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For sound propagation in a shallow water waveguide, a dedispersion transform which can remove the dispersive effect of signal is described in this paper. The transform is a modified Fourier transform with two variables: translation and dispersion. Dispersive effect of signal for normal modes can be removed when these two variables match to real parameters. The validity of the present approach is verified in simulation and real data processing.

Based on the wave theory and propagation characteristics of Lamb wave in the thin plate, Lamb wave is excited by signal actuator in the thin plate and signal sensor is received in real time. Employing the superior features of dispersion curve produced the Lamb wave and combining the dichotomy iterative principle with MATLAB tools to solve Lamb wave dispersion equation, the propagation characteristics of the Lamb wave in the thin plate are plotted. It is verified that the excited Lamb wave has multimode characteristics in a certain thickness, and the different modes are related to the frequency-thickness. The wavelength-thickness ratio is defined to simplify the calculation and provide convenience for the frequency bandwidth interception of Lamb wave. The results of the theoretical analysis show that the propagation multimode of Lamb and the distribution characteristics of dispersion curve can effectively simulate the transmission information of damage signal-excited thin plate, and identify damage region and determine the damage degree by $S_0$ and $A_0$ mode. The experimental results indicate that the established method to determine damage degree of thin plate attached PZT transducers based on Lamb wave active monitoring technology can achieve a certain precision, and can make a rough quantitative recognition of damage position.

This paper reports on the fabrication and characterization of polymer optical waveguide. The polymer films were used by dip coating technique. Various waveguide parameters such as refractive index, optical losses, thickness of guide has been reported. Polycyanurate synthesized as planar optical waveguide exhibits low optical loss (< 2 dB/cm) having refractive index 1.592 and excellent absorption spectra in the wavelength range (1540–1560 nm) which makes this polymer promising for integrated optical devices.

Presented herein is a computationally efficient 2D theoretical model for simulating the steady response of a floating slab track-tunnel-soil system. The track-tunnel coupled system is simplified as a beam-spring system and embedded in soil layers. The tunnel is modeled by a Timoshenko beam with its interaction with the soil layers accounted for by two transfer matrices, with each derived for the soil layer above and beneath the tunnel. The approach as proposed herein has been referred to as the Timoshenko beam-transfer matrix method (TTMM), that allows one to analyze the response of the coupled system, including the tunnel motion and soil stresses. The results obtained were compared with those furnished by the pipe-in-pipe (PIP) approach, and were found to be consistent for exciting frequencies smaller than the tunnel second-mode cut-on frequency. The origin of discrepancies was investigated by the dispersion characteristic analysis, which is attributed to the absence of several in-plane modes when the tunnel is simplified as a Timoshenko beam.

Dispersion curves for waveguide structures are an important prerequisite for the implementation of guided wave-based nondestructive evaluation (NDE) approach. Although many methods exist, each method is only applicable to a certain type of structures, and also requires complex programming. A Bloch theorem-based finite element method (FEM) is proposed to obtain dispersion curves for arbitrary waveguides using commercial finite element software in this paper Dispersion curves can be obtained for a variety of structures, such as homogeneous plates, multilayered structures, finite cross section rods and honeycomb sandwiches. The propagation of guided waves in honeycomb sandwich plates and beams are discussed in detail. Then, dispersion curves for honeycomb sandwich beams are verified by experiments.

Guided waves (GW) are massively used for structural health monitoring and defect evaluation in plate, pipe, and rail structures. To accurately and efficiently calculate the dispersive natures of GW in complex waveguides, this study proposes a novel Gauss–Lobatto–Legendre-based high-order semi-analytical finite element method (GLL-SAFE). Combining the GLL node collation and Lobatto quadrature into SAFE, the mass matrix in the developed GLL-SAFE is diagonal, which enables a faster solution speed and a reduced error of matrix inversion. Firstly, the GWs in the single-layer isotropic material, composite lamina, and composite laminates are calculated with both GLL-SAFE and the conventional Gauss-SAFE featuring an equidistant node collation and Gaussian quadrature. Before reaching the convergence limit, the calculated average relative errors for GLL-SAFE are smaller than those for Gauss-SAFE, and can reach an order of 10${}^{-6}$ and 10${}^{-4}$ for the phase and group velocity, respectively. Then a novel mesh automatic reconstruction with arbitrary element polynomial order is developed to calculate GW propagation in waveguides of complex cross section. As a hollow cylinder for validation, the calculated average relative errors reach below $9\times 10^{-5}$ and $9\times 10^{-4}$ for the phase and group velocity, respectively. Finally, with a complex rail track as the waveguide, the calculated dispersion characteristics with GLL-SAFE show an excellent match with those from the time-domain finite element analysis, and GLL-SAFE shows its higher calculation efficiency over Gauss–SAFE.

In this work, we use the phase velocity method in combination with finite element method to compute the dispersion curve for phase velocity of an ultrasonic pulse traveling in a thin isotropic plate. This method is based on the numerical solution of the wave propagation equations for several selected frequencies. To solve these equations, a second order difference scheme is used to discretize the temporal variable, while spatial variables are discretized using the finite element method. The variational formulation of the problem corresponding to a fixed value of time is obtained and the existence and uniqueness of the solution is proved. A priori error estimates in the energy norm and in the $L^2$ norm are also obtained. The open software FreeFem++ is used with quadratic triangular elements to compute the displacements. Numerical experiments show that the velocities computed from the approximated displacements for different frequency values are in good agreement with analytical dispersion curve. This confirms that the proposed symbiosis between finite element and phase velocity method is suitable for computing dispersion curves in more general wave propagation problems, where the geometry is complex and the material is anisotropic.

The propagational characteristics of free waves in wave guides can be utilized for NDE, vibration reduction, and oil exploration. A vast of researches have been conducted on isotropic and anisotropic laminated plates, but few concerning the behavior in high frequency range or at large wave numbers, for which numerical instability may generally be encountered in conventional analysis methods. Based on the state equation for anisotropic elasticity, this paper constructs the formulations for the method of reverberation-ray matrix to analyze the wave propagation in anisotropic elastic laminated plates. Since unknown wave amplitudes are appropriately retained in the formulations, large numbers at high frequencies are excluded, making the calculation stable in the high frequency range. The matrix inverse operation is also avoided in the scattering relations to assure the stability in the low frequency range. Numerical examples are presented and good agreement is obtained.

Ultrasonic guided wave mode conversion was studied for thin-plate defects by using lamb wave scattering. For lamb wave scattering analysis, the phase velocity dispersion curve and group velocity dispersion curve of the material were calculated. A mode conversion was investigated by the boundary element method (BEM) in terms of reflection and the transmission factor. Time domain wave analysis was performed with scattering field modeling and inverse fast Fourier transform (IFFT). The feasibility of the lamb wave technique was discussed for various practical applications, including the classification of defects.

Thin film bulk acoustic resonators (FBARs) vibrate in the thickness mode, unfortunately the constraints of the lateral edge induce spurious lateral modes, which reduces the Q of FBARs and causes ripples in the passband of FBAR filters. In this work, 3D vibration model is established to simulate membrane-type FBARs. The impedance curves, the Smith charts and the dispersion curves are obtained to analysis and compare the lateral modes of FBARs with different shapes and size of the active resonator area and with different piezo layers. The simulation results show that FBARs with circular and irregular-pentagon active areas have smoother impedance curves and less spurious circles in the smith chart compared with rectangular ones. With the active areas of FBARs increasing, the influence of the spurious lateral modes decreases. While operating at the same resonance frequencies, apodized FBARs consisting of ZnO piezoelectric film suffer less from spurious lateral modes compared with the ones consisting of AlN.