Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings

Kambampati, Sandilya; Ganguli, Ranjan

doi:10.1007/s00707-014-1238-6

Cited by 8 publications

(4 citation statements)

References 15 publications

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“…In the paper [13] it is reported that the preloading force need not to be constant; in the new types of magnetorheological elastomers for vibration isolators the magnetic attraction force is utilized to change the preloading. A similar result as for beams is obtained for the piano strings loaded with axial force [14]. Various methods are applied for free vibration of axially loaded beams: the corotational finite element formulation [15], the initial values method [16], the Adomian modified decomposition method [17], etc.…”

Section: Introductionsupporting

confidence: 59%

“…where ca = ca α, 1, ψ(t), sa = sa(1, α, ψ(t)), C =C(t) and θ = θ(t). Substituting (20), (21) and the time derivative of (21) into (14) we have…”

Section: Analytic Solving Proceduresmentioning

confidence: 99%

“…where Ω = Ω(C,τ). Equations (23) and (24) are two first order differential equations which represent the rewritten version of (14) in new variables C and ψ, i.e., θ. After some transformation and using (19) it is…”

Section: Analytic Solving Proceduresmentioning

confidence: 99%

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Variable Preloading Force in an Archetypal Oscillator

et al. 2019

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In this paper, the influence of the time variable preloading force on the vibration of an archetypal oscillator is investigated. The oscillator is modeled as a slider-string system which is mathematically described with a second order nonlinear differential equation with time variable parameters. An approximate procedure for solving the equation is introduced. It is based on the exact solution of the pure nonlinear equation in the form of the Ateb function. The obtained result gives the vibration amplitude and phase variation of the oscillator depending on the preloading force variation. Based on this result, the procedure for regulation of the preloading force as the function of the required vibration amplitude decrease is developed. It is concluded that the preloading force may be used as a control parameter of the oscillator.

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Section: Introductionsupporting

confidence: 59%

“…where ca = ca α, 1, ψ(t), sa = sa(1, α, ψ(t)), C =C(t) and θ = θ(t). Substituting (20), (21) and the time derivative of (21) into (14) we have…”

Section: Analytic Solving Proceduresmentioning

confidence: 99%

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Variable Preloading Force in an Archetypal Oscillator

et al. 2019

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“…Kambampati et al [15,16] found non-rotating beams isospectral to rotating uniform beams and rotating beams isospectral to axially loaded non-rotating uniform beams. Kambampati & Ganguli [17,18] found non-uniform beams and stiff springs isospectral to axially loaded uniform beams and piano strings, and non-rotating beams isospectral to tapered rotating beams. In their study, they used Barcilon–Gottlieb transformation to convert the fourth-order governing equation of one kind to the required one.…”

Section: Introductionmentioning

confidence: 99%

Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts

Ganguli

2018

R. Soc. open sci.

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In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.

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