Wave Finite Element Method Based on Reduced Model for One-Dimensional Periodic Structures

Zhou, Changwei; Lainé, Jean-Pierre; Ichchou, Mohamed; Zine, Abdelmalek

doi:10.1142/s1758825115500180

Cited by 51 publications

(23 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of sophisticated designs of periodic and locally resonant structural waveguides, 1D beam theories become unadapted and can be replaced by 3D elasticity numerical models solved by using finite element based methods [29,30,31,32]. For more details, the reader can refer to the above cited articles and related references.…”

Section: Introductionmentioning

confidence: 99%

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

Pelat

Gallot

Gautier

2019

Journal of Sound and Vibration

View full text Add to dashboard Cite

This work aims to provide better physical understanding of Bragg band gap effects in continuously periodic corrugated beams for flexural waves. The main outcome is the establishement of original algebraic formulas for the band gap width and central frequency. It is shown that the band gap width and central frequency only depend on a thickness contrast parameter. To do so, a so called two-skins geometry is proposed to approximate the usual solid beam cross section, in order to greatly simplify analytical derivations following the Plane Wave Expansion (PWE) method applied to Euler-Bernoulli theory. Theoretical predictions in the two-skins geometry successfully match the results in the practical case of a solid geometry obtained from both experiments on a beam demonstrator and numerical simulations done by classical PWE (1D Euler and Timoshenko theories) or finite element (3D elasticity theory) methods. The complete set of results is benchmarked in details so that the geometrical approximation is validated and the algebraic formulas are usable as design tools of such notch filters. Moreover, flexural and longitudinal motion coupling due to the non-symetrical thickness profile of the demonstrators leads to an additional band gap that is experimentally identified. A numerical study illustrates the resulting double filtering effect. Potential applications of the background provided by this work can concern Noise,Vibration and Harshness (NVH) engineering, for which meta-materials can be very relevant especially when structure lightening is required.

show abstract

Section: Introductionmentioning

confidence: 99%

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

Pelat

Gallot

Gautier

2019

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…However, the experimental method needs to spend a lot of manpower, material resources, and time to make it, and it is difficult to guarantee the accuracy of the experiment results. Fortunately, the finite element method is an effective and efficient calculation method of band gaps and vibration attenuation properties, the numerical calculation of finite array periodic structures by finite element method has been widely used to demonstrate the effectiveness of the band gaps calculation methods of periodic structures in the scholars’ research [ 47 , 48 , 49 , 50 ]. Thus, to validate the existence of the flexural wave vibration band gaps of the infinite long periodic oscillator coupled damping beam and study the vibration attenuation performance in the frequency ranges of band gaps, we investigated the band gaps and vibration attenuation characteristics by using the finite element method.…”

Section: Resultsmentioning

confidence: 99%

Band Gaps Characteristics Analysis of Periodic Oscillator Coupled Damping Beam

Tang

Yao

et al. 2020

Materials

View full text Add to dashboard Cite

The vibration of the periodic oscillator coupled damping beam model is reduced through the band gaps designing method, which can be applied in equivalent engineering structures. In this paper, the flexural wave dispersion relations of the infinite long periodic oscillator coupled damping beam were calculated using the reverberation-ray matrix method combined with the Bloch theorem. The flexural wave vibration frequency response function of the finite long periodic oscillator coupled damping beam was carried out using the finite element method. The flexural wave vibration band gaps occur in the infinite long periodic oscillator coupled damping beam model in both the analytical and numerical results. In these band gaps, flexural waves’ propagation is prohibited, and flexural vibration is significantly suppressed. Furthermore, the effects of structure and material parameters on the flexural wave vibration band gaps characteristics are studied. Thus, the structural vibration reduction design can be realized by adjusting the related parameters of the periodic coupled damping beam structures and the equivalent 2D periodic stiffened plate structures.

show abstract

“…where P mod represents modal participation factors vector for the set of retained modes; q nI is the whole set of degrees of freedom excluded the ones belonging to the internal nodes. The static boundary modes Ψ B and component modes Ψ C can be derived as in a Craig-Bampton (CB) framework [24,25]. Finally the stiffness and mass matrices of the condensed system can be calculated by pre and post multiplying for the projection matrix G, defined in Eq.…”

Section: A Numerical Approach For Elastic Waves In a Periodic Mediamentioning

confidence: 99%

“…where the subscript C refers to the mass and stiffness matrices of the cell being condensed. Then, at each frequency step, the modal participation factors can be statically condensed and the condensed dynamic stiffness equation D C obtained [24,25]. Assembling the links in Eq.…”

Section: A Numerical Approach For Elastic Waves In a Periodic Mediamentioning

confidence: 99%

Investigations about periodic design for broadband increased sound transmission loss of sandwich panels using 3D-printed models

Errico

Ichchou

Rosa

et al. 2020

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

Two types of sandwich panels are designed by using the periodic structure theory. A double-wall panel with mechanical links and a sandwich panel with rectangular core are studied. An oriented optimization of the elastic bending waves' propagation versus the acoustic wavenumbers is achieved by using shifted core walls and by keeping the mass and stiffness of the system constant. Standard and optimized configurations are 3D-printed and sound transmission measurements are carried out by using a facility with an uncoupled reverberant-anechoic configuration. The experimental evidences of enlarged bending band-gaps and deformation mechanisms are proved using a reverse approach based on the acoustic radiation of the panels.

show abstract

Wave Finite Element Method Based on Reduced Model for One-Dimensional Periodic Structures

Cited by 51 publications

References 23 publications

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

Band Gaps Characteristics Analysis of Periodic Oscillator Coupled Damping Beam

Investigations about periodic design for broadband increased sound transmission loss of sandwich panels using 3D-printed models

Contact Info

Product

Resources

About