An anti-plane propagating crack in a functionally graded piezoelectric strip bonded to a homogeneous piezoelectric strip

Summary A finite crack propagating at constant speed in a functionally graded piezoelectric strip (FGPS) bonded to a homogeneous piezoelectric strip is considered. It is assumed that the electroelastic material properties of the FGPS vary exponentially across the thickness of the strip, and that the bimaterial strip is under combined anti-plane mechanical shear and in-plane electrical loads. The analysis is conducted for the electrically unified crack boundary condition, which includes both the traditional permeable and the impermeable ones. By using the Fourier transform, the problem is reduced to the solution of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and the crack sliding displacement are presented to show the influences of the crack propagation speed, electric loads, FGPS gradation, crack length, electromechanical coupling coefficient, properties of the bonded homogeneous piezoelectric strip and crack location.     

Gyrotropic and piezoelectric coefficients and attenuation of elastic waves in BaTiO3

Using Landau theory of phase transition, expressions for gyrotropic coefficients and piezoelectric coefficients are obtained for barium titanate in the tetragonal phase. Both coefficients vanish at the ferroelectric phase transition temperature. The piezoelectric coefficients tallied with the literature values. The attenuation coefficients for elastic waves propagating along the principal directions in tetragonal, orthorhombic and rhombohedral phases are derived based on Landau theory. It is predicted that there will be slight amplification for both longitudinal and transverse modes in the rhombohedral phase at a temperature close to the rhombohedral phase transition temperature.     

含压电片梁的静变形控制

首先借助阶梯函数，建立了含有任意分布的用作执行器的压电片的梁挠曲轴线方程。然后利用该方程，进行了梁的静变形控制的研究。最后结合实例，用“遗传＋配点”法对压电片的位置和尺寸进行了优化。结果表明，本文建立的挠曲方程形式简洁，求解简单：“遗传＋配点”法优化效果明显。     

激光干涉法测压电陶瓷的压电常数d31

介绍迈克尔逊干涉仪原理在测微小位移中的应用。确定一种锆钛酸铅镧压电陶瓷的压电常数ｄ３１，得到了一种测ｄ３１的可行可靠的新方法。     

PROPAGATION OF SURFACE ACOUSTIC WAVES IN PRESTRESSED ANISOTROPIC LAYERED PIEZOELECTRIC STRUCTURES

The propagation of surface acoustic waves in layered piezoelectric structures withinitial stresses is investigated.The phase velocity equations are obtained for electrically free andshorted cases,respectively.Effects of the initial stresses on the phase velocity and the electrome-chanical coupling coefficient for the fundamental mode of the layered piezoelectric structures arediscussed.Numerical results for the c-axis oriented fihn of LiNbO_3 on a sapphire substrate aregiven.It is found that the fractional change in phase velocity is a linear function with the ini-tial stresses,and the electromechanical coupling factor increases with an increase of the absolutevalues of the compressive initial stresses.The results are useful for the design of surface acousticwave devices.     

Dynamic calibration of shock overpressure transducers

Piezoelectric transducers for dynamic overpressure measurements are commonly calibrated with static or quasistatic loads and the calibration is extrapolated to frequencies up to 30% of the resonant frequency of the piezoelectric crystal. Sinusoidal pressure generators are also used for dynamic calibration up to 500 Hz in the range of 3 MPa. This paper describes a method for dynamic calibration using transient overpressures, with rise time of 2 μsec and width 40 μsec, generated by exploding wires in air. The calibration is done in the range of 600 kPa.     

Dynamic behavior of two parallel symmetric permeable cracks in a piezoelectric strip

The dynamic behavior of two parallel symmetric cracks in a piezoelectric strip under harmonic anti-plane shear waves is studied using the Schmidt method for permeable crack surface conditions. The cracks are parallel to the edge of the strip. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the schmidt method. The results show that the stress and the electric displacement intensity factors depend on the geometry of the cracks, the frequency of incident waves, the distance between cracks and the thickness of the strip. It is also found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. Project supported by the Post Doctoral Science Foundation of Heilongjiang Province, the Natural Science Foundation of Heilongjiang Province, the National Science Foundation with the Excellent Young Investigator Award (No. 19725209) and the Scientific Research Foundation of Harbin Institute of Technology (HIT.2000.30).     

不同压电分流电路对声子晶体梁带隙的影响

通过在匀质基体梁上周期性对贴连有分流电路的压电片,可以形成一维声子晶体结构.不同分流电路将决定梁的带隙特性.电阻分流电路能够对梁的模态共振有一定的抑制作用,而且可以通过改变压电效应的强弱使Bragg带隙结构发生变化.LC分流电路会使梁产生局域共振带隙,其带隙是由压电片激励LC电路产生电磁振荡形成.引入电阻后会使LC电路的共振作用变弱,使得带隙衰减幅值变小,但可以扩宽带隙频率范围.     

The response of an elastic three-dimensional half-space to random correlated displacement perturbations on the boundary

The response of an elastic half-space to random excitations of displacements on the boundary under the condition of no shearing forces is studied. We analyze the white noise excitations and general random fluctuations of displacements prescribed on the boundary. We consider the case of partially ordered defects on the boundary whose positions are governed by an exponential-cosine-type correlation function. The analysis is based on a Poisson-type integral formula which we derive here for the case of zero shearing forces on the boundary. We obtain exact representations for the displacement correlation tensor and the Karhunen-Loève expansion for the solution of the Lamé equation itself, and analyze some features of the correlation structure of the displacements. The Monte Carlo technique developed can be applied to a wide class of differential equations with random boundary conditions.