Wave Motion Localization Effects in Elastic Waveguides

Dynamic effects characteristic of elastic bodies and associated with local disturbances in finite elastic bodies and inhomogeneous waveguides are analyzed and systematized. The physical causes of such disturbances are analyzed. It is shown that these disturbances are due to energy transfer from longitudinal to transverse waves and back, when they are reflected from the free surface of an elastic body __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 38–45, September 2005.     

Influence of Prestresses on Quasi-Lamb Modes in Hydroelastic Waveguides

International Applied Mechanics - The propagation of quasi-Lamb waves in a prestrained compressible elastic layer that interacts with a half-space of a compressible ideal fluid and in a prestrained...     

Propagation of Harmonic Waves in Anisotropic Piezoelectric Cylinders. Compound Waveguides

Waves in anisotropic homogeneous and piecewise-homogeneous piezoelectric cylinders are investigated for various types of anisotropy, boundary conditions, and interaction with the ambient acoustic medium and electromagnetic field     

Propagation of Harmonic Waves in Anisotropic Piezoelectric Cylinders. Homogeneous Piezoceramic Waveguides

The dispersive propagation of axisymmetric and nonaxisymmetric waves in piezoceramic homogeneous cylinders is studied for various prepolarization directions.     

Propagation,Dispersion, and Localization of Elastic Waves in Low-Symmetric Anisotropic Waveguides

The results of a theoretical investigation into ultrasonic linear normal wavefields in anisotropic three-dimensional bodies with mechanical orthorhombic symmetry are presented. A detailed study is made of the dispersion dependencies for higher normal wave modes in a single-layered orthorhombic plate-type waveguide. Moreover, the distribution of complex branches corresponding to the edge standing wave modes is studied and their role in the transformation of the entire spectrum upon a change in the travel direction in the waveguide plane is analyzed. A new type of localization of the higher modes of high-frequency short-range normal waves in a crystal layer is described. An efficient method is developed for studying the spectrum of ultrasonic normal waves in a circular cylindrical waveguide made of an orthorhombic monocrystal     

Elastic Buckling with Infinitely Many Local Modes

ABSTRACT

ABSTRACT In some cases, asymptotic methods present an appealing alternative to full nonlinear analyses. In other cases, the value of an asymptotic analysis may merely be that, in a qualitative way, it can characterize the behavior of a structure. Whether an asymptotic method is applied for one or the other purpose it is of interest to attempt an estimation of its range of validity. The present paper addresses this question for an asymptotic method to predict imperfection sensitivity of elastic structures with mode interaction. The particular structure that is investigated possesses an infinity of nearly simultaneous local buckling modes. It is found that very few of these modes need to be taken into account.     

Love Waves in a Piezoelectric Semiconductor Thin Film on an Elastic Dielectric Half-Space

In this paper,Love waves propagating in a piezoelectric semiconductor(PSC)layered structure are investigated,where a PSC thin film is perfectly bonded on an elastic dielectric half-space.The dispersion equations are derived analytically.The influence of semiconducting properties on the propagation characteristics is examined in detail.Numerical results show that the semiconducting effect reduces the propagation speed,and that the Love waves can propagate with a speed slightly higher than the shear wave speed of the elastic dielectric half-space.The wave speed and attenuation significantly depend on the steady-state carrier density and the thickness of the PSC thin film.It is also found that when the horizontal biasing electric field is larger than the critical value(corresponding to the zero attenuation),the wave amplitude is increased.These findings are useful for the analysis and design of various surface wave devices made of PSC.     

Dynamic Analysis of a Composite Hollow Sphere Composed of Elastic and Piezoelectric Layers

Dynamic analysis of a two-layered elasto-piezoelectric composite hollow sphere under spherically symmetric deformation is developed. An unknown function of time is first introduced in terms of the charge equation of electrostatics and then the governing equations of piezoelectric layer, in which the unknown function of time is involved, are derived. By the method of superposition, the dynamic solution for elastic and piezoelectric layers is divided into quasi-static and dynamic parts. The quasi-static part is treated independently by the state space method and the dynamic part is obtained by the separation of variables method. By virtue of the obtained quasi-static and dynamic parts, a Volterra integral equation of the second kind with respect to the unknown function of time is derived by using the electric boundary conditions for piezoelectric layer. Interpolation method is employed to solve the integral equation efficiently. The transient responses for elastic and electric fields are finally determined. Numerical results are presented and discussed.     

Normal Modes and Nonlinear Stability Behaviour of Dynamic Phase Boundaries in Elastic Materials

This paper considers an ideal nonthermal elastic medium described by a stored-energy function W. It studies time-dependent configurations with subsonically moving phase boundaries across which, in addition to the jump relations (of Rankine–Hugoniot type) expressing conservation, some kinetic rule g acts as a two-sided boundary condition. The paper establishes a concise version of a normal-modes determinant that characterizes the local-in-time linear and nonlinear (in)stability of such patterns. Specific attention is given to the case where W has two local minimizers U ^A ,U ^B which can coexist via a static planar phase boundary. Being dynamic perturbations of such interesting configurations, this paper shows that the stability behaviour of corresponding almost-static phase boundaries is uniformly controlled by an explicit expression that can be determined from derivatives of W and g at U ^A and U ^B .     

压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题

分析了压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题。利用傅立叶变换,使问题的求解转换为对一对以裂纹表面上的位移差为未知变量的对偶积分方程的求解。为了求解对偶积分方程,把裂纹面上的位移差展开为雅可比多项式形式,进而得到了裂纹长度、入射波波速及入射波频率对裂纹应力强度因子的影响。从数值结果可以看出,压电压磁复合材料中可导通裂纹的反平面问题的动应力奇异性与一般弹性材料中的反平面断裂问题动应力奇异性相同。     

Trapped modes in coastal waveguides

Postnova and Craster (Wave Motion, 45, 2008, pp. 565-579) describe a method for determining the frequency of trapped modes in slowly-varying elastic plates, and ocean and quantum waveguides. The purpose of the present note is to show that the accuracy of the frequency estimates for ocean waveguides can be significantly increased by taking into account the fact that, as posed, the ocean waveguide problem is not self-adjoint. For an example where the asymptotic problem has an exact solution, comparison with a numerical solution of the full problem shows that the correction to the asymptotically determined frequency is of order the fourth power of the ratio of the shelf width to the scale for longshore variations in the shelf. An explicit simple formula is also given for the trapped mode frequency of an arbitrarily, but extremely weakly and positively, curving coast.     

Trapped modes in bent elastic rods

We investigate the existence of trapped modes in elastic rods of constant circular cross-section that possess bends of arbitrary curvature and straighten out at infinity; such trapped modes consist of finite energy localized in regions of maximal curvature. An asymptotic model assuming smallness of dimensionless curvature is developed to describe the trapping. Existence conditions depending on Poisson’s ratio are offered, and the equations from which they derive are numerically validated. A physical explanation of why trapped modes should be expected is also given.     

Solitary Elastic Waves and Elastic Wavelets

A new group of wavelets that have the form of solitary waves and are the solutions of the wave equations for dispersive media is proposed to call elastic wavelets. That this group includes well-known Mexican-hat wavelets is proved. It is proposed to use elastic wavelets to study local features of the profile evolution of a solitary wave in an elastic dispersive medium     

A Hardy Inequality in Twisted Waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.     

Effect of the Boundary Conditions and Influence of the Rotational Inertia on the Vibrational Modes of an Elastic Ring

We present the small-amplitude vibrations of a circular elastic ring with periodic and clamped boundary conditions. We model the rod as an inextensible, isotropic, naturally straight Kirchhoff elastic rod and obtain the vibrational modes of the ring analytically for periodic boundary conditions and numerically for clamped boundary conditions. Of particular interest are the dependence of the vibrational modes on the torsional stress in the ring and the influence of the rotational inertia of the rod on the mode frequencies and amplitudes. In rescaling the Kirchhoff equations, we introduce a parameter inversely proportional to the aspect ratio of the rod. This parameter makes it possible to capture the influence of the rotational inertia of the rod. We find that the rotational inertia has a minor influence on the vibrational modes with the exception of a specific category of modes corresponding to high-frequency twisting deformations in the ring. Moreover, some of the vibrational modes over or undertwist the elastic rod depending on the imposed torsional stress in the ring.     

Analysis of a Circular Piezoelectric Semiconductor Embedded in a Piezoelectric Semiconductor Substrate

We analyze anti-plane electromechanical fields associated with a circular piezoelectric semiconductor of 6 mm symmetry embedded in a matrix of a different piezoelectric semiconductor. An exact solution is obtained. The solution shows the presence of field concentration near the interface. It is also found that the strain and electric fields inside the inclusion are not uniform.