Wave propagations of a periodic sandwich beam by FEM and the transfer matrix method

Yeh, Jia Yi; Chen, Lien Wen

doi:10.1016/j.compstruct.2005.01.026

Cited by 56 publications

(26 citation statements)

References 11 publications

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“…Only a small part work is related to multi-layer periodic structure (Mangaraju and Sonti, 2004;Yeh and Chen, 2006;Tian, 2014). However, most of the above work is based on numerical simulation or FEM method without analytical solution.…”

Section: Introductionmentioning

confidence: 99%

Bandgap of flexural wave in periodic bi-layer beam

Guo

Sheng

2016

Journal of Vibration and Control

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A periodic bi-layer beam structure is proposed and the bandgap characteristic of flexural wave is studied in this paper. The single cell is made up of two bi-layer beams with four components. For the infinite structure, the flexural wave bandgap frequency algorithm is theoretically derived through Timoshenko beam theory, Hamilton principle, BlochFloquet theory and transfer matrix method. An analytical example is presented to illustrate the bandgap characteristic and FEA software simulation is conducted to demonstrate the validation of the algorithm. For the finite structure, the vibration transmission characteristic is studied with FEA software to show the flexural wave attenuation behavior of the periodic bi-layer beam. The results reveal that, the flexural wave is attenuated gradually in the stopband along the direction of wave propagation, while in the passband, it will propagate without attenuation. Comparisons with periodic single layer beam are studied to verify the convenience and flexibility of bi-layer beam. Finally, parametric influences on bandgaps are discussed, which will help the designers to make a better design for vibration reduction.

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Section: Introductionmentioning

confidence: 99%

Bandgap of flexural wave in periodic bi-layer beam

Guo

Sheng

2016

Journal of Vibration and Control

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“…The next step is to use boundary conditions of the system in Eqs. (5) and (6) and solve for eigenvalues λ j (j = 1, 2, • • • ) and corresponding eigenfunctions Φ j (x), so that u (x, t) can be expanded as…”

Section: General Formulation Of the New Spatial Discretization Methodsmentioning

confidence: 99%

“…The local methods, such as finite difference and finite element methods [4,5], discretize a spatial domain into multiple smaller domains, and evaluate governing equations at connecting points between them. The finite element method can be combined with the transfer-matrix method to deal with wave propagation in a periodic structure [6]. The global methods, such as Trefftz, assumed modes, and Galerkin's methods, discretize a spatial domain using a set of trial functions.…”

Section: Introductionmentioning

confidence: 99%

On a comparative study of an accurate spatial discretization method for one-dimensional continuous systems

Zhu

Fan

2017

Journal of Sound and Vibration

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This work provides an in-depth investigation on advantages of a recently developed, new global spatial discretization method over the assumed modes method, and a clear description of the procedure and validity of the new method and its feasibility for arbitrary boundary conditions. A general formulation of the new spatial discretization method is given for second-and fourth-order continuous systems, whose displacements are divided into internal terms and boundary-induced terms, and two examples that consider the longitudinal vibration of a rod and the transverse vibration of a tensioned Euler-Bernoulli beam are used to demonstrate the new spatial discretization method. In the two examples, natural frequencies, mode shapes, harmonic steady-state responses, and transient responses of the systems are calculated using the new spatial discretization method and the assumed modes method, and results are compared with those from exact analyses. Convergence of the new spatial discretization method is investigated using different sets of trial functions for internal and boundary-induced terms. While the new spatial discretization method has additional degrees of freedom at boundaries of a continuous system compared with other global spatial discretization methods, it has the following advantages: (1) compared with the assumed modes method, the new method gives better results in calculating eigensolutions and responses of the system, and allows more terms to be retained in the trial function expansions due to the slowly growing condition number of the mass matrix of the system; and (2) compared with the exact eigenfunction expansion method, the new method can use sinusoidal functions as trial functions for the internal term rather than complicated eigenfunctions of the system.

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“…In the literature, most of the researchers directly solved the differential equations to obtain the transfer matrix for this kind of problems. Without using the analytical solution of wave equation, Solaroli et al (2003) and Yeh and Chen (2006) investigated the characteristics of wave propagation on the periodic stiffened shell and the periodic covered sandwich beam by the finite element method base on the transfer matrix method.…”

Section: Transfer Matrix Of the Periodicmentioning

confidence: 99%

Wave Propagation and Localization in a Randomly Disordered Periodic Piezoelectric Axial-Bending Coupled Beam

Zhu

Ding

Yin

2013

Advances in Structural Engineering

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The wave propagation and localization in periodic and randomly disordered periodic piezoelectric axial-bending coupled beams are studied in this paper. The dynamic stiffness matrix is derived based on the finite element model and the transfer matrix between two adjacent cells is obtained by using the continuity conditions. In addition, the Lyapunov exponent method is employed to calculate the localization factor characterizing the average exponential rate of decay of the wave amplitude in the disordered periodic structure. Through the comprehensive numerical simulations, the effects of different material and geometric properties as well as disordered parameters on the localization factors are investigated. The results show that wave propagation and localization in the periodic and disordered periodic piezoelectric beam can be altered by properly adjusting the structural parameters.

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Wave propagations of a periodic sandwich beam by FEM and the transfer matrix method

Cited by 56 publications

References 11 publications

Bandgap of flexural wave in periodic bi-layer beam

Bandgap of flexural wave in periodic bi-layer beam

On a comparative study of an accurate spatial discretization method for one-dimensional continuous systems

Wave Propagation and Localization in a Randomly Disordered Periodic Piezoelectric Axial-Bending Coupled Beam

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