Viscoelastic Foundation Research Articles

Analytical solution for vibrations of a curved tunnel on viscoelastic foundation excited by arbitrary dynamic loads

The paper proposes a new analytical solution for the dynamic response of a curved tunnel resting on a viscoelastic foundation subjected to dynamic loads in arbitrary forms. For the derivation, the governing differential equations and boundary conditions of the problem are established based on the Hamilton principle and the dynamic equilibrium theory. The modal superposition method is employed to obtain the explicit formulations of tunnel response, including deflection, velocity, acceleration, bending moment and shear force. The proposed solution is verified by providing comparisons between its results and those from the Finite Element program ABAQUS. Further parametric analysis explore the influence of radius of curvature and soil-structure relative stiffness ratio on the dynamic response of the tunnel. The proposed solution can be used by practitioners for the design of curved tunnels or pipelines.

Stress analysis of adhesively-bonded single stepped-lap joints based on three-parameter fractional viscoelastic foundation model

This paper aims to develop a viscoelastic analytical model for adhesively bonded single stepped-lap joints subjected to tensile loading. The adherends are aluminum alloy A6063 and modeled as Timoshenko elastic beams and the adhesive is epoxy type B. A three-parameter fractional viscoelastic foundation (3PFVF) model is proposed to express the governing stresses in the joint and the fractional Zener model is used to model the viscoelastic behavior of the adhesive layer. The proposed 3PFVF model makes it possible to have different peel stresses between the two interfaces of adhesive and adherends. The governing differential equations are derived in the Laplace domain, and then solved and transformed simultaneously in the time domain using the Gaver-Stehfest inverse Laplace transform method. The finite element simulation with ANSYS is applied to validate the proposed method. The results show that a simple fractional viscoelastic model, which has a short differential equation, offers the same results as the classical viscoelastic models, which have higher and more complex differential equations. Moreover, the results show that the maximum shear and peel stresses in the single stepped-lap joints are about 20% less than single-lap joints.

Normal Impact of A Rigid Cone-shaped against A Viscoelastic Plate on Viscoelastic Foundation

This paper considers the problem of a low-velocity normal impact of a rigid cone-shaped upon a viscoelastic plate. The contact force is defined by the modified Hertz's contact law. Approximate solutions of the system of nonlinear integro-differential equations for the contact force and local indentation have been obtained.

Wave propagation and free vibration of FG graphene platelets sandwich curved beam with auxetic core resting on viscoelastic foundation via DQM

Wave propagation and free vibration of FG graphene platelets sandwich curved beam with auxetic core resting on viscoelastic foundation via DQM

On numerical stability analysis of fluid flows in compliant pipes of elliptic cross-section

The temporal linear stability of the Poiseuille flow in an infinite pipe of uniform elliptic cross-section with a compliant wall is numerically investigated in a broad range of the problem parameters. The pipe wall is modeled as a thin elastic shell, which can be surrounded by viscoelastic foundation; the latter is considered as a distributed set of springs and dampers. In particular, it is shown that the influence of the pipe cross-sectional aspect ratio on the flow stability is significant and nontrivial. An increase in the aspect ratio can enhance or suppress the growth of disturbances depending on both their streamwise wavenumber and the symmetry with respect to the cross-sectional axes.

Transverse Response of an Axially Moving Beam with Intermediate Viscoelastic Support

This study presented the transverse vibration of an axially moving beam with an intermediate nonlinear viscoelastic foundation. Hamilton’s principle was used to derive the nonlinear equations of motion. The finite difference and state-space methods transform the partial differential equations into a system of coupled first-order regular differential equations. The numerical modeling procedures are utilized for evaluating the effects of parameters, such as axial translation velocity, flexure rigidities of the beam, damping, and stiffness of the support on the transverse response amplitude and frequencies. It is observed that the dimensionless fundamental frequency and magnitude of axial speed had an inverse correlation. Furthermore, increasing the flexure rigidity of the beam reduced the transverse displacement, but at the same instant, fundamental frequency rises. Vibration amplitude is found to be significantly reduced with higher damping of support. It is also observed that an increase in the foundation damping leads to lower fundamental frequencies, whereas increasing the foundation stiffness results in higher frequencies.

Influences on the Seismic Response of a Gravity Dam with Different Foundation and Reservoir Modeling Assumptions

The seismic design and dynamic analysis of high concrete gravity dams is a challenge due to the dams’ high levels of designed seismic intensity, dam height, and water pressure. In this study, the rigid, massless, and viscoelastic artificial boundary foundation models were established to consider the effect of dam–foundation dynamic interaction on the dynamic responses of the dam. Three reservoir water simulation methods, namely, the Westergaard added mass method, and incompressible and compressible potential fluid methods, were used to account for the effect of hydrodynamic pressure on the dynamic characteristics and seismic responses of the dam. The ranges of the truncation boundary of the foundation and reservoir in numerical analysis were further investigated. The research results showed that the viscoelastic artificial boundary foundation was more efficient than the massless foundation in the simulation of the radiation damping effect of the far-field foundation. It was found that a foundation size of 3 times the dam height was the most reasonable range of the truncation boundary of the foundation. The dynamic interaction of the reservoir foundation had a significant influence on the dam stress.

Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic–metal plate in a hygrothermal environment

This study presents the buckling response of functionally graded (FG) “sandwich plate” on a viscoelastic foundation and exposed to hygrothermal conditions. An accurate solution is developed using higher-order shear deformation theory (HSDT), with only four unknowns being placed to reach the solution. The displacement fields first utilize an indeterminate integral accompanied by a sinusoidal shape function to simulate the transverse shear deformation theory. The foundation’s mathematical model followed the two-Pasternak coefficient model, with one more term being added to represent the damping effect. The sandwich plate is essentially composed of three layers. This study presented three different FG sandwich plate geometric analytical solutions regarding layer orders and composition. The equations of motion were generated according to Hamilton’s principle. Thereafter, the analytical solution was based on Navier’s principle to solve the buckling temperature of a simply supported FG sandwich plate seated on a viscoelastic foundation. This paper shows a parametric study of the effect of the damping coefficient along with the aspect ratio, moisture condition, power-law index, and temperature variation over the buckling temperature of the FG “sandwich plate” on the viscoelastic foundation.

Numerical Study of Thermal Effect on the Stability of Carbon Nanotubes Resting on a Viscoelastic Foundation Subjected to Magnetic Field

Carbon nanotubes (CNTs) have emerged as efficient tools in drug delivery systems; therefore, it is essential to refer to the importance of the magnetic field, in addition to the fluid flow on the dynamic behavior of CNTs. Additionally, in such medical applications, the actual working environment of nanotube often contains temperature changes, and CNTs are surrounded by soft tissues with viscoelastic mechanical properties. In this study, the vibrational behavior of CNTs conveying magnetic-fluid flow and resting on a viscoelastic foundation is investigated under various temperature variations. To incorporate the influence of slip velocity at the nanoscale, a correction factor is employed on the basis of the Beskok–Karniadakis model. The nanotube is modeled by the Euler–Bernoulli beam theory, and governing equations of motion are derived by implementing Hamilton’s principle based on Eringen’s nonlocal elasticity theory. Results indicate that by applying a magnetic field with an intensity of 30[Formula: see text]T, the dimensionless critical flow velocity increases from 4.345 to 12.603. Also, the critical flow velocity shows an increase from 4.345 to 5.854 in the presence of a viscoelastic foundation. Furthermore, a temperature variation equal to 20[Formula: see text]K reduces the critical flow velocity dramatically from 4.345 to 1.802 at low temperatures, while an increase from 4.345 to 5.443 is observed at high temperatures. Consequently, while the magnetic field and the viscoelastic foundation affect the system stability, the temperature variation may improve or deteriorate the stability. Therefore, to plan for a medical application, the inclusion of temperature variation is required.

Dynamic Response of Bi-Directional Functionally Graded Materials (BDFGMs) Beams Rested on Visco-Pasternak Foundation Under Periodic Axial Force

Since the temperature or stress distribution in some advanced machines such as modern aerospace shuttles and craft develops in two or three directions, the need for a new type of FGMs is felt whose properties vary in two or three directions. On the other hand, dynamic buckling behavior of structures is a complicated phenomenon which should be investigated through the response of equations of motion. In this paper, dynamic response of beams composed of bi-directional functionally graded materials (BDFGMs) rested on visco-Pasternak foundation under periodic axial force is investigated. Material properties of BDFGMs beam vary continuously in both the thickness and longitudinal directions based on the two types of analytical functions (e.g. exponential and power law distributions). Hamilton's principle is employed to derive the equations of motion of BDFGMs beam according to the Euler-Bernoulli and Timoshenko beam theories. Then, the generalized differential quadrature (GDQ) method in conjunction with the Bolotin method is used to solve the differential equations of motion under different boundary conditions. It is observed that a good agreement between the present work and the literature result. Various parametric investigations are performed for the effects of the gradient index, length-to-thickness ratio and viscoelastic foundation coefficients on the dynamic stability region of BDFGMs beam. The results show that the influence of gradient index of material properties along the thickness direction is greater than gradient index along the longitudinal direction on the dynamic stability of BDFGMs beam for both exponential and power law distributions.

An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects

An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects

Dynamic interaction and instability of two moving proximate masses on a beam on a Pasternak viscoelastic foundation

The study analyzes the dynamic interaction of proximate masses using a new form of semi-analytical results for the moving mass problem developed by the author. This paper presents the results for a particular case of two moving masses of equal value acted upon by constant forces of equal values. The interaction level was demonstrated to be substantially high, making it impossible to superimpose the results obtained for one mass unless the masses were located at a significantly large distance apart. In the undamped case, the onset of instability occurred at the critical velocity, as with one moving mass; however, the onset of instability could be shifted significantly into the subcritical velocity range in the damped case. The critical distance between the moving masses was determined as the value at which the exponential increase in the amplitudes was severe. The implementation of dimensionless parameters revealed that this distance was slightly dependent on the damping. Moreover, the limiting moving mass ratio for such unexpected instability was derived.The results were validated by eigenmode expansion analysis on long finite beams, for which computational time savings were proposed by the rearrangement of the terms involved. Excellent agreement between the results was obtained, validating the new formulae. Furthermore, extension to more general cases and additional moving masses can easily be achieved.

Stability and Dynamics of a Slightly Curved Viscoelastic Pipe Resting on Linear and Nonlinear Viscoelastic Foundation

Stability and Dynamics of a Slightly Curved Viscoelastic Pipe Resting on Linear and Nonlinear Viscoelastic Foundation

Vibration analysis of sandwich beam with honeycomb core and piezoelectric facesheets affected by PD controller

Free vibration analysis of a sandwich beam with honeycomb core and piezoelectric face sheets, which is rested on the viscoelastic foundation is investigated. The thermal environment and the electric field are applied to this structure. Also, it is affected by the proportional-derivative (PD) controller. The amount of gain in this controller can affects the vibration frequency. The displacement components are expressed by improved high-order sandwich panel theory (IHSAPT) that considers continuity conditions for transverse shear stress at the interfaces and the zero transverse shear stresses conditions on the upper and lower surfaces of the beam and core flexibility. The motion equations are derived and solved by Hamilton's principle and Navier's method, respectively. This paper examines the effects of various parameters, such as the internal aspect ratio and the cell angle/thickness of the honeycomb core, temperature variations, viscoelastic environment, electric load, and control gain on its natural frequencies. The results show when the honeycomb core's to face sheet's thickness ratio increases, the beam dimensionless frequency increases, too. Also, by increasing the internal aspect ratio of honeycomb core, the frequency of sandwich beam decreases. The results of this study can be used to vibration control in aerospace engineering and constructions.

Computer modeling for frequency performance of viscoelastic magneto-electro-elastic annular micro/nanosystem via adaptive tuned deep learning neural network optimization

The presented paper is the first attempt to apply deep learning for predicting the frequency characteristics of a magneto-electro-elastic (MEE) annular nano/microdisk (MEEAD). The optimum amount of the factors participating in the mechanism of the fully connected neural network are achieved through the optimizer based on the momentum. The positive side of the mentioned approach employed in this investigation would be due to its high accuracy along with lower epochs required for training the multi-layered network. This scrutinization would be semi-computational research that estimates the vibrational behavior of a MEEAD employing a non-classical continuum model known as the modified couple stress (MCS) model. First-order shear deformation theory (FSDT) and shell model would be provided for presenting their displacement fields. Then, Kelvin-Voight theory has been applied to model the viscoelastic foundation. Its non-classical governing equations, as well as related boundary conditions (BCs) of small-scaled MEEAD, would be achieved by considering the symmetric spinning gradient along with higher-order stress tensors for the strain energy. The provided non-classical theory would be able to capture the small scale in the MEEAD employing just one length scale of a material factor, then, the mathematical modeling of MEEAD according to the classical theory would be able to be recovered from the provided model by eliminating the material length scale factor. Ultimately, the non-classical governing equations would be solved by applying the generalized differential quadrature (GDQ) approach for multifarious BCs. Moreover, parametric research has been conducted to analyze the influences of the viscoelastic foundation, length scale factor, geometry of MEE, radial and circumferential mode number, radius ratio, and BCs on the frequency behavior of the MEEAD by applying MCST. The outcomes reveal that there would be a crucial radius ratio in which the relationship between these elements and crucial inserted voltage alters from direct to indirect relation.

Nonlinear free and forced vibration of carbon nanotubes conveying magnetic nanoflow and subjected to a longitudinal magnetic field using stress-driven nonlocal integral model

In this paper primary and secondary resonance of carbon nanotube conveying magnetic nanofluid and subjected to a longitudinal magnetic field resting on viscoelastic foundation with different boundary conditions is investigated. To investigate the small scale effects, stress driven nonlocal integral model has been used and to show the more correctness of stress driven nonlocal integral model response, in studying the behavior of carbon nanotube with different boundary conditions, its results are compared with strain gradient model. The governing partial differential equations are derived from the Bernoulli–Euler beam theory utilizing the von Kármán strain–displacement relations. Using the Galerkin method, the governing equations are reduced to a nonlinear ordinary differential equation. The nonlinear natural frequencies are obtained from the perturbation method and the divergence and flutter instability due to the increase in nanofluid velocity is investigated. Then the frequency response for primary, subharmonic and superharmonic resonance is obtained using the method of multiple scales.Finally, the effects of length small scale parameters, longitudinal magnetic field, magnetic nanofluid and boundary conditions on nonlinear free and forced vibration of carbon nanotube are investigated. As the most important results, as the intensity of the magnetic field increases, the critical flow velocity increases and divergence and flutter occur later. But the critical flow velocity decreases with increasing the intensity of the magnetic field for a carbon nanotube conveying magnetic nanofluid. In forced vibration, increasing the intensity of the magnetic field increases the amplitude of the response for all boundary conditions in primary and secondary resonance.

An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation

This work studies the dispersion relations of wave propagation in infinite advanced functionally graded (FG) ceramic-metal plates. A simple integral hyperbolic higher-order shear deformation theory (HSDT), with undetermined integral terms and only four unknowns, is used to formulate a solution for the waves’ dispersion relations. The effective functionally graded materials’ (FGM) properties follow the power-law with three different types of uneven porosity distributions. The effect of foundation viscosity is investigated by considering the damping coefficient in addition to Winkler’s and Pasternak’s parameters. The wave propagation’s governing equations are derived based on the present integral hyperbolic HSDT using Hamilton’s principle. The eigenvalue problem describing the porous FG plate dispersion relations resting on a viscoelastic foundation is analytically determined. The theory accuracy is validated by numerically comparing the results with previously published works. Finally, the influences of gradation power, porosity parameters, and the viscoelastic foundation parameters on wave propagation in an FG plate are examined and discussed.

Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation

In this work, the bending behavior of an advanced functionally graded ceramic–metal plate subjected to a hygro-thermo-mechanical load and resting on a viscoelastic foundation is studied using a simple higher-order integral shear deformation theory. The power-law function in terms of volume fraction is used to vary the elastic material constituents through the plate's thickness. The in-plane displacement field uses a sine shape function which changes linearly through the plate thickness to calculate the out-of-plane shear deformation. Both the linear and nonlinear influence of temperature and moisture concentration on the bending response are investigated. For the first time, a three-parameter viscous foundation model is used to study the bending response utilizing the damping coefficient in addition to Winkler’s and Pasternak’s parameters. The governing equations are derived using the principle of virtual displacement, and the analytical solution is obtained by the Navier method. Non-dimensional numerical results is validated by existing results in the literature. A parametric investigation is established to discuss the effects of the power-law gradient index, temperature rise and moisture concentration, elastic foundation coefficients, and the viscoelastic damping coefficient on the FGM plate's bending response.

Eringen’s nonlocal and modified couple stress theories applied to vibrating rotating nanobeams with temperature effects

This study develops a comprehensive vibrational analysis of rotating nanobeams on visco-elastic foundations with thermal effects based on the modified couple stress and Eringen’s nonlocal elasticity theories. This approach accurately simulates the nonlocal stress and size effects. Higher-order shear deformation beam theory and the generalized differential quadrature method are used to obtain the numerical results. The effects of nonlocal parameters, length scale, Winkler–Pasternak coefficients, thermal gradient, slenderness ratios, rotating velocity, and viscoelastic coefficient are demonstrated and discussed in detail. Mode switching and the importance of the correct choice of theory and associated size effect parameters are highlighted.

The role of viscoelastic foundation on flexural gravity wave blocking in shallow water

A hydroelastic model is developed to study the interaction of linear long gravity waves with a very large floating flexible plate resting on a viscoelastic foundation, which is based on the Kelvin–Voigt model. Flexural gravity wave blocking occurs for specific values of the compressive force in the absence of viscous damping. During wave blocking, the group velocity vanishes, and mode swapping occurs. Within wave blocking and plate buckling limit in the presence of compressive force, three distinct propagating modes occur in the absence of viscous damping. Moreover, the study reveals that irrespective of the values of viscous damping constant, the blocking/buckling points shift to a higher wavenumber with an increase in the value of elastic foundation constant. On the other hand, the flexural gravity wave modes become complex in the presence of a viscoelastic foundation. The complex wave modes are classified as predominant progressive wave modes and rapidly decaying modes. In the presence of viscous damping, wave blocking does not happen before the buckling limit of the compressive force. However, the phase velocity vanishes, and the group velocity becomes continuous irrespective of the value of non-zero viscous damping at the buckling limit for the compressive force. The detailed behavior of the roots of the dispersion equation and the mode shapes are illustrated through contour plots and by analyzing the roots’ loci. Furthermore, plate deflections are exhibited for different wave and structural parameters.