Three problems for a discrete analog of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: (1) the problem with a point source on an entire plane; (2) the problem of diffraction by a Dirichlet half-line; (3) the problem of diffraction by a Dirichlet right angle. It is shown that the total field can be represented as an

We systematically employ the method of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity geometries precisely defined and provided explicitly for a wide range of geometries. With an eye towards modeling acoustic metasurfaces, we consider resonators embedded

To solve scattering problems with multi-transmitting boundary, we present an improved wave motion input method based on the idea that error caused by the difference between incident wave field used in calculation and waves propagating in finite element grids can be eliminated to suppress drift instability. In this method, a calculation scheme is proposed to obtain the numerical solution of incident

Based on the linear three-dimensional elastic theory and the mechanics theory of incremental deformation, using the Legendre orthogonal polynomial expansion (LOPE) method, the wave equations of Lamb wave propagation in the non-principal symmetry axes direction of anisotropic composite lamina was firstly derived when the initial stresses were applied in the horizontal and vertical directions. Subsequently

In this article we study the time evolution of broad banded, random inhomogeneous fields of deep water waves. Our study is based on solutions of the equation derived by Crawford, Saffman and Yuen in 1980, (Crawford et al., 1980). Our main result is that there is a significant increase in the probability of freak wave occurrence than that predicted from the Rayleigh distribution. This result follows

We study the model formulations of wave–current interactions in the framework of Euler equations. This work is intrigued by a recent paper from Wang et al. (2018) (hereafter WMY), which proposes such a model for the evolution of nonlinear broadband surface waves under the influence of a prescribed steady and irrotational current without vertical shear. We show that WMY’s model can be derived from a

The article describes an experimental study, which aims to detect signs of jump-like inelasticity in sandstone and to establish their influence on the P-wave attenuation. The measurements were taken in a sandstone sample using the reflection method at a pulse frequency of 1 MHz and with the strain amplitudes ε1 ≈ 0.1 microstrain and ε2 ≈ 0.24 microstrain at a hydrostatic pressure of 10 MPa. Using the

At long lapse times in randomly fluctuating media with macroscopic isotropy (texture-less media), the energy of elastic waves is equipartitioned between compressional (P) and shear (S) waves. This property is independent of the local isotropy or anisotropy of the heterogeneous constitutive tensor and of the type of source. However the local symmetry of the constitutive tensor does influence the rate

An apparent increase in the frequency and intensity of natural disturbances and anthropogenic activities accelerates the global degradation of coral reefs. The emergency planning for coastal erosion and flooding along the low-lying coasts fronted by coral reefs underscores the need to predict and evaluate reasonably the hydrodynamic consequences of reef degradation. Here the ability of the well validated

A systematic boundary-layer approach is for the first time applied to diffraction of a high-frequency plane wave by a contour with a jump of curvature. Assuming that the incident wave is non-tangent, we present a detailed description of the outgoing wavefield within a boundary layer surrounding the point of non-smoothness of the contour. This allows us to describe the wavefield within a transition

In this study, a 2-D infinite flexible waveguide is considered. The waveguide carries a weakly nonlinear acoustic fluid. It is bounded on one side by a weakly nonlinear flexible membrane and the other side is rigid. The infinite waveguide is driven at the origin by a piston oscillating at a single frequency. However, we focus only on the positive side of the piston. As the coupled waves propagate in

In the structural design of mechanical products, natural frequencies must be controlled to reduce noise and vibration. In particular, the stiffness of the joints which assemble the structural components affects the natural frequencies. Therefore, it is important to predict the influence of joint stiffness on natural frequencies. Generally, these effects are determined by iterative finite element analyses

The two-dimensional elastic wave propagation in an infinite layered structure with nonlinear interlayer interfaces is analyzed theoretically to investigate the second-harmonic generation due to interfacial nonlinearity. The structure consists of identical isotropic linear elastic layers that are bonded to each other by spring-type interfaces possessing identical linear normal and shear stiffnesses

This article presents a study of the dispersion characteristics of wave propagation in layered piezoelectric structures under plane strain and open-loop conditions. The exact dispersion relation is first determined based on an electro-elastodynamic analysis. The dispersion equation is complicated and can be solved only by numerical methods. Since the piezoelectric layer is very thin and can be modeled

We derive a volumetric source term for the Euler and Navier-Stokes equations that mimics the generation of unidirectional acoustic waves from an arbitrary smooth surface in three-dimensional space. The model is constructed as a linear combination of monopole and dipole sources in the mass, momentum, and energy equations. The singular source distribution on the surface is regularized on a computational

An analysis is presented of the diffraction of a pressure wave by a periodic grating including the influence of the air viscosity. The direction of the incoming pressure wave is arbitrary. As opposed to the classical nonviscous case, the problem cannot be reduced to a plane problem having a definite 3-D character. The system of partial differential equations used for solving the problem consists of