On a local energy decay estimate of solutions to the hyperbolic type Stokes equations

In this paper, we discuss a local energy decay estimate of solutions to the initial-boundary value problem for the hyperbolic type Stokes equations of incompressible fluid flow in an exterior domain and a perturbed half-space. The equations are linearized version of the hyperbolic Navier–Stokes equations introduced by Racke and Saal [15], which are obtained as a delayed case for the deformation tensor in the incompressible Navier–Stokes equations. Our proof of the local energy decay estimate is based on Dan and Shibata [2]. In [2], they treated the dissipative wave equations in an exterior domain and discussed the local energy decay estimate. Our approach uses the fact that applying the Helmholtz projection to the hyperbolic type Stokes equations, we obtain equations similar to the dissipative wave ones.     

Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder

Analytical study for electromagnetothermoelastic behaviors of a hollow cylinder composed of functionally graded piezoelectric material (FGPM), placed in a uniform magnetic field, subjected to electric, thermal and mechanical loads are presented. For the case that the electric, magnetic, thermal and mechanical properties of the material obey an identical power law in the radial direction, exact solutions for electric displacement, stresses, electric potential and perturbation of magnetic field vector in the FGPM hollow cylinder are determined by using the infinitesimal theory of electromagnetothermoelasticity. Some useful discussions and numerical examples are presented to show the significant influence of material inhomogeneity, and adopting a certain value of the inhomogeneity parameter β and applying suitable electric, thermal and mechanical loads can optimize the FGPM hollow cylindrical structures. This will be of particular importance in modern engineering design.     

Basic solution of four parallel non-symmetric permeable Mode-III cracks in a piezoelectric/piezomagnetic composite plane

The interaction of four parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic composite plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through a Fourier transform into four pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relationships among the electric displacement, magnetic flux and stress fields near the crack tips were obtained. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding effect is present in piezoelectric/piezomagnetic composites.     

Electroelastic behaviour of an annular interfacial crack between dissimilar piezoelectric layers

An annular interfacial crack between dissimilar piezoelectric layers subjected to electroelastic loadings was investigated under an electrically impermeable boundary condition on the crack surface by using the Hankel transform technique and the Cauchy singular integral equation method. The stress intensity factors and energy release rates were determined. Numerical results reveal the effects of crack configuration, electric loads and material parameters on crack propagation and growth. The results should be useful for the design of piezoelectric composite structures and devices of high performance.     

Low-temperature elastic constants and piezoelectric coefficients of langasite (La3Ga5SiO14)

A complete set of elastic constants C _ij and piezoelectric coefficients e _ij of a La₃Ga₅SiO₁₄ (langasite) single crystal was determined from 5.5 to 275.5?K by resonant ultrasound spectroscopy. Unlike a conventional crystal, the elastic constants C _ij of the langasite crystal showed three types of temperature dependence: (i) monotonic elastic stiffening upon cooling (C ₄₄ and C ₁₄); (ii) monotonic elastic softening (C ₆₆); and (iii) a stiffening-to-softening transition below 150?K (C ₁₁, C ₁₂, C ₁₃ and C ₃₃). In addition, a strong correlation between C ₆₆ and the piezoelectric coefficient e ₁₁ was confirmed. Group theoretical lattice dynamics analysis revealed that the novel phenomena of elastic softening and strong correlation are explained on the basis of two types of optical mode internal displacements which have the totally symmetric A ₁ and doubly degenerated E symmetries in the point group D ₃.     

Synthesis and physical properties of Ca- and Ta-modified (K,Na)NbO3 lead-free piezoelectric ceramics

Polycrystalline samples of lead-free Ca and Ta co-substituted potassium sodium niobate (K_0.5Na_0.5NbO_3, KNN) ceramics have been prepared by solid state reaction technique. X-ray diffraction showed formation of a single-phase perovskite structure with orthorhombic symmetry. Substitution inhibits the grain growth, improves densification and decreases the ferro-paraelectric phase transition temperature. Temperature dependent dielectric permittivity studies demonstrate significant decrease in peak-permittivity values in the substituted samples. Bulk longitudinal piezoelectric coefficient is significantly enhanced, up to ～155 pC/N for (K_0.48Na_0.48Ca_0.02)(Nb_0.85Ta_0.15O₃) as compared to 95 pC/N for pristine KNN ceramic. Local piezoelectric properties have been observed by piezoresponse force microscopy (PFM) technique. Distinct piezocontrast was studied in both vertical and in-plane modes of PFM for all samples. The samples exhibit self-polarization effect in the unpoled state and effective local vertical piezoelectric coefficient was the largest in Ca and Ta co-substituted sample whereas the in-plane piezoelectric coefficient was maximum for Ca-substituted KNN sample. These studies are important for using substituted lead free KNN materials in various piezoelectric applications.     

Crystal growth,crystal structure and physical properties of polar orthorhombic tris(glycine) zinc chloride

Large single crystals of the polar (point group mm 2) compound tris(glycine) zinc chloride, (NH₃CH₂COO)₃ · ZnCl₂, were grown from aqueous solutions. The refractive indices were measured in the wavelength region from 365 nm to 1083 nm and an unpolarised absorption spectrum was recorded (transparency range from 260 to 1550nm). The phase matching conditions for second harmonic generation were analysed: both, type I (ss‐f) and type II (sf‐f) are possible in the red and near IR region. All five components of the piezoelectric tensor [d_ijk ] were determined; the maximum values of longitudinal and transverse piezoelectric effects are less than one half of d₁₁₁ of α‐quartz. In addition, a redetermination of the crystal structure (including location of H atoms) is presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electric‐field‐induced internal deformation in piezoelectric BiB3O6 crystals

For the first time electric‐field‐induced atomic displacements (internal strains) in non‐ferroelectric polar BiB₃O₆ single crystal plates (point symmetry 2) were investigated using X‐ray diffraction technique. The intensity variations of selected Bragg reflections were collected for three different orientations of the applied external electric field vector with respect to the crystal lattice and used for calculating the microscopic structural response of BiB₃O₆. Due to the limited number of the reflections providing measurable changes in Bragg intensities we restricted ourselves in analyzing the shift of the B₃O₆ sublattice relative to the Bi one. In addition, we considered the deformation of the Bi‐O, B(1)‐O and B(2)‐O bond lengths and identified the [B(2)O₃] group as the most sensitive structural unit to an external electric perturbation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effective permittivity of materials containing graded ellipsoidal inclusions

We prove a generic theorem stating the equivalence between a graded dielectric ellipsoid (with gradation along a family of internal confocal ellipsoids) and an anisotropic homogeneous ellipsoid. We then describe a procedure to obtain the three principal permittivities of the effective ellipsoid for any given dielectric gradation profile. Finally, we apply a multiscale approach to homogenize dispersions of ellipsoidal graded particles.     

The transient suppression for piezoelectric ceramic emission transducer

A transient suppression method for piezoelectric ceramic transducer is presented. By adding some special pedestal pulses to the original transmitted signal, the transient effects in the output of the transducer can be just precisely transmission by use of a narrowband transducer. canceled, thereby achieving the broadband The experimental results show that the transient responses of the sinusoid pulses and coded signals are suppressed successfully and the acoustic waveforms radiated into the surrounding water are improved significantly.