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1.
One approach which is employed to solve dynamic point load problems in plates and laminates is to take integral transforms to reduce the governing equations to a system of ordinary differential equations with respect to the depth variable. The solution of this system leads to expressions for the transforms of the displacement and stress components at any level in the plate and the transient response at any location may then be recovered by inversion of the multiple transforms. The formal transform inversion involves a double infinite integral but by making a change of variable this may be replaced by an infinite integral associated with a line source and a finite integral with respect to the orientation of the line. A first attempt at applying this approach to obtain the point load response of quasi-isotropic fibre composite laminate led to a non-causal predicted signal. This paper deals with an investigation of this proposed method applied to the simpler model problem of wave propagation in a two-dimensional anisotropic medium. Results are obtained for two different time histories of point loads, namely: a delta function; and a single period of a sine function. In the case of the delta function source a comparison is made with the analytic solution and the errors arising from the numerical approach are discussed. Graphs are also presented showing the non-causal contributions to the overall response which arise at individual angles of orientation of the line source. 相似文献
2.
J. N. Sharma N. K. Sharma & K. K. Sharma 《advances in applied mathematics and mechanics.》2011,3(1):87-108
This paper deals with the study of transient waves in a homogeneous isotropic,
solid half-space with a permeating substance in the context of the theory of
generalized elasto-thermodiffusion. The half-space is assumed to be disturbed
due to mechanical loads acting on its boundary. The model comprising of basic
governing differential equations and boundary conditions has been solved by
employing Laplace transform technique. Noting that the second sound effects are
short lived, the small time approximations of solution for various physical
quantities have been obtained and the results are discussed on the possible
wave fronts. In case of continuous and periodic loads acting at the boundary,
the displacement is found to be continuous at each wave front while it is discontinuous
in case of impulsive load. The temperature and concentration fields are found to be
discontinuous at all the wave fronts. The displacement, temperature change and concentration
deviation due to impulsive, continuous and periodic mechanical loads have also been evaluated
in the physical domain at all times by employing numerical inversion technique of integral
transform. The computer simulated numerical results have been presented graphically in respect
of displacement, temperature change and concentration deviation for brass. A significant effect
of mass diffusion has been observed on the behaviour of mechanical and thermal waves. 相似文献
3.
In this article, the propagation of guided thermoelastic waves in the circumferential direction of orthotropic cylindrical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The convergency of the method is discussed through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic cylindrical plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement, temperature and stress distributions are shown to discuss the differences between the elastic modes and thermal modes. A thermoelastic cylindrical plate with a different ratio of radius to thickness is considered to discuss the influence of the ratio on the characteristics of circumferential thermoelastic waves. 相似文献
4.
《Journal of sound and vibration》1986,106(3):481-489
This paper is a study of the dynamic response of an infinitely long thick strip plate subjected to an impulsive load. The plate is simply supported along the edges and resting on an elastic foundation. The problem is studied on the basis of a plate theory in which the effects of rotatory inertias and shear deformations are retained. Governing equations are solved by applying the methods of the Laplace transform with respect to time and the Fourier transform with respect to a longitudinal space variable. Dynamic coefficients (maximum dynamic displacement/static displacement, maximum dynamic bending moment/static bending moment) are calculated numerically for plates subjected to a step line load and shown graphically for various values of the parameters included. 相似文献
5.
The collinear interaction of optical waveguide modes is considered in a thin semiconductor layer containing an optical inhomogeneity (space-charge wave) growing along the wave-propagation direction. Coupled-mode equations are solved for the case where interacting waves propagate in the same direction or in opposite directions. The mode conversion efficiency is shown to depend substantially on the space-charge wave amplification with allowance for the detuning from the phase matching condition. The incident and the oppositely propagating modes can be “degenerate,” in which case the modes have the same power over the entire disturbed region. 相似文献
6.
HU Wenxiang & QIAN Menglu Institute of Acoustics Tongji University Shanghai China Correspondence should be addressed to Hu Wenxiang 《中国科学G辑(英文版)》2004,47(2):199-207
In the 1920s, the solid-solid interface wave, Stoneley wave, was first studied by Stoneley. From the 1930s to 1940s, the fluid-solid interface waves, usually called Scholte wave or Scholte-Stoneley wave, were studied by Cagniard and Scholte respec-tively[1]. The Scholte wave corresponds to the real root of the fluid-solid interface secu-lar equation, which is usually called the Scholte equation, and the velocity of Scholte wave is only slightly lower than the longitudinal velocity of the f… 相似文献
7.
The effect of surface stress on the propagation of Lamb waves 总被引:1,自引:0,他引:1
A. Chakraborty 《Ultrasonics》2010,50(7):645-649
This work investigates the possibility of the propagation of Lamb waves in thin solid layers with external traction free surfaces, in the presence of surface elasticity, inertia and residual stress. It is demonstrated that such waves do exist and that their characteristics can be quite different from their classical counterparts. The governing equations with non-classical boundary conditions involving the bulk and surface stress are solved exactly in the frequency-wavenumber domain. This solution is utilized to compute the Lamb wave modes for different layer thicknesses. An efficient strategy to capture all the modes of Lamb waves within a given frequency window is outlined. It is shown that the effect of surface elasticity and inertia becomes significant with increasing frequency and decreasing layer thickness, where the number of modes participating within a given frequency window is more than that permitted by the classical theory. Further, it is observed that the nature of the Lamb wave modes (in terms of negative dispersion) in the presence of surface stress is similar to what predicted by the nonlocal theory and microstructure based continuum theory. 相似文献
8.
Yu. M. Aliev 《Bulletin of the Lebedev Physics Institute》2017,44(11):340-342
Quasi-static surface wave propagation in a plasma layer with anisotropic electron temperature is considered. The case is analyzed where the electron temperature in the direction normal to the plasma boundary is considered to be zero, while in the direction along the boundary, electrons are described by the Maxwellian velocity distribution. It is shown that the modes of such a layer are described by equations for bulk plasma waves with renormalization of the electron density affecting the surface wave dispersion and damping. 相似文献
9.
C. Devanathan 《Zeitschrift für Physik A Hadrons and Nuclei》1962,167(3):337-348
The plasma is taken to be composed of singly ionized molecules, free electrons and neutral molecules, each of the component being described by the hydromagnetic equations, modified to take into account the displacement current, existence of free charge in the medium, and the modified current equation without involving the scalar conductivity. The basic equations are linearized and only small amplitude waves are considered. In the absence of any external magnetic field, the transverse and longitudinal modes of oscillation separate out. In the transverse part a coupled plasma oscillation occurs which could be propagated only above a certain critical frequency and in the longitudinal part one extraordinary mode of propagation occurs having a forbidden range of frequencies. When there is an external applied magnetic field, ordinary and extraordinary waves are propagated along the direction of the magnetic field, whereas only ordinary waves are propagated transverse to the magnetic field. The critical frequencies above which these waves are propagated are evaluated and, the possible explanation of this medium like behaviour could be the implicit assumption of conductivity being not a scalar. 相似文献
10.
The method of wave function expansion is adopted to study the three dimensional scattering of a time-harmonic plane progressive sound field obliquely incident upon a multi-layered hollow cylinder with interlaminar bonding imperfection. For the generality of solution, each layer is assumed to be cylindrically orthotropic. An approximate laminate model in the context of the modal state equations with variable coefficients along with the classical T-matrix solution technique is set up for each layer to solve for the unknown modal scattering and transmission coefficients. A linear spring model is used to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the non-resonance (backgrounds) and resonance components. The solution is first used to investigate the effect of interlayer imperfection of an air-filled and water submerged bilaminate aluminium cylindrical shell on the resonances associated with various modes of wave propagation (i.e., symmetric/asymmetric Lamb waves, fluid-borne A-type waves, Rayleigh and Whispering Gallery waves) appearing in the backscattered spectrum, according to their polarization and state of stress. An illustrative numerical example is also given for a multi-layered (five-layered) cylindrical shell for which the stiffness of the adhesive interlayers is artificially varied. The sensitivity of resonance frequencies associated with higher mode numbers to the stiffness coefficients is demonstrated to be a good measure of the bonding strength. Limiting cases are considered and fair agreements with solutions available in the literature are established. 相似文献
11.
The effect of initial stress on the propagation behavior of SH waves in piezoelectric coupled plates
This study analytically investigates the propagation of shear waves (SH waves) in a coupled plate consisting of a piezoelectric layer and an elastic layer with initial stress. The piezoelectric material is polarized in z-axis direction and perfectly bonded to an elastic layer. The mechanical displacement and electrical potential function are derived for the piezoelectric coupled plates by solving the electromechanical field equations. The effects of the thickness ratio and the initial stress on the dispersion relations and the phase and group velocities are obtained for electrically open and mechanically free situations. The numerical examples are provided to illustrate graphically the variations of the phase and group velocities versus the wave number for the different layers comparatively. It is seen that the phase velocity of SH waves decreases with the increase of the magnitude of the initial compression stress, while it increases with the increase of the magnitude of the initial tensile stress. The initial stress has a great effect on the propagation of SH waves with the decrease of the thickness ratio. This research is theoretically useful for the design of surface acoustic wave (SAW) devices with high performance. 相似文献
12.
A new method of stability investigation is presented for solutions of nonlinear equations integrable with the help of the inverse scattering transform (IST). The stability problem for periodic nonlinear waves in weakly dispersive media is solved with respect to transverse perturbations. It is shown that for positive dispersion media one-dimensional waves are unstable, and for negative dispersion such waves are stable. 相似文献
13.
S. Asghar Tasawar Hayat 《International Journal of Infrared and Millimeter Waves》1999,20(7):1413-1424
An exact solution is developed for the problem of diffraction of an E-polarized and an H-polarized spherical waves by a slit in an impedance screen. This consideration is important in the sense that point sources are regarded as better substitutes for real sources than line sources/plane waves. The two independent problems are solved using the Fourier transform, the Wiener-Hopf technique and asymptotic approximations. 相似文献
14.
The shear-wave velocity profile can be obtained by the velocity of Rayleigh waves through the back-calculation based on dispersion
curves. However, the dispersion curves obtained in practical application are always discontinuous and correspond to different
mode branches due to mode jumping, especially in the presence of low-velocity layer. Mode misidentification may be encountered
in inversion based on these jumped dispersion curves. Mode analysis demonstrates that the mode jumping is caused by a different
surface displacement distribution with frequency for each mode. This indicates that the surface displacement distribution
of the modes should be taken into account for the case of a low-velocity layer. Shear-wave velocity profiles are inversed
based on the (possibly discontinuous) dispersion curves of fundamental and/or higher modes using a genetic algorithm (GA).
In addition to the dispersion characteristics, the surface displacement distribution is also taken into account for the case
of a low-velocity layer; as a result, mode misidentification is avoided.
Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp 811–824.
The text was submitted by the authors in English. 相似文献
15.
Hamidreza Mahmoodi Kordkheili Mahmood Hosseini 《Waves in Random and Complex Media》2018,28(4):760-783
By virtue of a new scalar potential function and Hankel integral transforms, the wave propagation analysis of a thermoelastic transversely isotropic half-space is presented under buried loading and heat flux. The governing equations of the problem are the differential equations of motion and the energy equation of the coupled thermoelasticity theory. Using a scalar potential function, these coupled equations have been uncoupled and a six-order partial differential equation governing the potential function is received. The displacements, temperature, and stress components are obtained in terms of this potential function in cylindrical coordinate system. Applying the Hankel integral transform to suppress the radial variable, the governing equation for potential function is reduced to a six-order ordinary differential equation with respect to z. Solving that equation, the potential function and therefore displacements, temperature, and stresses are derived in the Hankel transformed domain for two regions. Using inversion of Hankel transform, these functions can be obtained in the real domain. The integrals of inversion Hankel transform are calculated numerically via Mathematica software. Our numerical results for displacement and temperature are calculated for surface excitations and compared with the results reported in the literature and a very good agreement is achieved. 相似文献
16.
A nonlinear theory of propagating periodic and nonlinear solitary waves (like kinks and solitons) related to the motion of
defects in crystals and of specific periodic waves into which the former ones transform in the field of the compression stress
was developed. The role of intense tension stress leading to the heavy structural rearrangement of the crystal as a result
of the effect of the external stress on the interatomic potential barriers was taken into account as well. Crystals with a
complex lattice consisting of two sublattices were considered. Arbitrarily large displacements of sublattices were analyzed.
The nonlinear theory is based on an additional element of the translational symmetry typical for complex lattices but not
introduced earlier in solid-state physics. The variational equations of macroscopic and microscopic displacements turn out
to be a nonlinear generalization of the linear equations of acoustic and optical modes obtained by Carman, Born, and Huang
Kun. The microscopic displacement fields are described by the nonlinear sine-Gordon equation. In the one-dimensional case,
exact solutions of the nonlinear equations were found and their features were revealed. In the case of two-dimensional (2+1)
fields, new methods of the exact solutions of the sine-Gordon equation were developed. They describe the interaction of the
nonlinear waves with the structural inhomogeneities of solid state due to the external fields of stress and deformations. 相似文献
17.
Chen Guang Xu Bai Qiang Xu Gui Dong Xu 《Applied Physics A: Materials Science & Processing》2011,105(2):379-386
A model based on the theory of fluid–structure interaction is developed to simulate the laser thermoelastic generation and
propagation of Leaky Lamb waves at the water–aluminum interface. Each component of displacement, stress, and temperature are
derived in transform domain by the photothermoelastic transfer matrix method. The time domain solutions are obtained by numerically
inverting the transforms while the dispersion curves and attenuation curves for the leaky waves are also calculated. Then
the propagation characteristics of different modes are analyzed. The model establishes a quantitative relation between the
laser parameters, the material parameters, the corresponding waveforms, and the dispersion curves, which provides a useful
tool for the Leaky Lamb waves applied to nondestructive evaluation. 相似文献
18.
Influence of adhesive layer properties on laser-generated ultrasonic waves in thin bonded plates
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This paper studies quantitatively the generation of Lamb waves in thin bonded plates subjected to laser illumination, after considering the viscoelasticity of the adhesive layer. The displacements of such plates have been calculated in the frequency domain by using the finite element method, and the time domain response has been reconstructed by applying an inverse fast Fourier transform. Numerical results are presented showing the normal surface displacement for several configurations: a single aluminum plate, a three-layer bonded plate, and a two-layer plate. The characteristics of the laser-generated Lamb waves for each particular case have been investigated. In addition, the sensitivity of the transient responses to variations of material properties (elastic modulus, viscoelastic modulus, and thickness) of the adhesive layer has been studied in detail. 相似文献
19.
Evolutionary equations are derived and solved that describe the time dependence of the oscillation mode amplitudes on the
surface of a charged conducting liquid layer resting on a solid core. It is assumed that the layer experiences a multimode
initial deformation. The equations are solved asymptotically in the second order of smallness in the small dimensionless amplitude
of capillary oscillations on the surface of the layer. Mechanisms behind internal nonlinear resonance interaction between
the modes of the liquid layer oscillations and behind energy transfer between the modes both in degenerate and in secondary
combination resonances are investigated. It is found that in the degenerate resonance interaction between oscillation modes,
the energy may be transferred not only from lower to higher modes but also vice versa if the higher mode is excited at the
zero time. This conclusion is valid not only for a liquid layer on the surface of a solid core but also for a drop. 相似文献
20.
In this article, we consider the problem of a two-dimensional thermoelastic half-space in the context of generalized thermoelastic theory with one relaxation time. The surface of the half-space is taken to be traction free and thermally insulated. The solution of the considered physical quantity can be broken down in terms of normal modes. The nonhomogeneous basic equations have been written in the form of a vector-matrix differential equation, which is then solved by an eigenvalue approach. The exact analytical solution is adopted for the temperature, the components of displacement and stresses. The results obtained are presented graphically for the effect of laser pulse to display the phenomena physical meaning. The graphical results indicate that the thermal relaxation time has a great effect on the temperature, the components of displacement and the components of stress. 相似文献