Cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate

The physical process of cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate is presented by using the second-order perturbation and the technique of nonlinear reflection of acoustic waves at an interface. In general, the cumulative second-harmonic generation of a dispersive guided wave propagation does not occur. However, the present paper shows that the second-harmonic of Lamb wave propagation arising from the nonlinear interaction of the partial bulk acoustic waves and the restriction of the three boundaries of the solid plates does have a cumulative growth effect if some conditions are satisfied. Through boundary condition and initial condition of excitation, the analytical expression of cumulative second-harmonic of Lamb waves propagation is determined. Numerical results show the cumulative effect of Lamb waves on second-harmonic field patterns.

Non-equilibrium turbulent phenomena in transitional flat plate boundary-layer flows

Many recent laboratory experiments and numerical simulations support a non-equilibrium dissipation scaling in decaying turbulence before it reaches an equilibrium state.By analyzing a direct numerical simulation(DNS)database of a transitional boundary-layer flow,we show that the transition region and the non-equilibrium turbulence region,which are located in different streamwise zones,present different non-equilibrium scalings.Moreover,in the wall-normal direction,the viscous sublayer,log layer,and outer layer show different non-equilibrium phenomena which differ from those in grid-generated turbulence and transitional channel flows.These findings are expected to shed light on the modelling of various types of non-equilibrium turbulent flows.

Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel

By method of the Laplace transform, this arti- cle presents semi-analytical solutions for transient electro- osmotic and pressure-driven flows （EOF/PDF） of two-layer fluids between microparallel plates. The linearized Poisson- Boltzmann equation and the Cauchy momentum equation have been solved in this article. At the interface, the Maxwell stress is included as the boundary condition. By numerical computations of the inverse Laplace transform, the effects of dielectric constant ratio e, density ratio p, pressure ratio p, viscosity ratioμ of layer II to layer I, interface zeta potential difference △ψ, interface charge density jump Q, the ratios of maximum electro-osmotic velocity to pressure velocity , and the normalized pressure gradient B on transient veloc- ity amplitude are presented.We find the velocity amplitude becomes large with the interface zeta potential difference and becomes small with the increase of the viscosity. The ve- locity will be large with the increases of dielectric constant ratio; the density ratio almost does not influence the EOF ve- locity. Larger interface charge density jump leads to a strong jump of velocity at the interface. Additionally, the effects of the thickness of fluid layers （hi and h2） and pressure gradient on the velocity are also investigated.

Boundary layer flow over a moving surface in a nanofluid with suction or injection

An analysis is performed to study the heat transfer characteristics of steady two-dimensional boundary layer flow past a moving permeable flat plate in a nanofluid. The effects of uniform suction and injection on the flow field and heat transfer characteristics are numerically studied by using an implicit finite difference method. It is found that dual solutions exist when the plate and the free stream move in the opposite directions. The results indicate that suction delays the boundary layer separation, while injection accelerates it.

A Three-Dimensional Size-Dependent Layered Model for Simply-Supported and Functionally Graded Magnetoelectroelastic Plates

A three-dimensional size-dependent layered model for simply-supported and func- tionally graded magnetoelectroelastic plates is presented based on the modified couple-stress theory. The functionally graded material is assumed to be exponential in the thickness direc- tion of the plate. The final governing equations are reduced to an eigensystem by expressing the extended displacements in terms of two-dimensional Fourier series. Using the propagator matrix method, the exact solutions of the magnetic, electric and mechanical fields of sandwich nanoplates with couple-stress effect and under the surface loads are derived. Numerical examples for two functionally graded sandwich plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to demonstrate the effect of the functional gradient factor and material length-scale parameter on the induced fields. The exact solutions presented in this work can also serve as benchmarks to various numerical methods for analyzing the size-dependent features in layered systems.

GUIDED THERMOELASTIC WAVE PROPAGATION IN LAYERED PLATES WITHOUT ENERGY DISSIPATION

In this paper, the propagation of guided thermoelastic waves in laminated orthotropic plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi （GN） generalized thermoelastic theory （without energy dissipation）. The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The validity of the method is confirmed through a comparison. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement and temperature distributions are shown to discuss the differences between the elastic modes and thermal modes.

Acoustic reflection of rib-stiffened double plates coated with a viscoelastic layer

To predict sound-absorbing performance of anechoic materials,the acoustic reflection problem of a viscoelastic layer backed with periodically rib-stiffened infinite double plates is studied in this paper.The reason why structural theories of plates are not applicable to viscoelastic plates is explained through comparing dispersion and attenuation curves of flexural waves with those of Lamb waves.As a result,（visco-）elastic theory is adopted to deal with（visco-）elastic plates,and ribs are treated by structural theories of plates.The coupling between ribs and plates are solved by Hull＇s method,and solution of the reflected field is obtained.The accuracy of present method is validated by comparing with the results by the structural theories of plates.The influence of a backing on the acoustic reflection of the viscoelatic layer is analyzed by computing reflection coefficients.Performances of different viscoelastic materials are evaluated by the average reflection coefficients.The computational results show that,influence of a backing on the acoustic reflection cannot be suppressed by the viscoelastic materials in low frequencies.The resonance is determined by the coupling of the fluid layer and the double plates.And ribs,which are coupled with the double plates,mainly reduce the acoustic reflection.

The propagation of Lamb waves in an anisotropic plate bordered with liquid layers

Based on elastic wave propagation theory, the dispersion equation for a thin anisotropic plate (such as commonly used Zinc okide in micro-transducers) bordered with liquid layers is derived. Higher symmetry crystals, such as orthorhombic, tetragonal, cubic, isotropic, are included in this analysis as well. For the case of one liquid layer loading, numerical calcu- lations show that the phase velocity changes periodically with the thickness of the liquld layer. When the thickness 2d of the anisotropic plate is very small, mass sensing application of Ao mode Lamb wave is also discussed.

Vibrational power flow analysis on combined plates partially covered layer of discontinuous material

Vibrational power flow on combined plates with a change in mass and stiffness or with viscoelastic damping layer used widely in engineering is studied. The expressions of flexural displacement and other physical quantities are obtained using Laplace transformation and transfer matrix approach, then influences of changes in mass and stiffness of discontinuous material and the free damping layer on the input power flow and the transmitted power flow are discussed. The conclusions provide theory basis for structural optimization design and reducing noise and vibration

Noise radiation of an elastic plate excited by the turbulent boundary layer pressure fluctuations

A unified theory for calculating the noise radiation of an infinite elastic plate excited by the turbulent boundary layer pressure fluctuations is presented . Using the wave number frequency transfer function to desribe the whole system , consisting of the plate and the liquid loading, a general expression of the cross spectrum was derived. It is an integral in the complex wave number plane and leads to a sum of the residues at the poles of two types. One pole introduced by the convective ridge of the pressure fluctuations yields a direct transfer component , which is an evanescent wave in liquid because the pole lies in the high wave number region . The other poles introduced by the transfer function of structure produce the radiation field components with the resonance modes of a liquid loaded plate. The pole positions and their residues can be computed approximately by use of the Resonance Scattering Theory . For the case of hydrodynamic noise, where the range of the frequency-thickness product of interest is relatively low , the symmetric zero-order mode dominates the noise radiation.