Finite element prediction of wave motion in structural waveguides

Mace, B.R.; Duhamel, Denis; Brennan, M.J.; Hinke, L.

doi:10.1121/1.1887126

Cited by 385 publications

(243 citation statements)

References 13 publications

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“…Now determine the lowest two eigenvalues of (12)- (14), (16). To simplify the resulting expressions we employ the approximate relations between amplitudes 21 B , 22 B and 11 B , 12 B which may be obtained from (14), (16) …”

Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 99%

Vibration suppression for strings with distributed loading using spatial cross-section modulation

Sorokin

Thomsen

2015

Journal of Sound and Vibration

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Document VersionPeer reviewed version Link back to DTU Orbit Citation (APA): Sorokin, V., & Thomsen, J. J. (2015). Vibration suppression for strings with distributed loading using spatial cross-section modulation. Journal of Sound and Vibration, 335, 66-77. DOI: 10.1016/j.jsv.2014.09.028 Vibration suppression for strings with distributed loading using spatial cross-section modulation Abstract A problem of vibration suppression in any preassigned region of a bounded structure subjected to action of an external time-periodic load which is distributed over its domain is considered. A passive control is applied, in that continuous spatially periodic modulations of structural parameters are used as a means for vibration suppression. As an example, stationary vibrations of a string under action of a distributed time-periodic load are studied. This system in a simplified form models such processes as interaction between membranes and colloids, oscillations of transmission lines under action of rain and wind, and dynamics of suspension bridges and stay cables. Suppression of vibration in predefined regions of the string is performed by continuous spatial modulation of its cross-section. For analyzing the problem considered a novel approach named the method of varying amplitudes is employed. This approach is applicable for solving differential equations without a small parameter, and may be considered as a natural continuation of the classical methods of harmonic balance and averaging. As a result, optimal parameters for the string cross-sectional area modulation are determined for the cases of harmonically, uniformly and arbitrarily distributed load, which allows for completely suppressing or considerably reducing vibration in the prescribed part of the string (compared to the case without modulation). vibration suppression; bounded structure; distributed loading; continuous spatially periodic modulation; the method of varying amplitudes.

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Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 99%

Vibration suppression for strings with distributed loading using spatial cross-section modulation

Sorokin

Thomsen

2015

Journal of Sound and Vibration

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“…6(b), when the beam is subjected to an external time-harmonic excitation with a view to investigate the attenuation levels in the frequency gap 19 19 18 ω ω ω ∆ = − . From the Floquet theory (see [1]) and waveguide finite element (WFE) method [44], the wave propagation through the entire infinite periodic beam mentioned above can be determined by analyzing the wave motion within a single repeated beam segment, which is called a unit cell. The band-gaps can be explored by analyzing the unit cell.…”

Section: Free Wave Propagation and Forced Vibration In The Optimized mentioning

confidence: 99%

“…The transfer matrix T of the unit cell can be defined from the dynamic stiffness matrix of the conventional finite element analysis. Detailed derivation of the transfer matrix is available in [44]. The eigenvalues λ of the transfer matrix T are defined by the propagation constant K (Bloch parameter) as [3,45] …”

Section: Free Wave Propagation and Forced Vibration In The Optimized mentioning

confidence: 99%

On Optimum Design and Periodicity of Band-Gap Structures

Olhoff¹,

Niu²,

Cheng³

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. A band-gap structure usually consists of a periodic distribution of elastic materials or segments, where the propagation of waves is impeded or This paper extends earlier optimum shape design results for transversely vibrating Bernoulli-Euler beams by determining new optimum band-gap beam structures for (i) different combinations of classical boundary conditions, (ii) much larger values of the orders n (n>1) and n-1 of adjacent upper and lower eigenfrequencies of maximized band-gaps, and (iii) different values of a minimum beam cross-sectional area constraint. In the present paper, instead of maximizing band-gaps between frequencies of propagating waves or forced vibrations excited by external time-harmonic loads, the closely relatedproblem of maximizing the gap between two adjacent eigenfrequencies ω n and ω n-1 of any given consecutive orders n (n>1) and n-1, is considered. This is justified by the fact that external time-harmonic dynamic loads cannot excite resonance with high vibration levels of standing waves, if the eigenfrequencies of the structure are moved outside the range of the external excitation frequencies by the optimization.Finally, the present study shows that if an infinite beam structure is constructed by repeated translation of an inner beam segment obtained by the aforementioned frequency gap optimization, then a band-gap of traveling waves in this infinite beam is found to correlate almost perfectly with the maximized frequency gap in the finite structure.

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“…Theoretical modelling of the sound transmission loss through double-leaf lightweight partitions stiffened with periodically placed studs was studied by Wang, Lu, Woodhouse, Langley, and Evans [5], who established analytical model for sound transmission through double-leaf partitions to understand the physics involved and allow future work like optimization of partition design for better sound insulation. Mace, Duhamel, Brennan and Hinke [6] also predicted wave transmission in one-dimensional structural waveguides using the finite-element method. The method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves.…”

Section: Introductionmentioning

confidence: 99%