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The grid structure is widely used in architectural and mechanical field for its high strength and saving material. This paper will present a study on an acoustic metamaterial beam (AMB) based on the normal square grid structure with local resonators owning both flexible band gaps and high static stiffness, which have high application potential in vibration control. Firstly, the AMB with variable cross-section frame is analytically modeled by the beam–spring–mass model that is provided by using the extended Hamilton’s principle and Bloch’s theorem. The above model is used for computing the dispersion relation of the designed AMB in terms of the design parameters, and the influences of relevant parameters on band gaps are discussed. Then a two-dimensional finite element model of the AMB is built and analyzed in COMSOL Multiphysics, both the dispersion properties of unit cell and the wave attenuation in a finite AMB have fine agreement with the derived model. The effects of design parameters of the two-dimensional model in band gaps are further examined, and the obtained results can well verify the analytical model. Finally, the wave attenuation performances in three-dimensional AMBs with equal and unequal thickness are presented and discussed.

This paper deals with the axisymmetric acoustic wave propagating along the perfect gas in the presence of a uniform flow confined by a rigid-walled pipeline. Under the linear acoustic assumption, mathematical formulation of wave propagation is deduced from the conservations of mass, momentum and energy. Meanwhile a method based on the Fourier–Bessel theory is introduced to solve the problem. Comprehensive comparisons of the phase velocity and wave attenuation between the non-isentropic and isentropic acoustic waves are provided. Meanwhile the effects of flow profile, acoustic frequency, and pipeline radius are analyzed.

Random wave transformations with breaking in shallow water of 2-D bathymetry are computed with the parabolic equation. A new system of gradational breaker index, the value of which gradually decreases as the level of wave height within a wave group is lowered, is introduced to simulate gradual shape variations of wave height distribution in the surf zone. Wave attenuation in the trough area of a barred beach is treated with a secondary gradational breaker index, which is applied for locations in water of constant or increasing depth. Its empirical coefficients are assigned values different from those in water of decreasing depth. The wave attenuation factor due to bottom friction is formulated by evaluating the rate of energy dissipation by shear stress along the sea bottom. Computation is made for directional spectral components with multiple levels of wave heights under the Rayleigh distribution, and the results are synthesized for the calculation of wave height distributions. The new computational scheme succeeds in reproducing the random wave breaking diagrams by Goda (1975), and shows good agreements with several experimental results on wave transformations over horizontal shelves, barred beaches, and an elliptical shoal. The scheme also yields wave height predictions in good agreement with several field measurements across the surf zone.

This note marks the debut of a Mathcad worksheet, which has been developed to aid engineers in the calculation of properties of a surface wave propagating in water over a two-layer viscoelastic muddy bed. We first describe the problem formulation and then features of the worksheet. It is a very easy-to-use calculation tool. With the input of some basic parameters, such as the wave period and the fluid properties, one may get almost instantly the key results (wavenumber, wave damping rate, velocity and pressure fields, and so on) upon pressing a key. The worksheet has been extensively tested to ensure that it can produce reliable and accurate results.

Waves measured at a few locations along the west coast of India were analyzed to study modification and attenuation of wave energy in the nearshore regions. It has been found that the reduction in wave height is relatively lower (less than 10%) between two nearshore depths off Goa (25 m and 15 m) and Ratnagiri (35 m and 15 m), central west coast of India and is higher (22%) off Dwarka (30 m and 15 m), northwest coast of India. It is observed that the diurnal variation in waves decreases from north to south along the coast, as the intensity of sea breeze decreases from north to south. Swell attenuation due to opposing winds (from NE) is observed along the Ratnagiri coast during NE monsoon. The growth of wind seas (from NE) towards offshore and their modification by opposing swells (from SW/SSW) significantly contributed to the reduction in wave heights at shallow water depths off Dwarka. The role of opposing winds in the attenuation of swells along the west coast of India during NE monsoon season is significant. Numerical simulations were carried out to study the wave transformation between the depths 100, 50, 20, 10 and 5 m off Mumbai, Goa and Kochi. Diurnal variation is evident during the pre-monsoon season, and the magnitude of variation decreases from north to south.

Guided modes admissible in elastic hollow pipes are derived to establish their dispersion and attenuation characteristics in the presence of multi-layered viscoelastic coatings. Longitudinal waves propagating in the axial direction in response to displacement continuity boundary conditions signifying perfect interfacial bonds are evaluated against a baseline uncoated tubing. Viscoelastic bitumen and epoxy are coating materials applied to improve pipeline reliability. The impact of viscoelastic coating layers on wave dispersion and attenuation are investigated by incorporating complex material properties in the characteristic equation. The real and complex roots of the corresponding characteristic equation are determined, allowing the phase velocity and attenuation dispersion to be depicted as functions of the propagation frequency. The effects of varying attenuation parameter and coating thickness are also examined. Viscoelastic protective materials are found to have a substantial impact on the propagation and attenuation of longitudinal waveguide modes.

The extreme surges and waves generated in tsunamis can cause devastating damages to coastal infrastructures and threaten the intactness of coastal communities. After the 2004 Indian Ocean tsunami, extensive physical experiments and numerical simulations have been conducted to understand the wave attenuation of tsunami waves due to coastal forests. Nearly all prior works used solitary waves as the tsunami wave model, but the spatial-temporal scales of realistic tsunamis differ drastically from that of solitary waves in both wave period and wavelength. More recent work has questioned the applicability of solitary waves and been looking towards more realistic tsunami wave models. Therefore, aiming to achieve more realistic and accurate results, this study will use a parameterized tsunami-like wave based on wave observations during the 2011 Japan tsunami to study the wave attenuation of a tsunami wave by emergent rigid vegetation. This study uses a high-resolution numerical wave tank based on the non-hydrostatic wave model (NHWAVE). This work examines effects of prominent factors, such as wave height, water depth, vegetation density and width, on the wave attenuation efficiency of emergent rigid vegetation. Results indicate that the vegetation patch can dissipate a considerable amount of the total wave energy of the tsunami-like wave. However, the tsunami-like wave has a higher total wave energy, but also a lower wave energy dissipation rate. Results show that using a solitary instead of a tsunami-like wave profile can overestimate the wave attenuation efficiency of the coastal forest.

In this study, a numerical model was employed to determine the optimal location for vegetation as an environmentally friendly method of attenuating tsunami waves. The governing equations are shallow water equations solved using shock-capturing schemes with second-order accuracy model. This simulation was validated using experimental data and another numerical model for simulating the propagation of tsunami waves on a vegetated horizontal bed and vegetated sloping beach. The parameters of wave damping rate, maximum velocity, and height for the plant area at various locations and vegetation zone lengths were investigated using numerical models. By increasing the length of the plant zone, the height and velocity of the tsunami wave were reduced, and the wave damping was increased. The examination of various locations and lengths of the plant area demonstrated that the plant area’s distance from the shoreline is a significant factor in coastal protection. The results exhibit that the location of the forest area has a great impact on the control of destructive factors along the beach. As a result, this study provides some information for designing a tsunami-resistant forest area.

Theoretical and laboratory studies are performed to analyze the wave attenuation phenomenon over fluid mud under current. In the theoretical part, a semi-empirical formula is derived to model the attenuation process under current. Based on the linear wave theory, the change of wave amplitude is related with the averaged damping effect of the muddy bed. By solving a differential equation, the exponential decay of the wave amplitude is confirmed. A function called damping function is used in the formula, and it is expanded into a series of wave parameters and some undetermined coefficients called auxiliary damping factors. Based on the assumption that the mud properties do not change under current, the formula is combined with the dispersion relation for linear wave under uniform current to describe the attenuation process under current. Laboratory experiments are conducted first without current. The data of wave attenuation are collected and inserted to the formula obtained in the theoretical analysis to figure out the values of the auxiliary damping factors. The second set of experiments is conducted under current and the collected data are compared with the calculated values obtained by using the newly proposed formula with the dispersion relation. The result of comparison shows good applicability of the new formula to the wave attenuation under current.

In this paper, we discuss the applicability of a numerical wave channel CADMAS-SURF/3D with regard to hydrodynamics on a salt marsh by comparing numerical experimental results with previous studies for both flow and wave conditions. The present results indicate that the model is promising as long as appropriate values for numerical parameters such as the grid size are used. We present results for the bottom velocity and turbulence kinetic energy around a cylinder which are important understanding deposition in salt marsh vegetations. Furthermore, this paper shows that the drag coefficient and inertia coefficient for circular cylinders in waves depend on the density of the cylinders.