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1.
Low-frequency onset of the fundamental branches in piezoplates is studied with a view to identify the impact of piezoelectric coupling. General analytical expressions for the zero- and leading-order terms of the velocity versus wavenumber expansion in an anisotropic homogeneous piezoplate are obtained. On this ground, it is shown what types of anisotropy and electric boundary conditions enable the onset parameters of fundamental branches to be piezoactive. Particular attention is given to the linear dispersion at the origin of two upper fundamental branches. This property is entirely caused by the piezoeffect, being ruled out for elastic plates. An invariant hierarchy is established between the zero-order velocities of the fundamental waves under different electric boundary conditions in homogeneous and functionally graded plates. It is shown that some of these velocities in a metallized plate become piezoactive specifically if the piezoplate is functionally graded. 相似文献
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《International Journal of Solids and Structures》2007,44(7-8):2192-2208
A modified Stroh-type formalism for edge waves in unsymmetrical anisotropic plates is derived. Explicit expressions of the fundamental matrices for the formalism are presented. The existence conditions for one or two subsonic edge waves in the unsymmetrical anisotropic plates are discussed based on the formalism, and a procedure for finding an explicit secular equation for the edge-wave speed is proposed. 相似文献
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Long-wavelength onset of the fundamental branches is described for a free anisotropic plate with arbitrary through-plate variation of material properties. Main attention is given to the flexural branch. Closed-form expressions for the leading-order dispersion coefficient of the velocity and displacement are derived for a generic case and exemplified for the various types of either continuous, or discrete, or periodic inhomogeneity and for the monoclinic symmetry. The relevance of the static averaging is examined in detail. The bounds for the slope of the flexural velocity branch are established. The upper fundamental branches are considered for the case when these are uncoupled inplane and shear horizontal ones. 相似文献
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In the present paper the theory of micropolar generalized thermoelastic continua has been employed to study the propagation
of plane waves in micropolar thermoelastic plates bordered with inviscid liquid layers (or half-spaces) with varying temperature
on both sides. The secular equations in closed form and isolated mathematical conditions are derived and discussed. Thin plate
and short wave length results have also been deduced under different cases and situations and discussed as special cases of
this work. The results in case of conventional coupled and uncoupled theories of thermoelasticity can be obtained both in
case of micropolar elastic and elastokinetics from the present analysis by appropriate choice of relevant parameters. The
various secular equations and relevant relations have been solved numerically by using functional iteration method in order
to illustrate the analytical developments. Effect of characteristic length and coupling factors have also been studied on
phase velocity. The computer simulated results in case of phase velocity, attenuation coefficient and specific loss of symmetric
and skew symmetric are presented graphically. 相似文献
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The sextic approach to plane waves in infinite (visco)elastic plates of arbitrary anisotropy and transverse inhomogeneity is outlined. A particular thrust is set on continuous inhomogeneity when the propagator is defined by the Peano expansion. Despite underlying explicit intricacy, the basic framework of the pursued formalism is little affected by a through-plate variation of material. To make it evident, the principal algebraic symmetry of the propagator for unattenuated waves and the ensuing arrangement of the impedance as a Hermitian matrix with specific traits are inferred directly from energy considerations. Staying the same as for homogeneous plates, those features yield useful developments in the broader context of inhomogeneity. The formalism may be expressed in either pair picked among velocity, frequency and wavenumber, but different choices of a dispersion variable are shown to entail analytical dissimilarities. In addition, the impact of the profile symmetry and of the horizontal plane of crystallographic symmetry is examined. The surface-impedance method and some other aspects of the numerical treatment are discussed. 相似文献
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Summary Propagation of flexural waves in circularly cylindrical bars of anisotropic material on the basis of the exact three-dimensional theory of elasticity of small deformations is considered, the rigor of the analysis being the same as the one of the Pochhammer-Chree theory. A system of the governing equations of motion for the cylindrical orthotropy (its axis coinciding with the axis of the bar) is derived and expressed in terms of radial, tangential and axial displacement components. For a steady-state sinusoidal flexural wave the system reduces to coupled ordinary second order differential equations with a regular singular point. Solution for a transversely isotropic is obtained by means of Frobenius series method. Upon using two or three terms of the series approximate dispersion relations for isotropic material as well as for the pyrolytic graphite type material and two other types of anisotropic materials are obtained and illustrated by graphs. Higher order modes than those already known are found.
Research supported by a grant of the National Science Foundation. 相似文献
Übersicht Die Fortpflanzung von Biegewellen in kreiszylindrischen Balken aus anisotropem Material wird auf der Grundlage der exakten dreidimensionalen Elastizitätstheorie kleiner Verformungen betrachtet. Die Strenge der hier gegebenen Untersuchungen entspricht der in der Theorie von Pochhammer-Chree. Das System der Bewegungsgleichungen wird für zylindrische Orthotropie, deren Achse mit der Balkenachse zusammenfällt, abgeleitet und durch die radialen, atngentialen und axialen Verschiebungskomponenten ausgedrückt. Das System reduziert sich im Fall einer stationären sinusförmigen Biegewelle auf gekoppelte, gewöhnliche Differentialgleichungen 2. Ordnung mit einem singulären Punkt. Lösungen für transversale Isotropie werden mit Hilfe der Reihenmethode von Frobenius abgeleitet. Unter Verwendung von zwei oder drei Gliedern dieser Reihen werden angenäherte Dispersionsbeziehungen sowohl für isotropes Material als auch für Material vom Typ pyrolytischen Graphits und für zwei andere Typen anisotropischer Materialien erhalten und graphisch dargestellt. Es werden Schwingungsformen gefunden, die von höherer Ordnung als die bisher bekannten sind.
Research supported by a grant of the National Science Foundation. 相似文献
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The ray-path method is used to analyze the stress-strain state near mine workings acted upon by discontinuous waves. A dynamic
failure criterion is proposed for analyzing the stability of mine workings. The efficiency of the approach is demonstrated
with a specific example
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 56–64, April 2008. 相似文献
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A. L. Shuvalov 《Wave Motion》2001,34(4):401-429
In the theory of plane inhomogeneous elastic waves, the complex wave vector constituted by two real vectors in a given plane may be described with the aid of two complex scalar parameters. Either of those parameters may be taken as a free one in the characteristic condition assigned to the wave equation. This alternative underlies the two fundamental approaches in the theory, namely, one associated with the Stroh eigenvalue problem and the other with the generalized Christoffel eigenvalue problem. The two approaches are identical insofar as a partial nondegenerate wave solution (partial mode) is concerned, but they differ in the fundamental solution (wave packet) assembling, and their dissimilarity is also revealed in the presence of degeneracies, which may involve either of the two governing parameters or both of them. Therefore, use of both approaches is essential for studying the degeneracy phenomenon in the theory of inhomogeneous waves. The criteria for different types of degeneracy, related to a double eigenvalue of the Stroh matrix or the Christoffel matrix and at the same time to a repeated root of the characteristic condition, are formulated by appeal to the matrix algebra and to the theory of polynomial equations. On this basis, dimensions of the manifolds, associated with degeneracy of different types in the space of variables, are established for elastic media of unrestricted anisotropy. The relation to the boundary-value problems is discussed. 相似文献
14.
We experimentally investigated nonlinear combination resonances in two graphite-epoxy cantilever plates having the configurations (90/30/-30/-30/30/90)s and (-75/75/75/-75/75/-75)s. As a first step, we compared the natural frequencies and modes shapes obtained from the finite-element and experimental-modal analyses. The largest difference in the obtained frequencies for both plates was 6%. Then, we transversely excited the plates and obtained force-response and frequency-response curves, which were used to characterize the plate dynamics. We acquired time-domain data for specific input conditions using an A/D card and used them to generate time traces, power spectra, pseudo-state portraits, and Poincaré maps. The data were obtained with an accelerometer monitoring the excitation and a laser vibrometer monitoring the plate response. We observed the external combination resonance % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfM6axjabgIKi7kabeM8a3naaBaaaleaacaaIYaaabeaakiab% gUcaRiabeM8a3naaBaaaleaacaaI3aaabeaaaaa!45C9!\[\Omega \approx \omega _2 + \omega _7 \] in the quasi-isotropic plate and the external combination resonance % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfM6axjabgIKi7kaacIcacaaIXaGaai4laiaaikdacaGGPaGa% aiikaiabeM8a3naaBaaaleaacaaIYaaabeaakiabgUcaRiabeM8a3n% aaBaaaleaacaaI1aaabeaakiaacMcaaaa!4AAD!\[\Omega \approx (1/2)(\omega _2 + \omega _5 )\] and the internal combination resonance % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfM6axjabgIKi7kabeM8a3naaBaaaleaacaaI4aaabeaakiab% gIKi7kaacIcacaaIXaGaai4laiaaikdacaGGPaGaaiikaiabeM8a3n% aaBaaaleaacaaIYaaabeaakiabgUcaRiabeM8a3naaBaaaleaacaaI% XaGaaG4maaqabaGccaGGPaaaaa!4FDC!\[\Omega \approx \omega _8 \approx (1/2)(\omega _2 + \omega _{13} )\] in the ±75 plate, where the % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabeM8a3naaBaaaleaacaWGPbaabeaaaaa!3F16!\[\omega _i \] are the natural frequencies of the plate and is the excitation frequency. The results show that a low-amplitude high-frequency excitation can produce a high-amplitude low-frequency motion. 相似文献
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鉴于常规超声检测技术对分布式材料细微损伤和接触类结构损伤的检测效果不佳,近年来非线性超声技术逐渐引起广泛关注.超声波在板壳结构中通常以兰姆波的形式进行传播,然而由于兰姆波的频散及多模特性,使得非线性兰姆波的理论和实验研究进展缓慢.本文从经典非线性理论出发,总结了源于材料固有非线性诱发的非线性兰姆波的理论和实验两个方面的研究进展,井综述了兰姆波的二次谐波发生效应在材料损伤评价方面的若干应用;从接触声非线性理论出发,讨论了目前由于接触类结构损伤诱发的非线性兰姆波的研究现状.最后展望了非线性兰姆波的未来研究重点及发展趋势. 相似文献
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A. Prechtl 《Wave Motion》1980,2(2):125-138
The propagation and interaction of transverse electro-magnetic disturbances in a half space of anisotropic non-dispersive dielectric and the associated reflection problem are discussed. For certain types of material symmetry, solutions are obtained in the nearly linear approximation. It is shown that an incident pulse produces a reflected disturbance during a time interval larger than the duration of the pulse. In the case of a sinusoidal incident signal the spectrum of the reflected wave contains non-harmonic frequencies. 相似文献
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Wave propagation in anisotropic dissipative bodies is considered through the form of inhomogeneous waves. The dissipativity of the body is characterized by a restriction of thermodynamic character on the viscoelastic tensor. As a consequence, the divergence of the usual (time-averaged) energy flux is proved to be negative. This in turn is shown to imply that the amplitude of the wave decays in the direction of the energy flux and the angle, subtended by the imaginary part of the wave vector and the energy flux, is acute. Moreover, the symmetry of the viscoelastic tensor and the positive definiteness of its real part imply that also the imaginary part of the wave vector subtends an acute angle with the energy flux. Such properties are shown to hold in both solids and fluids. Because of anisotropy, the angle subtended by the real and imaginary parts of the wave vector need not be acute, which means that the amplitude may increase in the direction of phase propagation. 相似文献
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Application of the plane theory of elasticity to planar crack or angular corner geometries leads to the concept of stress singularity and stress intensity factor, which are the cornerstone of contemporary fracture mechanics. However, the stress state near an actual crack tip or corner vertex is always three-dimensional, and the meaning of the results obtained within the plane theory of elasticity and their relation to the actual 3D problems is still not fully understood. In particular, it is not clear whether the same stress field as found from the well-known 2D solutions of the theory of elasticity do describe the corresponding stress components in a plate made of a sufficiently brittle material and subjected to in-plane loading, and what effect the plate thickness has. In the present study we adopt, so called, first order plate theory to attempt to answer these questions. New features of the elastic solutions obtained within this theory are discussed and compared with 2D analytical results and experimental studies as well as with 3D numerical simulations. 相似文献