Analysis and optimal design of layered structures subjected to impulsive loading

Luo, Xiaobo; Aref, Amjad J.; Dargush, Gary F.

doi:10.1016/j.compstruc.2009.01.016

Cited by 11 publications

(8 citation statements)

References 10 publications

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“…6, the parameter n in Eqs. (17) and (18) needs to be replaced by n þ ð1=2Þ, but for the high-order modes (n ! 1), the form of the resonance frequencies remains the same as in Eq.…”

Section: Analytical Analysis Of Dynamic Behavior In Finite Elastic Mementioning

confidence: 99%

“…In the past, layered structures have demonstrated the ability to achieve vibration isolation and reduce the overall stress amplitude of dynamic disturbances [16,17]. The earliest theoretical discussions for wave propagation in media consisting of a number of elastic layers can be traced back to Thomson's derivation in 1950 [18], which introduced the transfer matrix approach in the time domain to relate the displacements and stresses at the bottom of a layer to those at its top.…”

Section: Introductionmentioning

confidence: 99%

“…The earliest theoretical discussions for wave propagation in media consisting of a number of elastic layers can be traced back to Thomson's derivation in 1950 [18], which introduced the transfer matrix approach in the time domain to relate the displacements and stresses at the bottom of a layer to those at its top. Due to the complexity of wave propagation in finite layered structures, frequency domain approaches have recently been proposed to perform analysis and determine optimal designs of layered structures [16,17]. However, it is extremely difficult to find suitable natural materials for the multilayered structures to actually control the displacement and stress transmission amplitudes quantitatively, due to the limitation of their inherent properties.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, spectrum and vibration analysis of finite elastic metamaterial-based rod is performed analytical and numerically to illustrate the effects of the frequency-dependent properties on the resonate frequency of the finite structure. Then, the spectral approach [16,17,20,21] is utilized and the transfer function for the general wave amplitudes is derived for wave propagation in the finite metamaterial-based layered structure. Finally, the transmitted wave amplitude and its range for one special case in which a layered structure comprised of continuum media with decreasing density is studied.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of Dynamic Behavior of the Finite Elastic Metamaterial-Based Structure With Frequency-Dependent Properties

Shen

Sun

Barnhart

et al. 2018

Journal of Vibration and Acoustics

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For practical applications of the elastic metamaterials, dynamic behavior of finite structures made of elastic metamaterials with frequency dependent properties are analyzed theoretically and numerically. First, based on a frequency-dependent mass density and Young's modulus of the effective continuum, the global dynamic response of a finite rod made of elastic metamaterials is studied. It is found that due to the variation of the effective density and Young's modulus, the natural frequency distribution of the finite structure is altered. Furthermore, based on the spectral approach, the general wave amplitude transfer function is derived before the final transmitted wave amplitude for the finite-layered metamaterial structure with decreasing density is obtained using the mathematical induction method. The analytical analysis and finite element solutions indicate that the increased transmission wave displacement amplitude and reduced stress amplitude can be controlled by the impedance mismatch of the adjacent layers of the layered structure.

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“…6, the parameter n in Eqs. (17) and (18) needs to be replaced by n þ ð1=2Þ, but for the high-order modes (n ! 1), the form of the resonance frequencies remains the same as in Eq.…”

Section: Analytical Analysis Of Dynamic Behavior In Finite Elastic Mementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of Dynamic Behavior of the Finite Elastic Metamaterial-Based Structure With Frequency-Dependent Properties

Shen

Sun

Barnhart

et al. 2018

Journal of Vibration and Acoustics

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show abstract

“…The authors used this analytical approach in order to minimise stress amplitudes with potential application in design of multilayered armour. An analogous optimisation problem is solved by Luo et al in [4]. The authors use the transfer matrix method to reach the optimal design of an elastic multilayered medium subjected to transverse pulse loading.…”

Section: Introductionmentioning

confidence: 99%

Propagation of Non-Stationary Waves in Viscoelastic Strip Composed of Orthotropic Layers

Adámek¹,

Valeš²,

Červ³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The analytical solution for transient waves caused by transverse impact on an infinite layered strip with free-free boundaries is presented in this work. The strip is composed of two horizontal layers of different heights. The materials of both layers are assumed to be linear viscoelastic and orthotropic. The case of special orthotropy is assumed for simplicity. The dissipative behaviour of each layer is modelled by the discrete model of standard linear viscoelastic solid in Zener configuration. The solving procedure used in this work follows the methods applied in previously published works dealing with the problems of a viscoelastic orthotropic strip and the symmetric case of a layered strip. The system of four linear partial integro-differential equations describing the non-stationary state of plane stress in the strip is solved by means of integral transform method. Concretely, the Laplace transform in time domain and the Fourier transform in spatial domain are applied. As a results of this procedure, the final formulas for displacement components in both layers are derived in Laplace domain. These transforms contain eight spectra of Fourier integrals which can be found as the solution of the system of eight complex equations arising from boundary conditions of the problem. When the spectra are known, the resulting formulas for the Laplace transforms of displacement components are obtained.The presented new formulation of non-symmetric problem enables to study the wave phenomena in general two-layered solids of strip-like geometry and it is fundamental for solving a problem with arbitrary number of layers.

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Interface profile optimization for planar stress wave attenuation in bi-layered plates

Rafiee-Dehkharghani

Bansal

Aref

et al. 2015

Composites Part B: Engineering

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Analysis and optimal design of layered structures subjected to impulsive loading

Cited by 11 publications

References 10 publications

Analysis of Dynamic Behavior of the Finite Elastic Metamaterial-Based Structure With Frequency-Dependent Properties

Analysis of Dynamic Behavior of the Finite Elastic Metamaterial-Based Structure With Frequency-Dependent Properties

Propagation of Non-Stationary Waves in Viscoelastic Strip Composed of Orthotropic Layers

Interface profile optimization for planar stress wave attenuation in bi-layered plates

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