scholarly journals Dynamic Property Investigation of Sandwich Acoustic Black Hole Beam with Clamped-Free Boundary Condition

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaofei Du ◽  
Dacheng Huang ◽  
Jianrun Zhang
Keyword(s):  
Boundary Condition ◽  
Black Hole ◽  
Free Boundary ◽  
Layer Thickness ◽  
Sandwich Beam ◽  
Middle Layer ◽  
Acceleration Response ◽  
Beam Structure ◽  
Layer Material ◽  
Vibration Attenuation

The geometric parameters of the acoustic black hole (ABH) structure are changed in power exponent, and this feature can be used to control the flexural wave to achieve energy concentration, vibration attenuation, or noise reduction. However, in practice, the ABH structure often has a truncation due to the limitation of manufacturing, which will cause the reflection coefficient to increase significantly and seriously affect the ABH effect. In this paper, a semianalytical model of the sandwich-truncated ABH beam structure with aluminum in the middle layer and steel in the upper and lower layers is constructed based on the energy principle. The ABH effect of the sandwich beam under the clamped-free boundary condition is analyzed. Meanwhile, the effects of damping layer parameters, middle layer material, and thickness on the vibrational acceleration response of the ABH region and the uniform beam region of the sandwich beam are also studied. It is observed that, for the sandwich ABH beam structure, the influence of damping layer thickness on the acceleration response peak values of both the ABH region and the uniform region is very obvious in middle and high frequencies and the peaks at about 9 kHz are completely suppressed when the damping layer thickness reaches 3 mm. It also reveals that the use of aluminum as the middle layer material can bring a vibration attenuation at around 9 kHz both for the ABH region and the uniform beam region compared with using steel as the middle layer material. Experiments are carried out to verify the accuracy of simulation analysis.

scholarly journals Extreme black hole anabasis

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Shahar Hadar ◽  
Alexandru Lupsasca ◽  
Achilleas P. Porfyriadis
Keyword(s):  
Boundary Condition ◽  
Black Hole ◽  
Spherically Symmetric ◽  
Asymptotically Flat ◽  
Flat Region ◽  
Extreme Black Hole ◽  
Condition Change ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

Abstract We study the SL(2) transformation properties of spherically symmetric perturbations of the Bertotti-Robinson universe and identify an invariant μ that characterizes the backreaction of these linear solutions. The only backreaction allowed by Birkhoff’s theorem is one that destroys the AdS2× S2 boundary and builds the exterior of an asymptotically flat Reissner-Nordström black hole with $$ Q=M\sqrt{1-\mu /4} $$ Q = M 1 − μ / 4 . We call such backreaction with boundary condition change an anabasis. We show that the addition of linear anabasis perturbations to Bertotti-Robinson may be thought of as a boundary condition that defines a connected AdS2×S2. The connected AdS2 is a nearly-AdS2 with its SL(2) broken appropriately for it to maintain connection to the asymptotically flat region of Reissner-Nordström. We perform a backreaction calculation with matter in the connected AdS2× S2 and show that it correctly captures the dynamics of the asymptotically flat black hole.

scholarly journals Propagation of North Atlantic Deep Water Anomalies

2018 ◽  
Vol 48 (8) ◽  
pp. 1831-1848 ◽  
Author(s):  
David Nieves ◽  
Michael Spall
Keyword(s):  
Boundary Condition ◽  
Layer Thickness ◽  
Time Scales ◽  
North Atlantic ◽  
Deep Water ◽  
Volume Flux ◽  
Reduced Gravity ◽  
Northern Boundary ◽  
Variable Source ◽  
Gravity Equations

AbstractWe present a simplified theory using reduced-gravity equations for North Atlantic Deep Water (NADW) and its variation driven by high-latitude deep-water formation. The theory approximates layer thickness on the eastern boundary with domain-averaged layer thickness and, in tandem with a mass conservation argument, retains fundamental physics for cross-equatorial flows on interannual and longer forcing time scales. Layer thickness anomalies are driven by a time-dependent northern boundary condition that imposes a southward volume flux representative of a variable source of NADW and damped by diapycnal mixing throughout the basin. Moreover, an outflowing southern boundary condition imposes a southward volume flux that generally differs from the volume flux at the northern boundary, giving rise to temporal storage of NADW within the Atlantic basin. Closed form analytic solutions for the amplitude and phase are provided when the variable source of NADW is sinusoidal. We provide a nondimensional analysis that demonstrates that solution behavior is primarily controlled by two parameters that characterize the meridional extent of the southern basin and the width of the basin relative to the equatorial deformation radius. Similar scaling applied to the time-lagged equations of Johnson and Marshall provides a clear connection to their results. Numerical simulations of reduced-gravity equations agree with analytic predictions in linear, turbulent, and diabatic regimes. The theory introduces a simple analytic framework for studying idealized buoyancy- and wind-driven cross-equatorial flows on interannual and longer time scales.

Flexural Vibration of Segmented Elastic-Viscoelastic Sandwich Beams

1975 ◽  
Vol 42 (4) ◽  
pp. 897-900
Author(s):  
B. E. Sandman
Keyword(s):  
Steady State ◽  
Numerical Study ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Middle Layer ◽  
Resonant Mode ◽  
Sandwich Beams ◽  
Simply Supported ◽  
Viscoelastic Core ◽  
Longitudinal Nonuniformity

A pair of governing differential equations form the basis for the study of steady-state forced vibration of a sandwich beam with longitudinal nonuniformity in the stiffness and mass of the middle layer. The spatial solution for simply supported boundary conditions is obtained by a Fourier analysis of both material and kinematic variations. The solution is utilized in the numerical study of a sandwich beam with a segmented configuration of elastic and viscoelastic core materials. The results exemplify a tuned configuration of core segments for optimum damping of the first resonant mode.

Edgewise Bending Vibration Analysis of a Rotating Sandwich Beam with Magnetorheological Elastomer Core

2018 ◽  
Vol 18 (11) ◽  
pp. 1850134 ◽  
Author(s):  
S. Bornassi ◽  
H. M. Navazi ◽  
H. Haddadpour
Keyword(s):  
Magnetic Field ◽  
Layer Thickness ◽  
Rectangular Cross Section ◽  
Ritz Method ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Core Layer ◽  
Magnetorheological Elastomer ◽  
Bending Vibration ◽  
Elastic Layers

The vibration of a rotating sandwich beam with magnetorheological elastomer (MRE) as a core between two elastic layers is theoretically analyzed in this paper. This study is focused on the bending vibration along the edgewise direction of a sandwich beam of rectangular cross-section, which, to the best of our knowledge, has not been addressed yet. The classical Euler–Bernoulli beam theory is used to model the dynamic behavior of the elastic layers. In the modeling, the effect of the MRE layer is considered by incorporating its shear strains and the inertia due to shear deformation and bending motion. The governing equations of motion of the rotating sandwich beam are derived by using the Ritz method and the Lagrange’s equations. The effects of the applied magnetic field, core layer thickness, rotational speed, setting angle and hub radius on the natural frequencies and the corresponding loss factors are investigated parametrically. The results show the significant effect of the magnetic field intensity and the MRE layer thickness on the modal characteristics of the MRE sandwich beam.

Effect of an elastically restrained boundary on SV-wave radiation patterns

1968 ◽  
Vol 58 (2) ◽  
pp. 497-520
Author(s):  
Y. T. Huang
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Solid Earth ◽  
Elastic Constants ◽  
Wave Radiation ◽  
Free Boundary Conditions ◽  
Elastically Restrained

Abstract In the solution of elastic wave propagation equations applied to solid earth, it is customarily assumed that free boundary conditions are satisfied at a surface which is in contact with the atmosphere. Situations which depart from this boundary condition have now been studied for arbitrary combinations of the Lamé elastic constants. The solutions are given for a homogeneous, isotropic half space.

Consideration of Both Extensional and Shear Strain of Core Material in Modal Property Estimation of Sandwich Plates

1995 ◽  
Author(s):  
Byung-Chan Lee ◽  
Kwang-Joon Kim
Keyword(s):  
Shear Strain ◽  
Layer Thickness ◽  
Sandwich Beam ◽  
Base Layer ◽  
Core Material ◽  
Viscoelastic Layer ◽  
Sandwich Plates ◽  
Modal Parameter ◽  
The Core ◽  
Plate Length

Abstract In vibration analysis of sandwich beam/plates, it is often assumed that there occurs shear deformation only, i.e. no extension or compression, in the core viscoelastic layer. Certainly, this assumption may have limitations, for example, with increase of the core thickness or frequency range of vibration. The purpose of this paper is to consider the extentional as well as shear strain of the core for modal parameter estimation of the sandwich plates and to investigate how much error will be caused by neglecting the extension or compression in the core material. Natural frequencies and modal loss factors are estimated for a simply supported square plates under each of the above two assumptions. Nondimensional characteristic equations are formulated and solved for various ratios of the base layer thickness to plate length, core to base layer thickness, and constraining layer to base layer thickness.

scholarly journals Exact and approximate reflection/transmission responses from a layer containing vertical fractures

2020 ◽  
Vol 222 (1) ◽  
pp. 260-288
Author(s):  
Song Jin ◽  
Alexey Stovas
Keyword(s):  
Plane Wave ◽  
Layer Thickness ◽  
Finite Thickness ◽  
Subsurface Layer ◽  
Symmetry Plane ◽  
Middle Layer ◽  
Second Order ◽  
First Order ◽  
Background Medium ◽  
Vertical Fractures

SUMMARY Analyses of vertical fractures are of great interest in characterizing the fluid flow and minimum in situ stress direction in reservoirs. Long-wavelength equivalent orthorhombic (ORT) media typically characterize the anisotropy induced by a set of vertical parallel fractures or two sets of vertical and mutually orthogonal fractures embedded into a transversely isotropic medium with a vertical symmetry axis (VTI). Reflection and transmission (R/T) responses quantify wave amplitude variations in 1-D media and help to reveal the model property enclosing the heterogeneity. Conventionally, the R/T responses are analysed for an interface bounded by two half-spaces. However, for a plane wave travelling through a subsurface layer, the wave scattering effects at the top and bottom of the layer interact with each other. For a continuous infinite ORT space cut in two halves along the horizontal symmetry plane, we focus on the plane wave R/T responses from an ORT layer that is placed between the two halves, where the azimuths of the vertical symmetry plane in the layer and in the upper and lower half-spaces are identical. The R/T coefficient modelling method can be found in many publications for the ORT layer with an arbitrary finite thickness. We decompose the exact R/T coefficients into series expansions that correspond to different orders of intrabed multiples in the ORT layer. Under the weak-contrast assumption for the ORT half-spaces and the ORT layer, we use the anisotropic background medium to obtain the first-order R/T coefficient approximations and second-order reflectivity approximations. There is no constraint for the middle layer thickness in the obtained first-order reflectivity approximations. In the proposed first-order transmissivity approximations and second-order reflectivity approximations, the layer thickness is assumed to be thin to obtain appropriate approximations for a few wave modes. The isotropic background medium is also considered for weakly anisotropic models to obtain simpler approximations that facilitate parametric analyses. For the ORT layer with its thickness much smaller than the propagating wave's wavelength, the influences of the layer thickness on R/T coefficients can be inspected conveniently from the derived approximations. Particularly, the R/T coefficients are analysed for the model which would be a homogeneous VTI medium, if the vertical parallel fractures were absent from the middle layer. Numerical tests demonstrate that the proposed R/T coefficient approximations perform well for the thin ORT layer. The approximation accuracy decreases when the thin layer thickness increases.

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