Anelastic Waves in Thin Plates

A computer-driven, swept-frequency measurement technique is developed on the basis of resonance birefringence acoustoelasticity to evaluate the stresses in thin plates. The resonance frequency depends on the thickness and the elastic wave velocity; they change with stress because of the Poisson effect and the acoustoelastic effect. The resonance frequency is obtained from the spectral response curve in the electric impedance of the piezoelectric transducer. The frequency displacement induced by acoustically coupling the transducer can be minimized by employing the resonance peak closest to the transducer fundamental frequency. To illustrate the method, the residual stress is measured in butt-welded aluminum alloy plates and is compared with the results of conventional methods.

In this study, we design periodic grille structures on a single homogenous thin plate to achieve anisotropic acoustic metamaterials that can control flexural waves. The metamaterials can achieve the bending control of flexural waves in a thin plate at will by designing only one dimension in the thickness direction, which makes it easier to use this metamaterial to design transformation acoustic devices. The numerical simulation results show that the metamaterials can accurately control the bending waves over a wide frequency range. The experimental results verify the validity of the theoretical analysis. This research provides a more practical theoretical method of controlling flexural waves in thin-plate structures.

Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity

Quantum revival is described as the time-periodic reconstruction of a wave packet initially localized in space and time. This effect is expected in finite-size systems which exhibit commensurable discrete spectrum such as the infinite quantum well. Here, we report on the experimental observation of full and fractional quantum revival for classical waves in a two dimensional cavity. We consider flexural waves propagating in thin plates, as their quadratic dispersion at low frequencies mimics the dispersion relation of quantum systems governed by Schrödinger equation. Time-dependent excitation and measurement are performed at ultrasonic frequencies and reveal a periodic reconstruction of the initial elastic wave packet.

In this paper, the linear transformation method (LTM) to control flexural waves propagating in thin plates is presented. Unlike earlier studies, only a small number of homogeneous materials with no requirement of in-plane forces or pre-stress are needed, which tremendously simplifies the implementation of devices for flexural waves. An invisibility cloak with homogeneous materials is studied to confirm the validity of the present approach, and to show its imperfection due to impedance mismatch at interfaces. Required materials can be further simplified as layered isotropic materials using the effective medium theory. Finally, the LTM can be extended to the case of flexural waves propagating in anisotropic thin plates. The present method opens a promising avenue toward the realization of advanced structured shields and other devices.

CHAPTER 4 - Bending Thermal Stresses in Thin Plates

Ribbed elastic metasurface with lateral scalability for flexural wave manipulation

Achromatic ribbed elastic meta-structure for ultra-broadband flexural wave manipulation

A pulsed laser has been used to generate ultrasonic transients in samples of metal and fiber-reinforced polymer composite material. These have been detected using an air-coupled piezoelectric transducer. It is demonstrated that such a transduction system can be used for longitudinal waves in bulk material, Rayleigh waves at solid surfaces and Lamb waves in thin plates.

Compact functional elastic waveguides based on confined mode

We designed and analyzed a piezo-lens to focus flexural waves in thin plates. The piezo-lens comprises a host plate and piezoelectric patches bonded on the surfaces of the plate. The piezoelectric patches are shunted with negative capacitance circuits. The effective refractive indexes inside the piezo-lens are designed to fit a hyperbolic secant distribution by tuning the negative capacitance values. A homogenized model of piezo-mechanical system is adopted in the designing process of the piezo-lens. The wave focusing effect is studied by the finite element method. Numerical results show that the piezo-lens can focus flexural waves by bending their trajectories, and is effective in a large frequency band. The piezo-lens has the ability to focus flexural waves at different locations by tuning the shunting negative capacitance values. Potential applications of the piezo-lens include energy harvesting, SHM, etc.

Spatial coordinate transformations can be used to transform boundaries, material parameters or discrete lattices. We discuss fundamental constraints in regard to cloaking and review our corresponding experiments in optics, thermodynamics and mechanics. For example, we emphasize three-dimensional broadband visible-frequency carpet cloaking, transient thermal cloaking, three-dimensional omnidirectional macroscopic broadband cloaking for diffuse light throughout the entire visible range, cloaking for flexural waves in thin plates and three-dimensional elasto-static core-shell cloaking using pentamode mechanical metamaterials.

We have developed a method for detecting acoustic fields in solids irradiated with dense electron beams. The method is based on laser Michelson interferometry. The electron source is a high-current DZhIN electron accelerator. The detection system features a short baseline Michelson interferometer located inside the experimental chamber with the sample, a stabilized initial beam pathlength difference within the interferometer, high temporal resolution, an analog-to-digital converter with output to a personal computer, and a program for reducing the interferometer data. We can measure both long pulses with minimum displacements of 10−10 m and durations of 10−8 sec, and flexure waves with large-amplitude displacements of 10−5 m and oscillation periods of 10−3 sec. We present results from studies of flexure waves in thin plates and rods of copper, silicon, alkali-halide crystals, quartz glasses, and D16T aluminum alloy irradiated by nanosecond high-density electron beams.

As a new kind of elastic materials, elastic wave metasurface has great research significance in the field of elastic wave regulation. However, most of the researches on elastic wave metasurface are guided by traditional Generalized Snell’s Law (GSL), and the effect of higher order diffraction waves caused by structural periodicity is not considered. Under the action of higher order diffraction wave, the incident wave will produce more complex transmission phenomenon when passing through the metasurface, and the angle of transmission does not conform to GSL in some cases. In order to verify whether the modified GSL theory considering the higher-order diffraction term is still applicable to the regulation of solid elastic waves, this paper designs a helical metasurface based on the elastic wave theory of plate-beam structure, which is composed of helical lines of different lengths, and uses this structure to explain the complex transmission phenomenon of elastic wave metasurface. Finally, the asymmetric transmission, modal separation and waveguide of Lamb waves in thin plates are realized by combining the theory with structural design, which proves that the structure has great application potential in ultrasonic detection and other fields.

A new approach based on the solution of a singular integral equation to analyzing the aeroelastic oscillations of thin plates is proposed. The velocity circulation is expanded into a series in the generalized coordinates of oscillations of the plate. This allows using a system with a finite number of degrees of freedom for the generalized coordinates to describe the aeroelastic oscillations. The following scenario is analyzed: the motion of the plate undergoes Neimark bifurcations and transform into quasiperiodic oscillations, which, in turn, transform into chaotic oscillations Here we propose a new method for analyzing the aeroelastic oscillations of plates undergoing geometrically nonlinear deformation. To determine the circulation density, we will solve a hypersingular integral equation. The velocity circulation will be expanded into a series in the generalized coordinates of flexural oscillations of the plate. The set of circulation density functions does not depend on time and is determined only once during the solution of the problem. The effectiveness of this method is in using a nonlinear system with a finite number of degrees of freedom for the generalized coordinates of flexural oscillations of the plate. This dynamic system of low dimension can be analyzed in detail. 2. Problem Formulation and Basic Equations. Consider a cantilevered thin rectangular plate (Fig. 1). Since it is thin, its shear and rotary inertia can be neglected. The stresses and strains of the plate are related by Hooke's law. When a gas flow is past a thin plate on both its sides (Fig. 1), flutter (self-sustained oscillations) occurs. These unstable oscillations of the plate are constrained by the forces due to geometrically nonlinear deformation. Then the displacements of the plate are commensurable with its thickness. Such deformation of the plate is described by the von Karman equations