Wave Propagation in Structures

Doyle, James F.

doi:10.1007/978-1-4684-0344-2

Cited by 219 publications

(107 citation statements)

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“…The resulting model can be classified as a Spectral Finite Element model, as described in (Doyle, 1988(Doyle, , 1997Gopalakrishnan and Doyle, 1994;Baz, 1999). The obtained sandwich beam model predicts the beam transverse vibration and assesses the influence of the core periodicity on the response of the beam.…”

Section: Modeling Of Wave Propagation In Periodic Sandwich Beams Overmentioning

confidence: 99%

“…The resulting model replicates the exact displacement distributions over the entire structural member and thus allows using a significantly reduced number of elements than conventional FEM. This modeling approach can be classified as a Spectral Finite Element technique, as described, among others, by Doyle (1997Doyle ( , 1998, Gopalakrishnan and Doyle (1994), Baz (1999). The spectral finite element model is used to predict the transverse vibrations of the beam at several nodal locations.…”

Section: Harmonic Responsementioning

confidence: 99%

“…A global dynamic stiffness matrix is then obtained by assembling the cell matrices through standard finite element assembly procedures. The resulting model can be classified as a Spectral Finite Element model, as described by Doyle (1988Doyle ( , 1997, Gopalakrishnan and Doyle (1994) and Baz (1999), and allows replicating the exact displacement distributions over the entire structural member using a significantly reduced number of elements if compared to a conventional Finite Element Model. The sandwich beam model predicts the beam transverse vibration and is used to assess the influence of the core periodicity on the response of the beam.…”

Section: Introductionmentioning

confidence: 99%

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Control of Wave Propagation in Sandwich Beams with Auxetic Core

Ruzzene

Scarpa

2003

Journal of Intelligent Material Systems and Structures

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The wave propagation in sandwich beams with cellular core is analyzed and controlled. The material properties of cellular cores are highly dependent on the geometry of the cell composing the honeycomb structure. Core materials of different geometry placed periodically along the beam length introduce the proper impedance mismatch necessary to impede the propagation of waves along the beam.A theoretical model is developed to describe the wave propagation characteristics and the vibration of the sandwich beam. The model is used to obtain the transfer matrix for a unit cell of the considered periodic structure, which is then used to analyze the dynamics of wave propagation along the beam. The transfer matrix is also properly recast in order to obtain the dynamic stiffness matrix and formulate a spectral finite element model for the periodic sandwich beam. The spectral finite element model employs dynamic shape functions obtained from the solution of the distributed parameter model, which allow predicting the dynamic behavior of the structure with a significantly reduced number of elements as compared to conventional FEM.The transfer matrix of the sandwich beam identifies the location of the frequency bands where traveling waves are attenuated. The influence of core geometry and periodicity on the location and extension of these stop bands is assessed through a series of simulations. The effect of the periodicity of the structure is also evaluated by considering the vibration response of a clamped free beam excited by the harmonic motion of the base. The results demonstrate the simplicity and the effectiveness of the proposed treatment whereby the transmission of waves and the vibration over specified frequency bands can be significantly reduced without requiring additional passive or active control devices. The unique characteristics of cellular solids therefore can be used to design light-weight composite panels that behave as mechanical filters. The filtering capabilities of such passive composite panels may be easily changed and optimized to reduce their transmissibility over a desired frequency range without compromising the size and the weight of the structure.

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Section: Modeling Of Wave Propagation In Periodic Sandwich Beams Overmentioning

confidence: 99%

Section: Harmonic Responsementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Control of Wave Propagation in Sandwich Beams with Auxetic Core

Ruzzene

Scarpa

2003

Journal of Intelligent Material Systems and Structures

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“…The SFEM replicates the exact displacement distributions over the entire structural member using a significantly reduced number of elements than conventional FEM (Doyle [6,7] Gopalakrishnan and Doyle [8], Baz [9]). A spectral finite element model is developed to predict the wave propagation characteristics and the beam transverse vibration.…”

Section: Introductionmentioning

confidence: 99%

<title>Control of wave propagation in sandwich beams with auxetic core</title>

Ruzzene

Scarpa

2001

SPIE Proceedings

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The wave propagation in sandwich beams with cellular core is analyzed and controlled. The material properties of cellular cores are highly dependent on the geometry of the cell composing the honeycomb structure. Core materials of different geometry placed periodically along the beam length introduce the proper impedance mismatch necessary to impede the propagation of waves along the beam.A Spectral Finite Element model is developed to describe the wave propagation characteristics and the vibration of the sandwich beam. The model uses dynamic shape functions obtained from the solution of the corresponding distributed parameter model and thus allows for predicting the dynamic behavior of the structure with a significantly reduced number of elements as compared with the conventional FEM. The model is used to derive the transfer matrix of the sandwich beam, which identifies the location of the frequency bands where traveling waves are attenuated. The influence of core geometry and periodicity on the location and extension of these stop bands is assessed through a series of simulations. The effect of the periodicity of the structure is also evaluated by considering the vibration response of a clamped free beam excited by the harmonic motion of the base. The results demonstrate the simplicity and the effectiveness of the proposed treatment whereby the transmission of waves and the vibration over specified frequency bands can be significantly reduced without requiring additional passive or active control devices. The unique characteristics of cellular solids therefore can be used to design light-weight composite panels that behave as mechanical filters. The filtering capabilities of such passive composite panels may be easily changed and optimized to reduce their transmissibility over a desired frequency range without compromising the size and the weight of the structure.Smart Structures and Materials 2001: Damping and Isolation, Daniel J. Inman, Editor,

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“…It is more accurate than the Euler-Bernoulli theory, since it also takes transverse shear effects into account. It is used, for example, to model aircraft wings (see, for instance, [3]). …”

mentioning

confidence: 99%

Asymptotics and stabilization for dynamic models of nonlinear beams

Araruna¹,

Silva²,

Zuazua³

2010

Proc. Estonian Acad. Sci.

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We prove that the von Kármán model for vibrating beams can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term through a fourth-order dispersive operator is added. We also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter k, when suitable damping terms are added. As k → ∞, one deduces the uniform exponential decay of the energy of the von Kármán model.

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Wave Propagation in Structures

Cited by 219 publications

References 0 publications

Control of Wave Propagation in Sandwich Beams with Auxetic Core

Control of Wave Propagation in Sandwich Beams with Auxetic Core

<title>Control of wave propagation in sandwich beams with auxetic core</title>

Asymptotics and stabilization for dynamic models of nonlinear beams

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