Stability of supersonic boundary layer on a porous plate with a flexible coating

The development of disturbances in the boundary layer of compressible gas on a flexible surface has been investigated in the linear and nonlinear approximations (the weakly nonlinear stability theory). The regimes of moderate (the Mach number M = 2) and high (M = 5.35) supersonic velocities as well as a model of a porous wall, on which a flexible film is spanned, have been considered. The boundary conditions for disturbances with regard for their transformation by a flexible porous coating have been derived. The character of the variation of the coefficients of the stream-wise growth of linear oscillations of different nature (the vortex waves of the first mode and the acoustic waves of the second mode) is shown. The direction and the degree of their deformations are determined by the flexible coating parameters. It is found that at moderate Mach numbers, the stabilization of disturbances and the diminution of increments occur, whereas at high M on a surface with a film, the acoustic components are destabilized, which may lead to an earlier onset of nonlinear processes. The nonlinear interactions in three-wave symmetric triplets between the vortex waves at M = 2 and between the waves of different nature at M = 5.35 are considered. In the latter case, the plane acoustic wave is the pumping wave, which excites the three-dimensional subharmonic components of vortex nature.     

Vibration and damping analysis of annular plates with constrained damping layer treatments

The natural frequencies and modal loss factors of annular plates with fully and partially constrained damping treatments are considered. The equations of free vibration of the plate including the transverse shear effects are derived by a discrete layer annular finite element method. The extensional and shear moduli of the viscoelastic material layer are described by the complex quantities. Complex eigenvalues are then found numerically, and from these, both frequencies and loss factors are extracted. The effects of viscoelastic layer stiffness and thickness, constraining layer stiffness and thickness, and treatment size on natural frequencies and modal loss factors are presented. Numerical results also show that the longer constrained damping treatment in radial length does not always provide better damping than the shorter ones.     

Effect of acoustical damping with a porous absorptive layer in the cavity to reduce the structure-borne sound radiation from a double-leaf structure

Structure-borne sound radiation from a double-leaf structure with a porous absorptive layer in the cavity is studied theoretically as well as experimentally. The study is for establishing a countermeasure to reduce the structure-borne noise radiated from an interior leaf into rooms and for clarifying its reduction effect. The sound field radiated from a double-leaf elastic plate with layers of arbitrary media in the cavity set into vibration by a point force excitation is theoretically analyzed. The effect of the bulk vibration of an absorptive layer is also considered by a simple model into the present theory. Radiation reduction of an inner-layer derived from the theory is experimentally validated. Parametric studies reveal that increasing the ratio of an absorptive layer thickness to the cavity depth is effective to reduce the structure-borne sound radiation but high flow resistivity of the absorbent material is not necessarily required. A practical equation to predict the mass-air-mass resonance frequency for absorbent cavity case is given in a simple form.     

Constrained layer damping with vitreous enamel

The concept of constrained layer damping with vitreous enamel has been experimentally evaluated. The constraining layer markedly broadens the free layer damping peak. The broadening has been explained on the basis of two simultaneous energy dissipation mechanisms and is related to the vitreous enamel's loss factor and viscosity.     

Dynamic stability of a rotating beam with a constrained damping layer

The dynamic behavior and dynamic instability of the rotating sandwich beam with a constrained damping layer subjected to axial periodic loads are studied by the finite element method. The influences of rotating speed, thickness ratio, setting angle and hub radius ratio on the resonant frequencies and modal system loss factors are presented. The regions of instability for simple and combination resonant frequencies are determined from the Mathieu equation that is obtained from the parametric excitation of the rotating sandwich beam. The regions of dynamic instability for various parameters are presented.     

An enhanced beam model for constrained layer damping and a parameter study of damping contribution

An enhanced analytical model is presented based on an extension of previous models for constrained layer damping (CLD) in beam-like structures. Most existing CLD models are based on the assumption that shear deformation in the core layer is the only source of damping in the structure. However, previous research has shown that other types of deformation in the core layer, such as deformations from longitudinal extension and transverse compression, can also be important. In the enhanced analytical model developed here, shear, extension, and compression deformations are all included. This model can be used to predict the natural frequencies and modal loss factors. The numerical study shows that compared to other models, this enhanced model is accurate in predicting the dynamic characteristics. As a result, the model can be accepted as a general computation model. With all three types of damping included and the formulation used here, it is possible to study the impact of the structure's geometry and boundary conditions on the relative contribution of each type of damping. To that end, the relative contributions in the frequency domain for a few sample cases are presented.     

Experimental determination of damping of plate vibrations in a viscous fluid

A method of determining the aerodynamic-drag coefficient of flat vibrating plates from the vibrogram of free damping vibrations of cantilever-fixed duralumin samples has been developed. From the results of our experiments, simple approximating formulas determining the decrement of damping vibrations and the aerodynamic-drag coefficient through the dimensionless vibration amplitude and the Stokes parameter are proposed. The approach developed in this study for determining the aerodynamic-drag coefficient of a vibrating plate can be a useful alternative to purely hydrodynamic methods of finding the drag of vibrating solids.     

Interaction of acoustic waves with porous layer

Interaction of sound impulse with porous layer is investigated. The presence of a barrier shielded by the layer and the gap between the porous layer and the barrier is possible. Method of calculation in linear approximation of pressures and tensions in the porous layer, gap, and on the barrier has been proposed. The method serves to interpret data on acoustic waves interaction with porous layer obtained experimentally or with the use of finite-difference methods. Specifics of acoustic wave propagation into the porous layer and further reflection from the barrier has been studied. Comparison of calculation data with experimental data of other authors on impulse propagation through the porous plate submerged in water has been carried out.     

Thermoelastic damping in micro-scale circular plate resonators

The governing equations of coupled thermoelastic problems are established for out-of-plane vibration of a circular plate. The analytical expression for thermoelastic damping is obtained. Then the thermoelastic damping is studied under different environmental temperature, plate dimensions and boundary conditions.     

Dynamic stability of a sandwich plate with a constraining layer and electrorheological fluid core

The dynamic stability problems of a sandwich plate with a constraining layer and an electrorheological (ER) fluid core subjected to an axial dynamic force are investigated. The rectangular plate is covered in an ER fluid core and a constraining layer to improve the stability of the system. Effects of the natural frequencies, static buckling loads, and loss factors on the dynamic stability behavior of the sandwich plate are studied in the paper. Rheological property of an ER material, such as viscosity, plasticity, and elasticity may be changed when applying an electric field. The modal damper and the natural frequencies for the sandwich plate are calculated for various electric fields. When an electric field is applied, the damping of the system is more effective. In this study, finite element method and the harmonic balance method are used to calculate the instability regions of the sandwich plate. The ER fluid core is found to have a significant effect on the dynamic stability regions.     

Sensor properties of structures with porous silicon layer

We have measured at room temperature current-voltage and noise characteristics of structures with a porous silicon (porosity 80%) layer at adsorption of gases ammonia, propane and butane mixture, and ethyl alcohol vapor. It was obtained that the largest change in CVC and low-frequency noise is observed under action of ammonia gas on the structure. Physical reasons of sensor properties of studied samples are discussed.     

The attenuation of the higher-order cross-section modes in a duct with a thin porous layer

A numerical method for sound propagation of higher-order cross-sectional modes in a duct of arbitrary cross-section and boundary conditions with nonzero, complex acoustic admittance has been considered. This method assumes that the cross-section of the duct is uniform and that the duct is of a considerable length so that the longitudinal modes can be neglected. The problem is reduced to a two-dimensional (2D) finite element (FE) solution, from which a set of cross-sectional eigen-values and eigen-functions are determined. This result is used to obtain the modal frequencies, velocities and the attenuation coefficients. The 2D FE solution is then extended to three-dimensional via the normal mode decomposition technique. The numerical solution is validated against experimental data for sound propagation in a pipe with inner walls partially covered by coarse sand or granulated rubber. The values of the eigen-frequencies calculated from the proposed numerical model are validated against those predicted by the standard analytical solution for both a circular and rectangular pipe with rigid walls. It is shown that the considered numerical method is useful for predicting the sound pressure distribution, attenuation, and eigen-frequencies in a duct with acoustically nonrigid boundary conditions. The purpose of this work is to pave the way for the development of an efficient inverse problem solution for the remote characterization of the acoustic boundary conditions in natural and artificial waveguides.     

Electrical characterization of plate piezoelectric transducers bonded to a finite substrate

This article presents a new technique for characterizing piezoelectric transducers attached to a finite substrate. It consists of determining the impedance of the transducer cleared of the effects caused by finite dimensions of the substrate. This technique is validated by comparison with measurements on a transducer mounted on an effectively half-infinite substrate. It is applied for the electrical matching of a lithium niobate plate transducer bonded to a fused quartz rod.     

Visco-acoustic modelling of a vibrating plate interacting with water confined in a domain of micrometric size

It is well established that concrete durability strongly depends on the capillary porosity of the material. Hence, structural health monitoring of concrete structure could take advantage of concrete microporosity monitoring. To this end, a new method for the in situ non-destructive testing of capillary porosity in cementitious materials has been proposed. A sensing device that seems well suited to this application is a capacitive ultrasonic transducer with a characteristic size of $1\mathrm{\mu }\mathrm{m}$. It is to be embedded in the material. Its vibrating membrane is made of aligned carbon nanotubes forming a thin layer with a typical thickness of 1 nm. It generates acoustic waves of micrometric wavelength into water-filled micropores, aiming at measuring their properties.The present paper focuses on the numerical simulation of the embedded sensor. In order to properly account for viscous effects in fluids at the micrometric scale, we have developed a specific computational method for the visco-acoustic modelling of a microplate vibrating between 10 MHz and 2 GHz in a water-filled domain of micrometric size. Our approach is based on the condensation of the fluid part of the fluid–structure problem on the structure by a finite element method, and on a spectral approximation of the structural equations.The numerical results indicate that the fluid domain is resonant despite the viscous terms, which causes a frequency downshift of the resonances and a decrease of the quality factor. In the coupled system, the plate does not perturb the fluid resonances, whereas the plate resonances are strongly upshifted by the water load. The resonance frequencies of the system are shown to display a clear dependence on the pore width, which makes the device a good candidate as a porosity sensor.     

Turbulent boundary layer over a flat plate with uniform wall suction

A complete theory of turbulent boundary layer flow over a flat plate with uniform wall suction is proposed. The theory relies on an asymptotic analysis of the Reynolds equations and dimensional considerations and does not involve any special closure hypotheses. Characteristics of the turbulent boundary layer with suction are calculated for the entire range of flow parameters by using the known characteristics of a reference flow (turbulent boundary layer over an impermeable flat plate). The velocity and shear stress profiles, the distribution of skin friction along the plate, and integral flow characteristics are obtained by using only the known velocity profile in the reference flow. The normal Reynolds stresses are calculated by using analogous characteristics of the reference flow. Results are presented in terms of scaling variables.     

Unsteady flow of a viscous incompressible fluid past a porous plate with constant suction

An exact solution of the flow of an incompressible viscous fluid past an infinite porous plate has been derived on taking into account a step-change in suction velocity. It has been observed that the skin-friction decreases with increasingS, the suction parameter.     

Fluctuating hydromagnetic flow through a porous medium bounded by an oscillatory porous plate

The two-dimensional flow of an incompressible, viscous electrically conducting fluid through a porous medium bounded by an infinite porous plate and subject to a uniform external magnetic field is treated. The mean velocity, the fluctuating parts of the velocity, the transient velocity, the amplitude and the phase of the skin friction, and the wall temperature are shown graphically and followed by discussions.Notation x, y, z cartesian coordinates - density - p pressure - kinetic viscosity - u, v velocity components - electrical conductivity - K permeability of the porous medium - H ₀ applied magnetic field - B ₀ magnetic induction (=H ₀) - magnetic permeability - fraquency of fluctuations - t time - T temperature - T temperature at the boundary layer - k thermal conductivity - C _p specific heat - P Prandtl number - E Eckert number The authors remain thankful to the referee for his valuable comments for the improvement of the paper.     

Heat and mass transfer of MHD convective boundary layer flow past a stretching porous wall embedded in a porous medium

The hydromagnetic convective boundary layer flow past a stretching porous wall embedded in a porous medium with heat and mass transfer in the presence of a heat source and under the influence of a uniform magnetic field is studied. Exact solutions of the basic equations of motion, heat and mass transfer are obtained after reducing them to nonlinear ordinary differential equations. The reduced equations of heat and mass transfer are solved using a confluent hypergeometric function. The effects of the flow parameters such as a suction parameter (N), magnetic parameter (M), permeability parameter (K _p ), wall temperature parameter (r), wall concentration parameter (n), and heat source/sink parameter (Q) on the dynamics are discussed. It is observed that the suction parameter appears in the boundary condition ensuring the variable suction at the surface. Transverse component of the velocity increases only when magnetic field strength exceeds certain value, but the thermal boundary layer thickness and concentration distribution increase for all values. Results presented in this paper are in good agreement with the work of the previous author and also in conformity with the established theory.