Equations of motion for damped longitudinal,torsional and flexural oscillations of piezoelectric bars

The equations of motion for pure (mutually independent) longitudinal, torsional and flexural oscillations of very thin piezoelectric bars are derived systematically and in detail first in integral and then in differential form. During derivation attention is paid to the effect of external and internal damping and the method of exciting the individual oscillations is considered.     

Coupled flexural-longitudinal wave motion in a periodic beam

Periodic structure theory is used to study the interactions between flexural and longitudinal wave motion in a beam (representing a plate) to which offset spring-mounted masses (representing stiffeners) are attached at regular intervals. An equation for the propagation constants of the coupled waves is derived. The response of a semi-infinite periodic beam to a harmonic force or moment at the finite end is analyzed in terms of the characteristic free waves corresponding to these propagation constants. Computer results are presented which show how the propagation constants are affected by the coupling, and how the forced response varies with distance from the excitation point. The spring-mounted masses can provide very high attenuation of both longitudinal and flexural waves when no coupling is present, but when coupling is introduced the two waves combine to give very low (or zero) attenuation of the longitudinal wave. The influence of different damping levels on spatial attenuation is also studied.     

Cubic nonlinearity in shear wave beams with different polarizations

A coupled pair of nonlinear parabolic equations is derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic elastic medium. The equations account for both quadratic and cubic nonlinearity. The present paper investigates, analytically and numerically, effects of cubic nonlinearity in shear wave beams for several polarizations: linear, elliptical, circular, and azimuthal. Comparisons are made with effects of quadratic nonlinearity in compressional wave beams.     

三层固体复合媒质中Lamb波的传播

本文导出了任意厚度的三层固体复合媒质中Lamb波特征方程式,给出了相邻固体层之间重要的两种界面条件(刚性联接和滑移联接)时Lamb波色散曲线。我们也计算了不同界面状况时Lamb波两个最低阶模式(对称模式s₀和反对称模式a₀)所产生的质点位移沿厚度方向的分布。     

Lamb wave propagation in three-layered composites

I.IntroductionThepropagationpropcrticsofLambwavesinasinglep1atchavebceninvestigatedwide1ysincel93o's,butthestudyofLambwavcsin1aycredsolidcompositesisre1ative1ynew.WuandZhuana1yzedthepropagationofLambwavcsinaso1idp1ateboundedbytwo1iquid1ayerswithidentica1thickncss.['lOntheothcrhand,L1oydandRedwoodstudiednumerica11yLambwavesinacompositeconsistingofa1iquidintcrmediate1ayerandtwosolidplates.['lInour'l,lwederivedthecharacteristicequationforLambwavesintwo-layeredsolidpreviouspaper,compositeswit…     

残余应力的超声横纵波检测方法

基于声弹性原理,研究板材厚度方向、螺栓轴向方向(以下简称z轴方向)宏观残余应力分布的超声无损检测方法。针对被测构件厚度不均匀对应力检测精度的影响非常大、检测原理繁杂不适合工程应用、拉伸实验中拉伸形变对应力系数测量精度的影响很大等问题,采取超声横波、纵波相结合的方法重新推导检测公式,并提出采用一发一收模式进行拉伸实验,通过对实验数据进行拟合,由公式计算出声弹性系数代替应力系数。然后结合插值、互相关等算法,采用VC++编制z轴方向残余应力超声检测软件并搭建检测系统。分别对性能为A2-70,4.8,8.8,长度依次为135 mm,100 mm,100mm的M20的螺栓进行拉伸实验,比对计算拉伸应力与检测拉伸应力,结果表明,该测量系统的绝对误差限为20 MPa,相对误差小于25%,且应力值较大时,相对误差有所减小,当应力值大于100 MPa时,相对误差小于5%,非常实用。     

An improvement of tilted AlN for shear and longitudinal acoustic wave

This study investigates c-axis tilted aluminum nitride (AlN) piezoelectric films for the improvement of both shear and longitudinal acoustic wave resonances. Solidly-mounted resonator (SMR) structure is adopted for the applications of high frequency wireless communications and high sensitivity sensors. As to the piezoelectric layer, c-axis tilted AlN has the capability to excite the dual-mode resonances, namely, the longitudinal and shear mode resonances. In this study, SMR devices made with a seven-layer molybdenum/silicon dioxide (Mo/SiO₂) Bragg reflector and the c-axis tilted AlN are carried out. A conventional off-axis sputtering technique is applied to grow the tilted AlN. The outcome frequency responses show dual resonant characteristics. However, the longitudinal resonance fades away with the AlN c-axis tilted angle, and the quality factor of the longitudinal resonance decreases. Consequently, we make an improvement by tilting the off-center substrates toward the sputtering source and successfully enhance the longitudinal resonance while preserving the shear resonance at the same time. Not only the shear resonance for the liquid-based sensing application, but also an outstanding longitudinal resonance could be obtained. The practicability of the dual-mode resonator is extended.     

Radiation efficiencies of beams in flexural vibration

To reduce the noise from any complex noise source, it is important to locate the highly radiating component in that noise source. At present there are many techniques in use for this purpose. Among these, the radiation efficiency method now receives most attention. To use this method one is required to know the radiation efficiency of each component in a noise source. In this paper simplified equations (similar to those in use to calculate the radiation efficiencies of plates) are given to estimate the radiation efficiencies of beams of arbitrary cross-section which are part of many fabricated machines found in industry.     

Diffraction-biased shear wave fields generated with longitudinal magnetic resonance elastography drivers

Magnetic resonance elastography (MRE) is a technique for quantifying the acoustic response of biological tissues to propagating waves applied at low frequencies in order to evaluate mechanical properties. Application-specific MRE drivers are typically required to effectively deliver shear waves within the tissue of interest. Surface MRE drivers with transversely oriented vibrations have often been used to directly generate shear waves. These drivers may have disadvantages in certain applications, such as poor penetration depth and inflexible orientation. Therefore, surface MRE drivers with longitudinally oriented vibrations are used in some situations. The purpose of this work was to investigate and optimize a longitudinal driver system for MRE applications. A cone-like hemispherical distribution of shear waves being generated by these drivers and the wave propagation being governed by diffraction in the near field are shown. Using MRE visualization of the vector displacement field, we studied the properties of the shear wave field created by longitudinal MRE drivers of various sizes to identify optimum shear wave imaging planes. The results offer insights and improvements in both experimental design and imaging plane selection for 2-D MRE data acquisition.     

纵波的波形与媒质的运动状态

根据媒质疏密程度来分析纵波传播时媒质的运动状态,并能过媒质间相互作用力与媒质运动状态的关系,证明媒质单位面积相互作用力的功率等于能流密度。     

Effect of a longitudinal wave on the self-resonant motion of electrons

The effect of the longitudinal component of an electromagnetic wave on the self-resonant motion of electrons in waveguides is considered. The equation of motion for electrons in a plane, longitudinal-transverse, circularly polarized wave has been solved by the method of successive approximations with allowance for the longitudinal integral of motion present in such a wave. The expansion parameter is the ratio of the amplitudes of the longitudinal and transverse components of the wave. For the case n < 1 the longitudinal field of the wave does not change the nature of the electron motion, but only induces weak oscillations about a solution that does not include the longitudinal field. For n > 1 with spontaneous phasing of the electrons a criterion is obtained for neglecting the effect of the longitudinal field, and numerical estimates are given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 66–71, September, 1978.     

Guided wave polaritons in the ir range in three-layered structures

The properties of guided wave polaritons of E- and H-types are studied both theoretically and experimentally. The ranges of existence, field spatial structure, dispersion dependence, attenuation and absorption factors, of guided wave polaritons in three-layered structures are investigated.     

Reflectometry using longitudinal, shear and Rayleigh waves

A new technique of reflectometry using longitudinal, shear and Rayleigh waves is presented. Reflection coefficient as a function of angle incidence of an ultrasound beam with a finite beamwidth was measured for water-aluminum, water-brass, and water-glass interfaces. The measured values have matched very favorably with the results of numerical calculations based on the angular spectrum of waves method. It has been shown that the speeds of longitudinal, shear and Rayleigh waves of a solid can be determined very accurately by measuring a spectacularly reflected signal versus angle of incidence.     

Effect of longitudinal or inplane deformation and inertia on the large amplitude flexural vibrations of slender beams and thin plates

Large amplitude flexural vibrations of slender beams, and thin circular and rectangular plates have been studied when a compatible longitudinal or inplane mode is coupled with the fundamental flexural mode. It is shown that the effect of longitudinal or inplane deformation and inertia is to reduce the non-linearity in the flexural frequency-amplitude relationship. Further, for slender beams and thin plates, the effect of longitudinal or inplane inertia is negligible.     

Formation,reflection, and refraction of magnetostatic wave beams

Excitation of a magnetostatic surface wave beam in a thin magnetic film is studied theoretically and experimentally. Unique features in the propagation of such a beam are found, and the laws of beam reflection and refraction are studied. It is shown that there are significant features from Snell's and Euclid's law for such beams.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 67–75, November, 1988.     

Coupled axial and flexural vibration of 1-D members

The method of characteristics is used to model vibrations of one-dimensional members in the presence of coupling between axial and flexural waves. Only small deflections are considered and so the couple F_xδ_y is large only when the axial force F_x is large. Alternative numerical schemes are presented for the integration of terms describing coupling and a suitable explicit scheme is identified. The analysis is used to illustrate the influence of axial loads on frequencies and amplitudes of lateral oscillations of cantilever structures. Strong parametric behaviour is reproduced for a single-storey shear structure, including unstable resonance at double the linear natural frequency.     

Symmetry and chaos in the motion of the damped driven pendulum

The damped, driven pendulum equation is studied numerically. A relation is pointed out between the symmetry of the initial period-m dynamical state of am×2ⁿ period-doubling sequence and the form of the chaotic attractor for the final chaotic dynamical state reached after completion of the inverse-doubling sequence. Effects of extrinsic noise are also mentioned.