetoelectric effects, without the use of magnetostrictive material.

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confidence: 99%

Giant magnetoelectric effect in Pb(Zr,Ti)O3-bimorph/NdFeB laminate device

Xing

Viehland

2008

Applied Physics Letters

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“…For example, Ozguven and Candir [1] and Manikanahally and Crocker [2] have investigated the dynamic characteristics of the absorbers composed of one and multiple degrees of freedom (dof) spring-mass systems, respectively. Gürgöze [3,4], Wu and Chen [5], Wu and Chou [6], Larrondo et al [7], and Rossit and Laura [8] have researched the natural frequencies or/and mode shapes of beams carrying one or/and multiple single-dof spring-mass systems. Wu and Chen [9] and Wu et al [10] have used the analytical-and-numerical-combined method to study the free vibration characteristics of a uniform cantilever beam carrying multiple one-dof spring-mass systems with dampers.…”

Section: Introductionmentioning

confidence: 98%

Use of equivalent mass method for free vibration analyses of a beam carrying multiple two‐dof spring–mass systems with inertia effect of the helical springs considered

2005

Numerical Meth Engineering

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SUMMARYThis paper investigates the free vibration characteristics of a beam carrying multiple two-degree-offreedom (two-dof) spring-mass systems (i.e. the loaded beam). Unlike the existing literature to neglect the inertia effect of the helical springs of each spring-mass system, this paper takes the last inertia effect into consideration. To this end, a technique to replace each two-dof spring-mass system by a set of rigidly attached equivalent masses is presented, so that the free vibration characteristics of a loaded beam can be predicted from those of the same beam carrying multiple rigidly attached equivalent masses. In which, the equation of motion of the loaded beam is derived analytically by means of the expansion theorem (or the mode superposition method) incorporated with the natural frequencies and the mode shapes of the bare beam (i.e. the beam carrying nothing). In addition, the mass and stiffness matrices including the inertia effect of the helical springs of a two-dof spring-mass system, required by the conventional finite element method (FEM), are also derived. All the numerical results obtained from the presented equivalent mass method (EMM) are compared with those obtained from FEM and satisfactory agreement is achieved. Because the equivalent masses of each two-dof spring-mass system are dependent on the magnitudes of its lumped mass, spring constant and spring mass, the presented EMM provides an effective technique for evaluating the overall inertia effect of the two-dof spring-mass systems attached to the beam. Furthermore, if the total number of two-dof spring-mass systems attached to the beam is large, then the order of the overall property matrices for the equation of motion of the loaded beam in EMM is much less than that in FEM and the computer storage memory required by the former is also much less than that required by the latter.

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“…Gürgöze (1984Gürgöze ( , 1985 used the normal mode summation technique to determine the fundamental frequency of the cantilever beams carrying masses and springs. Gürgöze (1996) obtained the frequency equation of a clamped-free Bernoulli-Euler beam with attached tip mass and a spring-mass system by using the Lagrange multipliers method. Gürgöze (1998) presented two alternative formulations for the frequency equation of a clamped-free Bernoulli-Euler beam to which several spring-mass systems.…”

Section: Introductionmentioning

confidence: 99%

Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

Yeşilce

Demirdağ

Catal

2008

Sadhana

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Structural elements supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass system and Bernoulli-Euler multi-span beams carrying multiple spring-mass systems are plenty, but on Timoshenko multi-span beams carrying multiple spring-mass systems is fewer. This paper aims at determining the natural frequencies and mode shapes of a Timoshenko multi-span beam. The model allows to analyse the influence of the shear effect and spring-mass systems on the dynamic behaviour of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1-4 span beams are studied. The natural frequencies of Timoshenko multi-span beam calculated by using secant method for non-trivial solution are compared with the natural frequencies of multi-span beam calculated by using Bernoulli-Euler Beam Theory (EBT) in literature; the mode shapes are presented in graphs.

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On the Eigenfrequencies of a Cantilever Beam With Attached Tip Mass and a Spring-Mass System

Cited by 98 publications

References 0 publications

Giant magnetoelectric effect in Pb(Zr,Ti)O3-bimorph/NdFeB laminate device

Giant magnetoelectric effect in Pb(Zr,Ti)O3-bimorph/NdFeB laminate device

Use of equivalent mass method for free vibration analyses of a beam carrying multiple two‐dof spring–mass systems with inertia effect of the helical springs considered

Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

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