Stagnant waves in an elastic wedge-shaped plate

Stagnant antisymmetric waves in an elastic wedge-shaped plate were studied theoretically and experimentally. The solution to the nonuniform problem was obtained in the approximation of a small and smooth field nonuniformity. The vibration amplitudes in a standing wave were calculated and measured for a small wedge angle. Experimental measurements were performed on an original setup.     

Nonstationary wave turbulence in an elastic plate

We report experimental results on the decay of wave turbulence in an elastic plate obtained by stopping the forcing from a stationary turbulent state. In the stationary case, the forcing is seen to induce some anisotropy and a spectrum in disagreement with the weak turbulence theory. After stopping the forcing, almost perfect isotropy is restored. The decay of energy is self-similar and the observed decaying spectrum is in better agreement with the prediction of the weak turbulence theory. The dissipative part of the spectrum is partially consistent with the theoretical prediction based on previous work by Kolmakov. This suggests that the nonagreement with the weak turbulence theory is mostly due to a spurious effect of the forcing related to the finite size of the system.     

Fourier analysis of wave turbulence in a thin elastic plate

The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of the Weak Turbulence theory. A isotropic continuous spectrum of waves is excited with a non linear dispersion relation slightly shifted from the linear dispersion relation. The spectral width of the dispersion relation is also measured. The non linearity of this system is weak as expected from the theory. Finite size effects are discussed. Despite a qualitative agreement with the theory, a quantitative mismatch is observed which origin may be due to the dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov casade.     

Bending wave propagation along a symmetric groove in an elastic plate

Normal bending waves propagating along a symmetric groove in an infinite elastic plate are considered. The characteristic equations in wave numbers of these modes are obtained for symmetric and antisymmetric modes of vibration. Critical frequencies and eigenfunctions of the problem are determined. Results of numerical calculations for the wave numbers, critical frequencies, and modes of vibration are presented.     

Modulating lamb wave band gaps using an elastic metamaterial plate

Modulating band gaps (extending the bandwidths or shifting into a lower frequency range) is a challenging task in phononic crystals. In this paper, elastic metamaterial plates composed of a square array of “hard” stubs or “soft” stubs on both sides of a 2D binary locally resonant plate are proposed, and their band structures are studied. The dispersion relationships and the displacement fields of the eigenmodes are calculated using finite element methods. Numerical results show that the band gaps are shifted to lower frequencies and the bandwidths are enlarged compared to classic elastic metamaterial plates. A conceptual “analogousrigid mode” that includes an “out-of-plane analogous-rigid mode” and an “in-plane analogous-rigid mode” is developed to explain these phenomena. The “out-of-plane analogous-rigid mode” mainly adjusts the band gaps into the lower frequency range, and the “in-plane analogous-rigid mode” mainly enlarges the bandwidth. Furthermore, the band gap effects of composite “hard” stubs and “soft” stubs are investigated. The results show that the location of the band gaps can be modulated into a relatively lower frequency and the bandwidth can be extended by the use of different composite stubs. These elastic wave properties in the proposed structure can be used to optimize band gaps and possibly produce low-frequency filters and waveguides.     

Time-domain analysis of second-harmonic generation of primary Lamb wave propagation in an elastic plate

Within the second-order perturbation approximation,this paper investigates the physical process of generation of the time-domain second harmonic by a primary Lamb wave waveform in an elastic plate.The present work is performed based on the preconditions that the phase velocity matching is satisfied and that the transfer of energy from the primary Lamb wave to the double frequency Lamb wave is not zero.It investigates the influences of the difference between the group velocities of the primary Lamb wave and the double frequency Lamb wave,the propagation distance and the duration of the primary Lamb wave waveform on the envelope shape of the time-domain second harmonic.It finds that the maximum magnitude of the envelope of the second-harmonic waveform can grow within some propagation distance even if the condition of group velocity matching is not satisfied.Our analyses also indicate that the maximum magnitude of the envelope of the second-harmonic waveform is kept constant beyond a specific propagation distance.Furthermore,it concludes that the integration amplitude of the time-domain second-harmonic waveform always grows with propagation distance within the second-order perturbation.The present research yields new physical insight not previously available into the effect of generation of the time-domain second harmonic by propagation of a primary Lamb wave waveform.     

Reliability assessment of different plate theories for elastic wave propagation analysis in functionally graded plates

The importance of elastic wave propagation problem in plates arises from the application of ultrasonic elastic waves in non-destructive evaluation of plate-like structures. However, precise study and analysis of acoustic guided waves especially in non-homogeneous waveguides such as functionally graded plates are so complicated that exact elastodynamic methods are rarely employed in practical applications. Thus, the simple approximate plate theories have attracted much interest for the calculation of wave fields in FGM plates. Therefore, in the current research, the classical plate theory (CPT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) are used to obtain the transient responses of flexural waves in FGM plates subjected to transverse impulsive loadings. Moreover, comparing the results with those based on a well recognized hybrid numerical method (HNM), we examine the accuracy of the plate theories for several plates of various thicknesses under excitations of different frequencies. The material properties of the plate are assumed to vary across the plate thickness according to a simple power-law distribution in terms of volume fractions of constituents. In all analyses, spatial Fourier transform together with modal analysis are applied to compute displacement responses of the plates. A comparison of the results demonstrates the reliability ranges of the approximate plate theories for elastic wave propagation analysis in FGM plates. Furthermore, based on various examples, it is shown that whenever the plate theories are used within the appropriate ranges of plate thickness and frequency content, solution process in wave number-time domain based on modal analysis approach is not only sufficient but also efficient for finding the transient waveforms in FGM plates.     

An integral equation in theory of wave diffraction in wedge-shaped region

Leningrad State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 11, pp. 1398–1403, November, 1989.     

Pulse polarization splitting in a transient wave plate

We demonstrate propagation of ultrafast laser pulses through a molecular gas acting as a transient wave plate under conditions of strong phase modulation. The resulting decomposition of a linearly polarized laser pulse into two nearly distinct, orthogonally polarized laser pulses is demonstrated with transiently aligned, linear molecules.     

Dynamic analysis of an elastic plate on a thin,elastic foundation

An improved theory for the motion of an elastic foundation is developed. Included is the interaction of two or more plates resting on a common foundation. A simplified model is deduced which appears useful for some applications.     

Dynamic equations for a fully anisotropic elastic plate

A hierarchy of dynamic plate equations is derived for a fully anisotropic elastic plate. Using power series expansions in the thickness coordinate for the displacement components, recursion relations are obtained among the expansion functions. Adopting these in the boundary conditions on the plate surfaces and along the edges, a set of dynamic equations with pertinent edge boundary conditions are derived on implicit form. These can be truncated to any order and are believed to be asymptotically correct. For the special case of an orthotropic plate, explicit plate equations are presented and compared analytically and numerically to other approximate theories given in the literature. These results show that the present theory capture the plate behavior accurately concerning dispersion curves, eigenfrequencies as well as stress and displacement distributions.     

Weak pressure wave in a gas filled elastic tube

The propagation of a small but finite shock disturbance through gas contained within a cylindrical tube is examined theoretically for the case where both the hoop elasticity and radial inertia of the tube are taken into account. Governing equations so derived are found to admit a non-dispersive wave of variable pressure behind the advancing shock front in direct contrast with the situation existing for an initially sharp-fronted infinitesimal disturbance where no steady wave form is possible. Detailed calculations are carried out for the case where the gas filling the tube is air. Results show that increases in either the tube or shock strength are sufficient to make the pressure distribution behind the wave front approach that which would exist in a rigid tube under similar conditions.     

粗糙界面板Lamb波的传播特征

弹性波在粗糙界面板中的传播问题对无损检测、地震波传播等问题有实际意义,但是多年来的研究限于相屏近似等方法。本文从严格的理论出发,把粗糙界面起伏看作空间位置变量的随机过程,在粗糙表面起伏很小的条件下,用多次散射相互独立假设得到了平均意义下的Rayleigh-Lamb频散方程。通过对方程进行求解,得到了Lamb波在粗糙界面板中传播时的衰减。结果表明Lamb波的衰减和界面的粗糙起伏方差近似成正比,和粗糙起伏相关长度关系不大。在理论分析的基础上,进行了实验验证。     

兰姆波在自由端面上的反射

对于板材的内部缺陷,常用兰姆波作超声无损检测。兰姆波在板材自由端面上的反射呈现复杂现象,即使在纯模入射条件下,通常也要产生无数个其它模式的反射兰姆渡。由于兰姆波本征模式正交关系同时涉及位移和应力,使其反射问题的分析较复杂,我们采用了一种新方法,应用最小二乘原理,将兰姆波本征模式作为试验函数,实现了一种较简单的分析方法。在一般情形下,利用8位微处理机就可取得满意的结果。应用该方法,给出了兰姆波在自由端面上反射时各模式的反射系数,阐明了纯模反射条件,并发现了关于模式转换的一些有趣的新现象。     

Lamb wave radiation from plate termination in a liquid

The liquid wedge method is used to excite leaky Lamb waves on an aluminium plate while the plate is immersed in water. The excitation occurs near the end of the plate so that sonic energy of the excited mode radiates into the liquid. A Schlieren method is used to observe the radiation pattern and a correlation is made between the radiation lobe structure and the symmetric or antisymmetric nature of the excited mode. Theoretical calculations of the transfer of energy from the plate to the liquid are made and agreement between theory and experiment is obtained.     

弹性体内平面波

由胡克定律直接得到弹性体内平面波波动方程.     

Two-dimensional wave propagation in a rotating elastic solid with voids

Two-dimensional wave propagation is studied in an isothermal linear isotropic elastic material with voids rotating with constant angular velocity based on a theory of elastic material with voids developed by Ie?an (1986) in the thermoelastic context. It is found that there exist three coupled plane waves propagating with distinct phase speeds. The presence of voids and the rotation of the medium are responsible for this coupling. In the absence of voids, the classical longitudinal and transverse waves are found to be coupled through the rotation of the medium. At very large frequency or when the angular rotation is very small relative to the wave frequency the waves are decoupled and propagate with distinct phase speeds. These are (i) a longitudinal wave, (ii) a transverse wave and (iii) a longitudinal wave corresponding to the change in void volume fraction. The first two correspond to the waves of classical elasticity, while the third is new and arises from the presence of the voids. The results are illustrated graphically.     

固体板中SH板波非线性效应的实验观察

采用微扰近似和导波的模式展开分析方法,从理论上简要分析了SH板波的二次谐波发生效应;尽管在无限大固体介质中单个切变波的二次谐波发生效应非常微弱,但在一定条件下由两个切变波构成的SH板波可具有强烈的非线性效应;本文的主要工作就是对此结论加以实验验证。试制了激发SH板波的切变波斜劈换能器和接收二次谐波信号的液体斜劈换能器,建立了非线性SH板波的实验研究系统;通过详细的理论分析和对比实验研究,阐明了在一定条件下实验观察到的显著二次谐波信号来源于SH板波传播过程中的强烈非线性效应。此外,针对不同的SH板波传播距离,在远场条件下分别测量了相应的二次谐波幅频曲线;在基频SH板波与二倍频对称兰姆波相速度相等所对应的频率值附近,分析了二次谐波的振幅随传播距离的变化关系,结果证明在一定条件下SH板波的二次谐波振幅可随传播距离积累增长,即SH板波可具有强烈的非线性效应。     

Coherent backscattering of an elastic wave in a chaotic cavity

We report the first experimental evidence of coherent backscattering enhancement for transient elastic waves propagating in a two-dimensional chaotic cavity. The time-integrated squared amplitude at the point source is twice as large as at the other points around the source. Contrary to analogous optical experiments, this effect is already clearly observable on a single realization. Especially, the spatial shape of the coherent backscattering enhancement is well predicted by a generalization of the existing theory.