Layer Of Viscoelastic Material Research Articles

Beam on Viscoelastic Foundation and Layered Beam

The studies of the free vibration, dynamic response, and static buckling of a layered beam are presented. This layered beam is composed of two identical parallel beams with a viscoelastic-material layer in between. The boundary conditions of these two parallel beams (called the upper and lower beams in the present paper) can be different. The dynamic shape functions and the dynamic-stiffness matrix of such a layered beam are established directly based on the theory of an axially loaded damped Timoshenko beam on a viscoelastic foundation by superposition scheme. The dynamic interactions between these two parallel beams and the viscoelastic layer of a layered beam are emphasized. A simple layered-beam example is included for demonstrations and discussions.

Higher-order mode acoustic radiation from fluid-loaded, multi-layer composite plate

One of the outstanding features of the composite plate is that one can reduce the longitudinal wave (the first symmetrical mode) speed significantly at higher frequencies by intelligently arranging the various layers of elastic and viscoelastic materials. In such cases, however, the higher-order modes shift to a lower frequency region as compared to those of a single-layer elastic plate. Consequently, those higher-order modes may now become susceptible to an excitation band. An exact mathematical formalism was developed to calculate the acoustic radiation of a fluid-loaded, multi-layer composite plate subjected to a harmonic excitation. The formal solution is developed using the classical integral transform technique incorporated with the multilayer elasticity theory. The formalism was validated with the solution of a fluid-loaded, infinite, single-layer elastic plate. Numerical results are then presented for the far-field directivity pressure pattern of various plate configurations subjected to normal- and tangential-line forces. The pressure pattern and in-vacuo dispersion curve of the plate are used to explain radiating mechanisms and evaluate the acoustic significance of the higher-order modes. In addition, the effects of fluid-loading and damping on higher-order supersonic waves are also discussed. [Work supported by ONR.]

Dispersive waves in fluid-loaded, multilayer, composite plates with lossy material

One of the outstanding features of the multilayer composite plate is that it can be tailored for a specific structural-acoustic application by intelligently arranging the various layers of elastic and viscoelastic materials. In this study, the multilayer composite plate under consideration possesses a layer of viscoelastic material with high material loss factor for attenuating the propagating waves. For a fluid-loaded case, certain propagating modes dissipate their energy through radiation into surrounding fluid medium, and decreases in amplitude in the direction of propagation even if no material loss factor is assumed. Study of the wave dispersion of this composite plate indicates that the dispersion characteristics and the mode shape of the propagating wave are affected by the amount of damping in the viscoelastic material. The reasons for the aforementioned effect are discussed. Numerical examples are presented for various plate configurations with the viscoelastic layer given a range of material loss factor. [Work supported by ONR.]

Vibration Control of Conical Shells Using Viscoelastic Materials

The vibration and damping analysis of multi-layered conical shells incorporating layers of viscoelastic materials in addition to elastic ones, the former causing dissipation of vibratory energy, is the subject matter of this paper. The analysis given herein uses Hamilton's variational principle for deriving equations of motion of a general multi-layered conical shell. In view of the correspondence principle of linear viscoelasticity which is valid for harmonic vibrations, the solution is obtained by replacing the moduli of viscoelastic layers by complex moduli. An approximate solution for axisymmetric vibrations of multi-layered conical shells with two end conditions—simply supported edges and clamped edges—is obtained by utilizing the Galerkin procedure. The damping effectiveness in terms of the system loss factor for all families of modes of vibrations for three-, five- and seven-layered shells is evaluated and its variation with geometrical parameters is investigated.

Analysis of the response of damped cylindrical shells carrying discontinuously constrained beam elements

A simple analysis is presented of the forced vibratory response of a cylindrical shell having a number of axial beams adhered to it by a viscoelastic material layer. The attached beams are identical, closely spaced and distributed around the full circumference of the shell. The excitation is a concentrated vibratory force acting radially at the mid-section on the surface of the shell. The end conditions of the shell and the attached beams are all assumed to be simply supported. The effects of the operational temperature and frequency on the viscoelastic material properties are considered. An experiment was conducted, for comparison, on a damped cylindrical shell suspended in air by lightweight elastic shock cords and driven at the mid-section by an electromechanical vibration shaker. Good correlations between the test data and analytical solutions were obtained over a wide range of frequencies.

Damping effects of rectangular viscoelastic sandwich plates.

The effects of in-plane force on the composite loss factor and natural frequency of a rectangular viscoelastic sandwich plate, which is composed of a core layer of viscoelastic material and thin elastic outer layers, are investigated. Assuming the vibratory energy dissipation to take place due to the shear deformation of the viscoelastic layer, the equation of motion and boundary conditions for a rectangular viscoelastic sandwich plate are derived from Hamilton's principle. The value of the composite loss factor of the sandwich plate increases as the in-plane compressive force increases, and decreases as the in-plane tensile force increases. Experiments have been carried out with a square sandwich plate with all edges built-in, subjected to no in-plane forces and to in-plane forces. Good agreement has been found between the experiments and calculations.

Soft Mud Response to Water Waves

Motion within soft mud beds, wave‐induced bed shear stress, and wave attenuation under small amplitude waves are briefly examined using an analytic approach to gain insight into the mechanism by which coastal mud responds to water waves. The cohesive mud bed is discretized into layers of simple linear viscoelastic material characterized by constant density, viscosity, and shear modulus of elasticity, for approximately simulating depth‐varying bed properties as well as energy dissipation. Model results on wave orbital velocities, dynamic pressure, and wave attenuation are compared with limited data from wave flume tests on partially consolidated beds under relatively low deformations and show acceptable agreement. Wave attenuation coefficients exhibit dual dependence on the degree of bed consolidation and sediment composition. In the absence of adequate data on bed shear stress over mobile, partially consolidated mud beds, this method offers an approximate procedure useful for bed shear stress estimation r...

Some acoustic properties of layered‐composite plates

This paper discusses a method of calculating the modes of wave propagation in a composite plate. A composite plate consists of layers of different elastic and/or viscoelastic materials. A novel three‐layer sandwich plate, which utilizes a light weight soft core sandwiched between stiffer septums (to increase flexural rigidity without severe weight or cost penalty), will be closely examined in terms of its antisymmetrical (flexural or bending) and symmetrical (longitudinal or bulge) modes of wave propagation. The dispersion relationship and the coincidence frequency of the flexural wave will be discussed. Effects of fluid loading and some other acoustic properties of the composite plate, such as the transmissibility and reflectivity of sound, will also be discussed.

A proposed method of measuring the complex modulus of a thick viscoelastic layer

A simple, non-destructive method of measuring the complex modulus of a layer of viscoelastic material is proposed. The method relies upon an analysis of the frictionless contact of a rigid smooth indentor and the layer. The contact is maintained by means of a fluctuating normal load. The total load (or the indentation) is required to vary in a simple sinusoidal way. The complex modulus may then be determined from the results of observations made when the contact area is maximum (or minimum).

Composite loss factor of viscoelastic sandwich beams.

The effects of axial force on the composite loss factor and natural frequency of a viscoelastic sandwich beam which is composed of a core layer of viscoelastic material and thin elastic outer layers are investigated. Assuming the vibratory energy dissipation to take place due to the shear deformation of the viscoelastic layer, the equation of motion and boundary conditions for a viscoelastic sandwich beam is derived from Hamilton's principle. The value of the composite loss factor of the sandwich beam increases as the compressive force increases and decreases as the axial tensile force increases. Experiments have been carried out with a cantilever sandwich beam subjected to no axial forces and the fixed ends one subjected to axial force. Good agreement has been found between the experiments and calculations.

The stability of boundary-layer flow over single-and multi-layer viscoelastic walls

In this paper, we are concerned with the linear stability of zero pressure-gradient laminar boundary-layer flow over compliant walls which are composed of one or more layers of isotropic viscoelastic materials and backed by a rigid base. Wall compliance supports a whole host of new instabilities in addition to the Tollmien-Schlichting mode of instability, which originally exists even when the wall is rigid. The perturbations in the flow and the compliant wall are coupled at their common interface through the kinematic condition of velocity continuity and the dynamical condition of stress continuity. The disturbance modes in the flow are governed by the Orr-Sommerfeld equation using the locally-parallel flow assumption, and the response of the compliant layers is described using a displacement-stress formalism. The theoretical treatment provides a unified formulation of the stability eigenvalue problem that is applicable to compliant walls having any finite number of uniform layers; inclusive of viscous sublayer. The formulation is well suited to systematic numerical implementation. Results for single- and multi-layer walls are presented. Analyses of the eigenfunctions give an insight into some of the physics involved. Multi-layering gives a measure of control over the stability characteristics of compliant walls not available to single-layer walls. The present study provides evidence which suggests that substantial suppression of disturbance growth may be possible for suitably tailored compliant walls.

Piecewise constant optimal controls and minimal acoustic transmission

The existence of completely piecewise constant optimal controls in the wide bandwidth, normal incidence, minimal acoustic transmission problem [MIN(γ2)] for layers of viscoelastic materials is examined numerically. It has been found that such solutions exist if the Hamiltonian is linear in the controls and the dynamic compressibility is defined in terms of fractional derivatives which approximate a generalized Maxwell model of the dilatation modulus. The low‐frequency dynamic compressibility and the low‐ to high‐frequency step of the compressibility in the relaxation region are assumed to be the controls. Calculations are presented that show the resulting optimal, multilayered structures. For shallow slopes of the compressibility the optimal controls are partially continuous (singular). As the slope increases, the controls become piecewise constant. Piecewise constant optimal controls are the exception. Their appearance seems to be restricted to relatively simple definitions of the control functions. Their occurrence may also be limited to the MIN(γ2) problem in the set of three basic problems defined by transmission, reflection, and absorption.

The influence of highly stratified dissipative soil on ground motion

AbstractThe influence of the depth and material properties of a sedimentary deposit on earthquake ground motion is examie through theoretical modelling. The strong stratification of a typical deposit is represented by a number of homogene layers of dissipative viscoelastic material. The motion is assumed to be produced by a line source. The calculations carried out by means of a recently developed theoretical technique. The near surface low velocity layers are found to has a very strong amplification effect on the ground motion at some frequencies. The widely used one dimensional approae for site effect evaluation is shown to be valid for smaller epicentral distances only. The deamplification effect of mate dissipation is shown to be extremely important in most cases.

Comparison of constrained layer damping models

The constrained layer damping technique is based on the application of a layer of viscoelastic material onto the surface to be damped and beneath a layer of stiff material. The damping mechanism is dissipation of energy caused by shear motion in the damping layer. An early model for the propagation of straight-crested waves in a constrained plate by Kerwin [J. Acoust. Soc. Am. 31, 952–962 (1959)] uses thin-plate theory for the base plate and is limited to flexural waves. This model was extended to cover extensional as well as flexural waves in thick plates by describing the base plate by exact elasticity theory [P.S. Dubbelday, J. Acoust. Soc. Am. 80, 1097–1102 (1986)]. The present study proposes the formulation of a model based on exact elasticity theory for all three layers. A computer program based on the exact equations for the case of an infinite composite plate in vacuum has been developed. It is used as a basis for comparison of results from previous models and to investigate certain anomalies in the calculated results of those models. [Work supported by the ONR.]

Vibration isolating coupling

A vibration isolating coupling ideally suited for coupling the bobbin (31) of a linear actuator (23) to a flexure supported printer carriage (11) is disclosed. The two main sources of vibration in a system that includes a flexure (13, 15) supported carriage coupled to a linear actuator (23) are low-frequency vibration resulting from the pivot arc motion of the flexures (13, 15), and high frequency vibration resulting from the change in bobbin shape occurs as AC energy is applied to the bobbin (31). The first source of vibration is reduced by configuring the interface plane between the linear actuator and the flexure supported carriage such that contact occurs at spaced apart points located on either side of the flexure movement plane. Preferably, four contact points equally spaced from the flexure motion plane are used. The region between the contact points and the flexure motion plane is cut out so that no contact occurs in and on either side of the flexure motion plane. It is the absence of contact that reduces the first source of vibration. The second source of vibration is reduced by mounting a damping plate (61), preferably comprising a layer of viscoelastic material sandwiched between two layers of steel or some other rigid material, at the interface plane between the linear actuator (23) and the flexure supported carriage (11).

Calculations of turbulent boundary layer pressure fluctuations transmitted into a viscoelastic layer

The objective of this paper is to develop a model for calculating the turbulent boundary layer pressure fluctuation transmitted into a layer of viscoelastic material. The theoretical model used here is a plane elastomer layer backed by a rigid plane surface. The other side of the plane surface is exposed to a turbulent flow. The transmitted flow noise received by a rectangular hydrophone embedded in the elastomer layer was calculated for various turbulent boundary layer forcing functions developed by Corcos, and by Chase. The transmitted flow noise was characterized by the frequency spectral density expressed in decibels. Wave‐vector spectral densities of various turbulent wall pressures were discussed. Effects of the elastomer layer thickness, material properties and flow conditions on the transmitted noise level are presented.

Dynamic response of pipelines to moving loads

AbstractVibration of buried pipelines induced by moving axial and radial loads has been studied in this paper. A thin shell model has been used for the pipeline, which is assumed to be lying in an infinite isotropic homogeneous elastic medium. In order to allow for the possible motion of the pipe out of phase with the surrounding ground a very thin layer of viscoelastic material is assumed to separate the pipe from the ground. Calculations indicate the presence of the interfacial viscoelastic layer does not influence the pipe response in a significant manner. So all the numerical results presented here are for the case when the pipe is assumed to be perfectly bonded. These show that the maximum pipewall displacements and stresses occur in a soft soil at long wavelengths.

Sound reflection from a fluid‐loaded and masked elastic plate

We have extended available computer codes that predict the classical reflections and transmissions of sound fields through sets of plane elastic layers [i.e., D. Folds and C. Loggins, J. Acoust. Soc. Am. 62, 1102–1115 (1977)]. The present layers separate possibly dissimilar fluids, are possibly viscoelastic, and are isonified from one side. The results we display include reflection (R) and transmission (T) coefficients as functions of frequency f and incidence angles θ. This computational tool has been used to predict the reflections from a single fluid‐loaded elastic plate ideally covered with a lossy layer of homogeneous viscoelastic material, isonified from the coated side. Resonances in the coefficients are analyzed in the light of the resonance scattering theory (RST), which has not yet been applied to coated plates. The present model serves to assess the effectiveness of the masking layer to reduce the reflections from the metal plate. The predicted displays of calculations are presented for values of the material parameters in the ranges commonly found in practice. The lossy nature of the absorbing layer complicates the otherwise real parameters present in the analysis, and we quantitatively determine the shifts in resonance locations, the widening of the resonance peaks, and the overall reduction of the returned reflections caused by the masker's viscoelasticity.

Effectiveness of a two‐layer damping treatment partially covering a beam

A damping treatment for an elastic beam consisting of a layer of viscoelastic material beneath an elastic bar is considered. The treatment extends axially over a portion of the beam. Under the assumption of simple end supports and a point force excitation, the vibrational response of the damped structure is analyzed by expanding the beam displacement in a series of normal modes. The normal modes for the bar are taken to be those of a free‐free beam and are therefore coupled to each of the simply supported beam modes. A numerical procedure is used to calculate the modal response of the beam from the system of coupled equations. The damping effectiveness of the partial treatment is determined by evaluating the modal loss factor as a function of the extent of coverage. Several equivalent methods are examined to evaluate conveniently the modal loss factor. An efficient numerical scheme is to evaluate the loss factor using the real and imaginary parts of the damped resonance frequency. The results obtained are interpreted with the aid of asymptotic limits for the loss factor of the damped dynamic vibration absorber, and conclusions regarding sensitivity of damping effectiveness to extent of coverage are drawn.

Transient wave propagation normal to the layering of a finite layered medium

Plane wave propagation in the direction normal to the layering of a periodically layered medium is studied. A period consists of two layers of homogeneous, isotropic, linear elastic or viscoelastic materials. The layered medium is of finite extent and hence consists of a finite number of layers. A theory is presented by which the layered medium is replaced by an “equivalent” linear homogeneous viscoelastic material such that the stress or the velocity in the latter and in the layered medium are identical at the centers of the alternate layers. Transient waves in the layered medium are then obtained by solving the transient waves in the “equivalent” homogeneous viscoelastic medium. Solutions at points other than the centers of the alternate layers are also presented. Numerical examples are given for transient waves in an elastic layered medium due to a step load applied at one of the boundary while the other boundary is fixed. Comparisons with the exact solutions by the ray theory show that the present theory can predict very satisfactorily transient waves in a finite layered medium.