Bloch–Floquet bending waves in perforated thin plates

2007 ◽  
Vol 463 (2086) ◽  
pp. 2505-2518 ◽  
Author(s):  
A.B Movchan ◽  
N.V Movchan ◽  
R.C McPhedran
Keyword(s):  
Plane Waves ◽  
Low Frequency ◽  
Free Edge ◽  
Multipole Expansion ◽  
Thin Plates ◽  
Band Diagram ◽  
Single Defect ◽  
Bending Waves ◽  
Zero Radius ◽  
Square Array

This paper presents a mathematical model describing propagation of bending waves in a perforated thin plate. It is assumed that the holes are circular and form a doubly periodic square array. A spectral problem for the biharmonic operator is formulated in a unit cell containing a single defect, and its analytical solution is constructed using a multipole method. The overall system for the coefficients in the multipole expansion is then solved numerically. We generate dispersion diagrams for the two cases where the boundaries of holes are either clamped or free. We show that in the clamped case, there is a total low-frequency band gap in the limit of inclusions of zero radius, and give a simple formula describing the corresponding band diagram in this limit. We show that in the free-edge case, the band diagram of the vibrating plate is much closer to that of plane waves in a uniform plate than for the clamped case.

scholarly journals Low-frequency sinusoids for enhanced shear buckling performance of thin plates

2021 ◽  
Vol 177 ◽  
pp. 106475
Author(s):  
Peter Y. Wang ◽  
Maria E.M. Garlock ◽  
Ted P. Zoli ◽  
Spencer E. Quiel
Keyword(s):  
Low Frequency ◽  
Thin Plates ◽  
Shear Buckling

Effect of Coriolis force on edge waves (I) Investigation of the normal modes

2020 ◽  
Vol 78 (4) ◽  
pp. 229-261
Author(s):  
Robert O. Reid
Keyword(s):  
Coriolis Force ◽  
Wind Stress ◽  
Formal Solution ◽  
Wave Length ◽  
Normal Modes ◽  
Low Frequency ◽  
Phase Speed ◽  
Free Edge ◽  
Edge Wave ◽  
Edge Waves

Essentially two classes of free edge waves can exist on a sloping continental shelf in the presence of Coriolis force. For small longshore wave length, fundamental waves of the first class behave like Stokes edge waves. However, for great wave lengths (of several hundred kilometers or more) the characteristics of the first class are significantly altered. In the northern hemisphere the phase speed for waves moving to the right (facing shore from the sea) exceeds the speed for waves which move to the left. Also, the group velocity for a given edge wave mode has a finite upper limit. Waves of the second class are essentially quasigeostrophic boundary waves with very low frequency and, like Kelvin waves, move only to the left (again facing shore from the sea). Unlike Stokes edge waves, those of the quasigeostrophic class are associated with large vorticity. Examination of the formal solution for forced edge waves indicates that those of the second class may be excited significantly by a wind stress vortex. Also, in contrast to the conclusion of Greenspan (1956), it is proposed that a hurricane can effectively excite the higher order edge wave modes in addition to the fundamental if wind stress is considered.

Band Gap Control in an Active Elastic Metamaterial With Negative Capacitance Piezoelectric Shunting

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Y. Y. Chen ◽  
G. L. Huang ◽  
C. T. Sun
Keyword(s):  
Band Gap ◽  
Elastic Waves ◽  
Low Frequency ◽  
Lattice System ◽  
Band Gaps ◽  
Negative Capacitance ◽  
Bending Waves ◽  
Stiffness Constant ◽  
Elastic Metamaterials ◽  
Gap Control

Elastic metamaterials have been extensively investigated due to their significant effects on controlling propagation of elastic waves. One of the most interesting properties is the generation of band gaps, in which subwavelength elastic waves cannot propagate through. In the study, a new class of active elastic metamaterials with negative capacitance piezoelectric shunting is presented. We first investigated dispersion curves and band gap control of an active mass-in-mass lattice system. The unit cell of the mass-in-mass lattice system consists of the inner masses connected by active linear springs to represent negative capacitance piezoelectric shunting. It was demonstrated that the band gaps can be actively controlled and tuned by varying effective stiffness constant of the linear spring through appropriately selecting the value of negative capacitance. The promising application was then demonstrated in the active elastic metamaterial plate integrated with the negative capacitance shunted piezoelectric patches for band gap control of both the longitudinal and bending waves. It can be found that the location and the extent of the induced band gap of the elastic metamaterial can be effectively tuned by using shunted piezoelectric patch with different values of negative capacitance, especially for extremely low-frequency cases.

On the Use of Transfer Approaches to Predict the Vibroacoustic Response of Poroelastic Media

2016 ◽  
Vol 24 (02) ◽  
pp. 1550020 ◽  
Author(s):  
Q. Serra ◽  
M. N. Ichchou ◽  
J.-F. Deü
Keyword(s):  
Transfer Matrix ◽  
High Frequency ◽  
Plane Waves ◽  
Finite Size ◽  
Low Frequency ◽  
Acoustic Response ◽  
Frequency Range ◽  
Finite Size Effects ◽  
Poroelastic Media ◽  
Lateral Boundary Conditions

The transfer matrix method (TMM) is a famous analytic method in the vibroacoustic community. It is classically considered as a high frequency approach, because of the hypothesis of acoustic plane waves impinging on a flat infinite panel. Thus, it cannot take into account directly finite-size effects or lateral boundary conditions (BCs), and it needs specific algorithms to correct its results in the low frequency range. Within the transfer matrix framework, the use of finite elements makes it possible to generalize the range of applications of transfer approaches. Thus, the study of wave propagation in poroelastic media, in presence of lateral BCs can be carried out. The links between theses waves and the acoustic response of a sample are investigated. Finally, it shows that transfer approaches are not limited in the low frequency range, as usually stated. In fact, the validity of analytic transfer approaches depends more on the material and on the geometry than on the frequency range.

scholarly journals RBF-Based Meshless Method for Large Deflection of Elastic Thin Rectangular Plates with Boundary Conditions Involving Free Edges

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammed M. Hussein Al-Tholaia ◽  
Husain Jubran Al-Gahtani
Keyword(s):  
Boundary Condition ◽  
Basis Function ◽  
Meshless Method ◽  
Iterative Procedure ◽  
Large Deflection ◽  
Free Edge ◽  
Thin Plates ◽  
Rectangular Plates ◽  
Numerical Examples ◽  
Complex Boundary

An RBF-based meshless method is presented for the analysis of thin plates undergoing large deflection. The method is based on collocation with the multiquadric radial basis function (MQ-RBF). In the proposed method, the resulting coupled nonlinear equations are solved using an incremental-iterative procedure. The accuracy and efficiency of the method are verified through several numerical examples. The inclusion of the free edge boundary condition proves that this method is accurate and efficient in handling such complex boundary value problems.

The Acoustical Impedance at the Junction of Non-Coaxial Cylindrical Ducts

1992 ◽  
Vol 11 (4) ◽  
pp. 114-123 ◽  
Author(s):  
Keith S. Peat
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Plane Waves ◽  
Low Frequency ◽  
Evanescent Waves ◽  
Wave Analysis ◽  
Cross Sectional ◽  
Low Frequencies ◽  
Duct Systems

At low frequencies, only plane waves can continuously propagate along uniform ducts, but evanescent, non-planar waves arise from discontinuities in the duct cross-section. The effect of these evanescent waves can be considered as an acoustical impedance to the propagation of plane waves. It is then possible to increase the accuracy of low frequency plane-wave analysis of duct systems with cross-sectional discontinuities, by inclusion of these impedance corrections. This paper considers the derivation of the acoustical impedance at the junction of non-coaxial circular ducts, a common feature within silencer systems.

Characteristics of In-Plane Waves in Composite Plates

2019 ◽  
Vol 24 (3) ◽  
pp. 458-466
Author(s):  
K. Renji ◽  
S. Josephine Kelvina Florence ◽  
Sameer Deshpande
Keyword(s):  
Composite Structures ◽  
Plane Waves ◽  
Phase Speed ◽  
Composite Plates ◽  
Laminated Plates ◽  
Composite Panel ◽  
Plane Shear ◽  
Aerospace Applications ◽  
Bending Waves ◽  
Isotropic Plates

The high frequency dynamic excitations generate both in-plane as well as bending waves in structures. In aerospace applications, many of these structures are made of composite materials. There are two types of in-plane motions, longitudinal and in-plane shear. Although these motions are uncoupled in isotropic materials, composite structures show coupled behaviour. The works reported on in-plane waves in composite structures assume that two in-plane motions are uncoupled as in isotropic plates. In this work, characteristics of the in-plane waves in composite laminated plates are investigated. Expressions for wavenumber, phase speed and group speed are derived. It is seen that in composite plates the two in-plane waves are coupled in longitudinal and shear propagations and are non-dispersive. The phase speeds of in-plane waves in composite plates can be much different from those determined using the expressions for isotropic plates where the waves are uncoupled. To validate the expressions derived the phase speeds of in-plane waves in a typical composite panel are determined experimentally. It is seen that the experimentally obtained phase speeds match well with the theoretical results.

Scattering of Plane Waves by a Constriction

2011 ◽  
Author(s):  
E. Alenius ◽  
M. A˚bom ◽  
L. Fuchs
Keyword(s):  
Acoustic Waves ◽  
Plane Waves ◽  
Low Frequency ◽  
Acoustic Energy ◽  
Flow Noise ◽  
Times Series ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Low Frequency Waves ◽  
Good Agreement

Liner scattering of low frequency waves by an orifice plate has been studied using Large Eddy Simulation and an acoustic two-port model. The results have been compared to measurements with good agreement for waves coming from the downstream side. For waves coming from the upstream side the reflection is over-predicted, indicating that not enough of the acoustic energy is converted to vorticity at the upstream edge of the plate. Furthermore, the sensitivity to the amplitude of the acoustic waves has been studied, showing difficulties to simultaneously keep the amplitude low enough for linearity and high enough to suppress flow noise with the relatively short times series available in LES.

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