This paper presents a tunable planar auxetic metamaterial (PAM) for controlling and filtering acoustic waves and provides guidelines for bandgap design of the proposed PAMs. Numerical results for deformed and undeformed PAMs were obtained from several finite element analyses based on Bloch–Floquet theory. The acoustic band structures of the PAMs were calculated with periodic boundaries. Tunable bandgaps in certain frequency ranges were generated by various deformations applied to the PAMs. Wave attenuation in experimental transmission loss at specific frequencies was demonstrated, showing favorable agreement with the bandgaps obtained from numerical calculations. Both the numerical and experimental results indicate that the proposed structure demonstrates great tunability and offers significant advantages over the regular materials for controlling sound wave propagation and filtering sound waves within specific frequency ranges.

In this study, wave propagation in beams is studied using different beam theories like Euler-Bernoulli, Timoshenko and Reddy beam theories. Dispersion curves obtained for these beam theories are compared with the exact plane elasticity solutions. It is obtained that, there are two branches for Reddy beam theory similar to the Timoshenko beam theory. However, one branch is obtained for Euler-Bernoulli beam theory. The effects of in-plane load on Timoshenko and Reddy beam theories are examined and dispersion curves of the Timoshenko and Reddy beams are compared with exact plane elasticity solution. In Timoshenko beam theory, qualitative difference between the two spectrums has been lost with in-plane loads for some wave numbers.

In this paper, nonconforming mixed finite element method is proposed to simulate the wave propagation in metamaterials. The error estimate of the semi-discrete scheme is given by convergence order O(h2), which is less than 40 percent of the computational costs comparing with the same effect by using Nédélec-Raviart element. A Crank-Nicolson full discrete scheme is also presented with O(τ2 + h2) by traditional discrete formula without using penalty method. Numerical examples of 2D TE, TM cases and a famous re-focusing phenomena are shown to verify our theories.

The paper is to solve the problem of the response of stratified half-space subjected to triangularly distributed time-harmonic loadings on an axial symmetric area in the stratified half-space. Since the distributed area can be very small, the solution can be employed to deal with the problems of elastodynamics using the fundamental solution method. The advantage of the presented solution over Green function is that no singularity will occur in the presented solution. Some numerical results are given and some conclusions have been made. The presented solution is very efficient in computation.

A systematic procedure is developed to calculate ground vibration at any specific location in layered medium due to harmonic loadings applied at a circular plate on the medium. In the procedure, the technique decomposing the interaction tractions between excited plate and layered medium will be employed. The decomposed tractions will automatically match boundary values of general solutions of three dimensional wave equations in cylindrical coordinates. In numerical results, the effect of layered stratum on ground vibration will be investigated and how ground vibration in layered medium decreases with depth will be presented. Also, from the numerical results, one can observe ground vibration may not decay monotonically along distance away from vibration source. The presented scheme is proved to be effective and efficient for accurately predicting near-field ground response to harmonic loadings applied at a rigid circular plate on layered medium. Comments on the presented scheme and numerical results will be given.

This paper extends the recently developed method of reverberation-ray matrix for planar structures to three-dimensional framed structures. The propagation of steady state axial, flexural and torsional waves, as well as the mode conversions through scattering of all three waves at connecting joints are evaluated in the frequency domain. The transient waves in all members are then determined by the Fourier synthesis. The transient responses of a two-storey framed building subject to a step time loading are calculated in detail. Numerical results are obtained for early time as well as moderately long time records. The results are shown to be accurate in arrival times of all three types of waves and in asymptotic values at times.

Using a piezoelectric unimorph vibrator with constraint-tuning modified-mode (CTMM) mechanism, a novel design of a thin-disc ultrasonic actuator was developed to drive an optical sled. The theoretical estimation of in-plane wave propagation on a thin disc is introduced to explain the novel actuating mechanism, via a modal expansion technique and modal participation factors. Furthermore, the approximate wave propagations could be illustrated by the practical estimated wave equations in this study. Applying four screws at the exact distribution of angles on the thin-disc vibrator, the actuating mechanism of ultrasonic modified modes is generated and propagated. The in-plane vibration modes could be tuned by these desired screw constraints on the piezoelectric vibrator. The ultrasonic actuator offers the output force to drive an optical sled by friction contact in bilateral motions. To implement the equilibrium structure force in bilateral directions, natural and forced analysis as well as impedance comparison of FEM software ANSYS are also introduced into the constrained design. Hence, there are two various modified modes chosen at the different resonant frequencies within the electromechanical coupling of piezoelectric material to pursue more efficiency in energy conversion. Experimental results have demonstrated consistency with the approximate theoretical approach of the in-plane wave propagation and simulations based on the concept of constrained-tuning modified modes.

When gas flows through corrugated pipes, pressure waves interacting with vortex shedding can produce distinct tonal noise and structural vibration. Based on established observations, a model is proposed which couples an acoustic pipe and self-excited oscillations with vortex shedding over the corrugation cavities. In the model, the acoustic response of the corrugated pipe is simulated by connecting the lossless medium moving with a constant velocity with a source based on a discrete distribution of van der Pol oscillators arranged along the pipe. Our time accurate solutions exhibit dynamic behavior consistent with that experimentally observed, including the lock-in frequency of vortex shedding, standing waves and the onset fluid velocity capable of generating the lock-in.

The rise-time of the pulse on the diode of the intense electron-beam accelerators (IEBA) is one of the important factors that affect the quality and characteristic of the output beam current of the IEBA. In this paper, effect of the transition section between the main switch and middle cylinder of strip spiral Blumlein line (SSBL) on the diode voltage of IEBA is analyzed in theory, based on the theoretical analysis of the wave propagation along the Blumlein pulse forming line (BPFL), the traveling time of the transition section has a great effect on the rise-time, the plateau-time, and the fall-time of the output voltage at the matching load. Furthermore, the operation of the whole accelerator consisting of the primary energy-storage capacitor, the Tesla transformer, a main switch, the transition section, BPFL, and a resistive load was simulated using a circuit-simulation code called PSpice, and the dependence of the output voltage on the inductance of the main switch and the transition section was obtained. It was found from the wave propagation theory and the circuit simulation using computer results that the wave traveling time of the transition section between the main switch and the middle cylinder of the SSBL influences considerably the rise-time, plateau-time, and fall-time of the voltage waveform at the matching load. In order to get an ideal square pulse voltage waveform at the matching load and to improve the electron beam quality of such an accelerator, the wave traveling time of the transition section should be designed as soon as possible. At last, a couple of contrastive experiments are performed on two kinds of IEBA. The experimental results agree with the theoretical analysis and simulated results.

The transient dynamics of evacuated and fluid-filled circular elastic shells, submerged in an infinite fluid medium and subjected to an external weak shock wave,is considered in this paper. This circular shell/acoustic medium interaction problem has already been tackled with simplified thin shell models, based on the Love-Kirchhoff hypotheses for thestructural dynamics. In this case, the resulting radiated pressure field displays some discrepancies related to the A0/S0 waves when compared to the experimental data available inthe literature for the evacuated case. These drawbacks are overcome here by the use of an isotropic elastic model for the structural dynamics and an inviscid acoustic flow for the fluid dynamics,in a two-dimensional framework. The approach is based on the methods of Laplace transform in time, Fourier series expansions and separation of variables in space. For the fluid-filled case,the transient thick shell-weak shock wave interaction problem is explored and the radiated acoustic field described.

We are concerned with a finite element approximation for time-harmonic wave propagation governed by the Helmholtz equation. The usually oscillatory behavior of solutions, along with numerical dispersion, render standard finite element methods grossly inefficient already in medium-frequency regimes. As an alternative, methods that incorporate information about the solution in the form of plane waves have been proposed. We focus on a class of Trefftz-type discontinuous Galerkin methods that employs trial and test spaces spanned by local plane waves. In this paper we give a priori convergence estimates for the h-version of these plane wave discontinuous Galerkin methods in two dimensions. To that end, we develop new inverse and approximation estimates for plane waves and use these in the context of duality techniques. Asymptotic optimality of the method in a mesh dependent norm can be established. However, the estimates require a minimal resolution of the mesh beyond what it takes to resolve the wavelength. We give numerical evidence that this requirement cannot be dispensed with. It reflects the presence of numerical dispersion.

A simple derivation of the explicit form of the transition density of a planar random motion at finite speed, based on some specific properties of the wave propagation on the plane R2, is given.

Dans ce papier, nous élaborons une technique d'interprétation des ondes réfléchies. Cette technique est basée sur une approche analytique permettant de maîtriser la propagation pure d'une onde incidente et par suite d'interpréter toute information transportée par l'onde réfléchie. L'objectif essentiel de cette démarche est de développer une méthodologie pour la détermination des sites de réflexions telles que la localisation d'une jonction avec ou sans obstruction.

This article presents a numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit ħ → 0 of the nonlinear paraxial equation. In a general setting of both dimension and nonlinearity, the essential differences between the “defocusing” and “focusing” cases are observed. Numerical comparisons of the oscillations are made between the linear (“free”) and the cubic (defocusing and focusing) cases in one dimension. The integrability of the one-dimensional cubic nonlinear paraxial equation is exploited to give a complete global characterization of the weak limits of the oscillations in the defocusing case.

In this paper we outline the hyperbolic system of governing equationsdescribing one-dimensional blood flow in arterial networks. Thissystem is numerically discretised using a discontinuous Galerkinformulation with a spectral/hp element spatial approximation. Weapply the numerical model to arterial networks in theplacenta. Starting with a single placenta we investigate the velocity waveformin the umbilical artery and its relationship with the distalbifurcation geometry and the terminal resistance. We then present resultsfor the waveform patterns and the volume fluxes throughout a simplifiedmodel of the arterial placental network in a monochorionic twin pregnancy with an arterio-arterial anastomosis and an arterio-venous anastomosis. Theeffects of varying the time period of the two fetus' heart beats, increasing the input flux of one fetus and the role ofterminal resistance in the network are investigated and discussed. The results show that the main features of the in vivo, physiological waves are captured by thecomputational model and demonstrate the applicability of themethods to the simulation of flows in arterial networks.