Vibroacoustic Comparisons and Acoustic Power Insulation Mechanisms of Multidirectional Stiffened Laminated Plates

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Xiongtao Cao ◽  
Hongxing Hua
Keyword(s):  
Fourier Transform ◽  
High Efficiency ◽  
Three Dimensional ◽  
Acoustic Power ◽  
Higher Order ◽  
Laminated Plates ◽  
Transverse Displacement ◽  
Third Order ◽  
First Order ◽  
Implicit Equations

Vibroacoustic characteristics of multidirectional stiffened laminated plates with or without compliant layers are explored in the wavenumber and spatial domains with the help of the two-dimensional continuous Fourier transform and discrete inverse fast Fourier transform. Implicit equations of motion for the arbitrary angle ply laminated plates are derived from the three-dimensional higher order and Reddy third order shear deformation plate theories. The expressions of acoustic power of the stiffened laminated plates with or without complaint layers are formulated in the wavenumber domain, which is a significant method to calculate acoustic power of the stiffened plates with multiple sets of cross stiffeners. Vibroacoustic comparisons of the stiffened laminated plates are made in terms of the transverse displacement spectra, forced responses, acoustic power, and input power according to the first order, Reddy third order, and three-dimensional higher order plate theories. Sound reduction profiles of compliant layers are further examined by the theoretical deductions. This study shows the feasibility and high efficiency of the first order and Reddy third order plate theories in the broad frequency range and allows a better understanding the principal mechanisms of acoustic power radiated from multidirectional stiffened laminated composite plates with compliant layers, which has not been adequately addressed in its companion paper. (Cao and Hua, 2012, “Sound Radiation From Shear Deformable Stiffened Laminated Plates With Multiple Compliant Layers,” ASME J. Vib. Acoust., 134(5), p. 051001.)

Enhanced First-Order Shear Deformation Theory for Laminated and Sandwich Plates

2005 ◽  
Vol 72 (6) ◽  
pp. 809-817 ◽  
Author(s):  
Jun-Sik Kim ◽  
Maenghyo Cho
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Sandwich Plates ◽  
First Order ◽  
Transverse Shear Strains

A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

Square-root-like higher-order topological states in three-dimensional sonic crystals

2021 ◽  
Author(s):  
Zhiguo Geng ◽  
Huanzhao Lv ◽  
Zhan Xiong ◽  
Yu-Gui Peng ◽  
Zhaojiang Chen ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Surface States ◽  
Higher Order ◽  
Square Root ◽  
Root Lattice ◽  
Third Order ◽  
Topological Materials ◽  
Topological States ◽  
Sonic Crystal ◽  
Sonic Crystals

Abstract The square-root descendants of higher-order topological insulators were proposed recently, whose topological property is inherited from the squared Hamiltonian. Here we present a three-dimensional (3D) square-root-like sonic crystal by stacking the 2D square-root lattice in the normal (z) direction. With the nontrivial intralayer couplings, the opened degeneracy at the K-H direction induces the emergence of multiple acoustic localized modes, i.e., the extended 2D surface states and 1D hinge states, which originate from the square-root nature of the system. The square-root-like higher order topological states can be tunable and designed by optionally removing the cavities at the boundaries. We further propose a third-order topological corner state in the 3D sonic crystal by introducing the staggered interlayer couplings on each square-root layer, which leads to a nontrivial bulk polarization in the z direction. Our work sheds light on the high-dimensional square-root topological materials, and have the potentials in designing advanced functional devices with sound trapping and acoustic sensing.

Effect of Dissipative Terms on the Quality of Two and Three-Dimensional Euler Flow Solutions

2008 ◽  
Author(s):  
Seyed Saied Bahrainian
Keyword(s):  
Euler Equations ◽  
Hyperbolic Conservation Laws ◽  
Three Dimensional ◽  
Strong Shock ◽  
Computational Domain ◽  
Third Order ◽  
First Order ◽  
Proper Values ◽  
Dissipative Terms

The Euler equations are a set of non-dissipative hyperbolic conservation laws that can become unstable near regions of severe pressure variation. To prevent oscillations near shockwaves, these equations require artificial dissipation terms to be added to the discretized equations. A combination of first-order and third-order dissipative terms control the stability of the flow solutions. The assigned magnitude of these dissipative terms can have a direct effect on the quality of the flow solution. To examine these effects, subsonic and transonic solutions of the Euler equations for a flow passed a circular cylinder has been investigated. Triangular and tetrahedral unstructured grids were employed to discretize the computational domain. Unsteady Euler equations are then marched through time to reach a steady solution using a modified Runge-Kutta scheme. Optimal values of the dissipative terms were investigated for several flow conditions. For example, at a free stream Mach number of 0.45 strong shock waves were captured on the cylinder by using values of 0.25 and 0.0039 for the first-order and third-order dissipative terms. In addition to the shock capturing effect, it has been shown that smooth pressure coefficients can be obtained with the proper values for the dissipative terms.

On Some Physical Properties of a Unified Lepton-Hadron Field Model with Composte Bosons

1982 ◽  
Vol 37 (11) ◽  
pp. 1295-1300 ◽  
Author(s):  
H. Stumpf
Keyword(s):  
Physical Properties ◽  
Permutation Group ◽  
Field Model ◽  
Higher Order ◽  
Lepton Number ◽  
Third Order ◽  
First Order ◽  
Unified Field ◽  
Intrinsic Parity ◽  
Pseudo Color

In preceding papers a lepton-hadron unified field model was introduced by means of a third order nonlinear spinorfield equation. In this paper an improved interpretation to this model is given which tries to incorporate the advantages of various current matter models and to avoid their drawbacks. In particular charge and lepton number are introduced, while the extended unstable baryon states are distinguished from lepton states by an intrinsic parity. A theorem is derived which allows a biunique decomposition of the nonlinear higher order spinorfield equation into nonlinear first order spinorfield equations and the simultaneous introduction of a permutation group of the subfields. These subfields are identified as pseudo-color fields.

scholarly journals Mathematical model of falling of a viscous jet onto a moving surface

2007 ◽  
Vol 18 (6) ◽  
pp. 659-677 ◽  
Author(s):  
A. HLOD ◽  
A. C. T. AARTS ◽  
A. A. F. van de VEN ◽  
M. A. PELETIER
Keyword(s):  
Three Dimensional ◽  
Integral Condition ◽  
Stationary Flow ◽  
Third Order ◽  
Convex Shape ◽  
Dimensional Parameter ◽  
Moving Surface ◽  
First Order ◽  
Existence Region ◽  
Unknown Length

The stationary flow of a jet of a Newtonian fluid that is drawn by gravity onto a moving surface is analyzed. It is assumed that the jet has a convex shape and hits the moving surface tangentially. The flow is modelled by a third-order ODE on a domain of unknown length and with an additional integral condition. By solving part of the equation explicitly, the problem is reformulated as a first-order ODE with an integral constraint. The corresponding existence region in the three-dimensional parameter space is characterized in terms of an easily calculable quantity. In a qualitative sense, the results from the model are found to correspond with experimental observations.

The formation of O2(a1Δg) in homogeneous and heterogeneous atom recombination

1986 ◽  
Vol 64 (12) ◽  
pp. 1614-1620 ◽  
Author(s):  
A. A. Ali ◽  
E. A. Ogryzlo ◽  
Y. Q. Shen ◽  
P. T. Wassell
Keyword(s):  
Kinetic Study ◽  
Gas Phase ◽  
Molecular Oxygen ◽  
Rate Constant ◽  
Room Temperature ◽  
High Efficiency ◽  
Flow System ◽  
Order Reaction ◽  
Third Order ◽  
First Order

The recombination of oxygen atoms has been studied in a discharge flow system at room temperature. The yield of O2(a1Δg) in the recombination on Pyrex has been found to be 0.08 (±0.02). In the gas phase, O2(a) was found to be formed in a process that is second order in [O] and first order in [N2]. The rate constant for this third-order reaction was found to be 3.4 (±0.4) × 10−34 cm6∙molecule−2∙s−1, representing a yield of 0.07 (±0.02). In the presence of molecular oxygen, the rate of production of O2(a) was found to increase. A kinetic study of this effect led to the conclusion that collisions of molecular oxygen with an unidentified precursor can produce O2(a) with high efficiency.

scholarly journals On conditions of solvability of three-dimensional integralsystem in quadratures

2017 ◽  
Vol 21 (10) ◽  
pp. 40-46
Author(s):  
E.A. Sozontova
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Original System ◽  
Goursat Problem ◽  
System Of Differential Equations ◽  
Third Order ◽  
First Order ◽  
Three Dimensional Space

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

Higher-order schemes for 3D first-arrival traveltimes and amplitudes

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. T47-T56 ◽  
Author(s):  
Songting Luo ◽  
Jianliang Qian ◽  
Hongkai Zhao
Keyword(s):  
Point Source ◽  
Helmholtz Equation ◽  
Higher Order ◽  
Two Dimensional ◽  
Order Convergence ◽  
Third Order ◽  
First Order ◽  
First Arrival ◽  
Function Smooth ◽  
Good Agreement

In the geometrical-optics approximation for the Helmholtz equation with a point source, traveltimes and amplitudes have upwind singularities at the point source. Hence, both first-order and higher-order finite-difference solvers exhibit formally at most first-order convergence and relatively large errors. Such singularities can be factored out by factorizing traveltimes and amplitudes, where one factor is specified to capture the corresponding source singularity and the other factor is an unknown function smooth near the source. The resulting underlying unknown functions satisfy factored eikonal and transport equations, respectively. A third-order Lax-Friedrichs scheme is designed to compute the underlying functions. Thus, highly accurate first-arrival traveltimes and reliable amplitudes can be computed. Furthermore, asymptotic wavefields are constructed using computed traveltimes and amplitudes in the WKBJ form. Two-dimensional and 3D examples demonstrate the performance of the proposed algorithms, and the constructed WKBJ Green’s functions are in good agreement with direct solutions of the Helmholtz equation before caustics occur.

scholarly journals GENERATION OF HIGHER ORDER NONCLASSICAL STATES VIA AN INTENSE ELECTROMAGNETIC FIELD

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1421-1427 ◽  
Author(s):  
ANIRBAN PATHAK
Keyword(s):  
Anharmonic Oscillator ◽  
Higher Order ◽  
Intense Laser ◽  
Squeezed State ◽  
Order Operator ◽  
Nonclassical States ◽  
Third Order ◽  
Operator Solution ◽  
First Order ◽  
Model Hamiltonian

Interaction of intense laser beam with an inversion symmetric third order nonlinear medium is modeled as a quartic anharmonic oscillator. A first order operator solution of the model Hamiltonian is used to study the possibilities of generation of higher order nonclassical states. It is found that the higher order squeezed and higher order antibunched states can be produced by this interaction. It is also shown that the higher order nonclassical states may appear separately, i.e. a higher order antibunched state is not essentially higher order squeezed state and vice versa.

Improved Data Processing by Application of Brault's Method to Ultra-Rapid-Scan FT-IR Spectrometry

2002 ◽  
Vol 56 (10) ◽  
pp. 1281-1288 ◽  
Author(s):  
Husheng Yang ◽  
Peter R. Griffiths ◽  
Christopher J. Manning
Keyword(s):  
Fourier Transform ◽  
Data Processing ◽  
Processing Time ◽  
Phase Relationship ◽  
Fourier Transform Infrared ◽  
Order Correction ◽  
Infrared Spectrometry ◽  
Third Order ◽  
First Order ◽  
First Order Correction

In Fourier transform infrared spectrometry, the use of analog-to-digital converters clocked at a constant rate leads to interferograms the data points of which are evenly spaced in time. An interpolation step is generally required to resample these data to equal intervals of retardation. Three methods of resampling the data were compared: Fourier interpolation (i.e., zero-filling), cubic interpolation, and digital filter interpolation as described by Brault. These approaches were investigated using both simulated data and interferograms acquired from an ultra-rapid scanning Fourier transform infrared spectrometer. In both cases, the optical path difference varied sinusoidally with time and interferograms were sampled at equal time intervals. It was shown that the data processing time can be reduced significantly, relative to previous methods, through the application of Brault's method, which can be considered as three separate steps involving a first-, second-, and third-order correction. If only the first-order correction for the local phase relationship between the sampling grids is applied, the noise level of resulting spectra is similar to that obtained by cubic fitting, but the data processing time is reduced significantly. If the second-order correction for the variation of velocity is also used, the data processing time is approximately the same as the first-order correction, while the signal-to-noise ratio of the spectra is increased significantly. The implementation of the third-order correction for channel delay mismatch appears to be unnecessary for this instrument because the detector channel delays are small.

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