Viscoelastic Foundation Research Articles

A finite element approach for forced dynamical responses of porous FG nanocomposite beams resting on viscoelastic foundations

A finite element approach for forced dynamical responses of porous FG nanocomposite beams resting on viscoelastic foundations

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Dynamic Behavior of FG-TPMS Plates on a Viscoelastic Foundation Subjected to Moving Loads Using Moving Element Method

Dynamic Behavior of FG-TPMS Plates on a Viscoelastic Foundation Subjected to Moving Loads Using Moving Element Method

Nonlinear electro-thermo-mechanical dynamic behavior of complexly curved GPL-reinforced panels with auxetic core

This research aims to study the nonlinear electro-thermo-mechanical dynamic responses of cylindrical, sine, and parabolic graphene platelets reinforced panels with auxetic cores and piezoelectric layers. By applying the higher-order shear deformation theory, viscoelastic foundation model, approximate technique for stress function, Rayleigh dissipation function, and energy method, the governing formulations are established. The natural frequency is determined explicitly, and the Runge-Kutta method is used to acquire the time amplitude responses of panels numerically. The noticeable effects of piezoelectrical layers, auxetic core, and GPL parameters on the mechanical and thermal dynamic buckling and vibration responses are recognized from the numerical investigations.

Vibration response of nanobeams subjected to random reactions

Nanobeams composed of materials exhibiting flexoelectric properties have been successfully used in advanced technological equipment, including electronic circuits and very sensitive sensors, owing to their remarkable unique effects. Therefore, it is essential to determine their mechanical behavior as a practical need. This study employs an analytical methodology to provide a precise solution to the vibration issue of nanobeams under random stationary loads. Under such circumstances, the nanobeam is influenced by both the temperature and moisture conditions simultaneously. Additionally, the beam is supported by a viscoelastic foundation that considers both the viscous resistance parameter and the elastic parameter. Analytical formulations are derived by integrating classical beam theory with nonlocal strain gradient theory in order to elucidate the impact of size effects on nanobeams. This research also demonstrates the reliability verification, which clearly validates the accuracy of the calculation formula used in this work. This study examines the impact of material parameters, viscoelastic foundation, temperature, and moisture on the displacement spectrum at the middle and entire length of the beam. The study also explores how the flexoelectric effect decreases the displacement in the nanobeam. Subsequently, we provide scientifically derived findings that have significant relevance for building practical nanobeam specifications.

Research on cutting mode and thrust force of major cutting edge for drilling CFRP composite plates based on viscoelastic mechanics and foundation beam theory

Research on cutting mode and thrust force of major cutting edge for drilling CFRP composite plates based on viscoelastic mechanics and foundation beam theory

Poroelastic size dependent dynamics of viscoelastic microbeams connected via a viscoelastic layer

This article aims to investigate the dynamics of clamped-clamped porous viscoelastic double microbeams interconnected via a viscoelastic layer within the framework of the modified couple stress theory (MCST). Different types of porosity distributions are considered to examine the material imperfection effects on the dynamics of the double microbeam. A closed-cell porosity model is employed to model the variation of the material properties in the thickness plane. The coupled longitudinal and lateral equations of motion are derived using Hamilton’s principle. The governing equations of motion are solved using the modal decomposition method. The equations of motion are verified against the literature for simplified cases (i.e., a non-porous single viscoelastic microbeam and a porous single microbeam resting on a viscoelastic foundation). The numerical results are validated for simpler versions of the system using the finite element method and against the existing literature for a simplified case of a uniformly distributed porous double macrobeam connected via an elastic layer. Influences of viscoelasticity in the double microbeam, viscoelastic layer, porosity, and small-scale influences on the dynamics of the viscoelastic double microbeams are studied. It was found that increasing the material length-scale factor causes the complex fundamental lateral vibrational frequencies to increase for all the porosity patterns.

SLIDING FRICTION IN CONTACTS WITH ONE- AND TWO-DIMENSIONAL VISCOELASTIC FOUNDATIONS AND VISCOELASTIC HALF-SPACE

Solid viscoelasticity is one of the essential origins of sliding friction, as every solid exhibits energy dissipation due to it during deformation processes. In this paper, we first show theoretical solutions for one-dimensional (1D) problems of viscoelastic friction with a 1D viscoelastic foundation. Then, we extend the 1D model to a two-dimensional (2D) model to find theoretical solutions for 2D problems of viscoelastic friction. Finally, we apply the Method of Dimensionality Reduction (MDR) to the theoretical solutions for the 1D problems to discuss three-dimensional (3D) problems of viscoelastic friction.

Nonlinear temperature dependent and visco-elastic foundation effects on the free vibration of functionally graded sandwich plates with ceramic foam core

This paper investigates the vibrations of a functionally graded sandwich plate (FG sandwich plate) with a ceramic foam core resting on a viscoelastic foundation. The focus is on the influence of temperature changes on sandwich plates that have foam core and FG face sheet on the free vibration. The damping coefficient and different schemes of sandwich plate have been considered in the current work. The analysis uses a quasi-3D theory, which reduces the number of unknown displacements and simplifies the equations by incorporating integral terms. Two models are employed to represent the non-uniformity of the ceramic foam core. To account for the influence of the supporting layer, a viscoelastic foundation is included. The governing equations are derived using Hamilton’s principle and solved using the Navier solution method. The paper comprehensively discusses how the volume fraction index k, geometric properties, ceramic foam distribution, viscoelastic foundation, and different temperature rise profiles impact the vibration response of the FG sandwich plate.

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

Combined effect of track-bridge interaction on the dynamic response of a simply supported railway bridge

In this work, the objective is to understand the effect of the nonlinear behaviour of the ballasted track, or the mechanism of vertical and horizontal track-bridge interaction behaviour, on the dynamic response of a simply supported railway bridge, carrying a single ballasted track characterized by a fractional order viscoelastic nonlinear Winkler foundation type, and acted by a moving train load with constant speed. The main feature of the model is that the horizontal and vertical interactions at the interface between the bridge deck and the ballasted track, composed by rails, sleepers and ballast, is introduced through a nonlinear cubic force-displacement relation, schematizing the nonlinear stiffness, plus fractional derivative term for simulating the rail bed’s damping behaviour and a system of horizontally orientated spring-damper elements. By applying the two numerical methods, fourth-order Runge-Kutta method and Finite Difference Method, the validation of the dynamic behaviour of the rail-bridge system is performed, and numerical simulations demonstrate the accuracy of the proposed theoretical model for predicting the real behaviour of the studied bridge taking into account the track-bridge interaction effect. The influence of the fractional-order derivative and the distance between sleepers on the critical velocities, associated with resonance effects, is also addressed.

Finite element approach for free vibration and transient response of bi-directional functionally graded sandwich porous skew-plates with variable thickness subjected to blast load

At the first time, the finite element method was used to model and analyze the free vibration and transient response of non-uniform thickness bi-directional functionally graded sandwich porous (BFGSP) skew plates. The whole BFGSP skew-plates is placed on a variable visco-elastic foundation (VEF) in the hygro-thermal environment and subjected to the blast load. The BFGSP skew-plate thickness is permitted to vary non-linearly over both the length and width of the skew-plate, thereby faithfully representing the real behavior of the structure itself. The analysis is based on a four-node planar quadrilateral element with eight degrees of freedom per node, which is approximated using Lagrange Q4 shape function and C1 level non-conforming Hermite shape function based on refined higher-order shear deformation plate theory. The forced vibration parameters of the non-uniform thickness BFGSP skew-plate are fully determined using Hamilton's principle and the Newmark-β direct integration technique. Accuracy of the calculation program is validated by comparing its numerical results with those from reputable sources. Furthermore, a thorough assessment is conducted to determine the impact of various parameters on the free and forced vibration responses of the non-uniform thickness BFGSP skew-plate. The findings of the paper may be used in the development of civil and military structures in situations that are prone to exceptional forces, such as explosions and impacts load.

Effect of the span length for using finite to analogize infinite beam on viscoelastic foundation under a harmonic moving load

Railways with continuous rails are often modeled as infinite beams. In this paper, closed-form solution is firstly derived for the response of an infinite beam supported by viscoelastic foundation under a harmonic moving load by residue theorem method. The most suitable span length will be found for the analogic finite beam to best represent the deflection of the infinite beam for practical reasons. Starting from the equations of motion, closed-form solution is firstly derived for the infinite beam. Then, a FEM modeling procedure will be adopted to conform the validity of the solution derived analytically. The deflection curves of the infinite beam and analogic finite beam are compared for various parameters.

Hygrothermal-Magnetic Dynamics of Functionally Graded Porous Nanobeams on Viscoelastic Foundation

Hygrothermal-Magnetic Dynamics of Functionally Graded Porous Nanobeams on Viscoelastic Foundation

Exact three-dimensional elasticity analysis for buckling of composite laminated plates resting on viscoelastic foundation

This paper aims to present novel exact solutions for the buckling of a laminated plate resting on the viscoelastic foundation with both normal and shear viscoelastic layers. The governing equations of plate buckling are derived using three-dimensional elasticity theory and state-space formulation. The normal and shear layers of the viscoelastic foundations are modeled using the generalized Maxwell model to represent both the elastic and viscose properties of the foundation. To couple the viscoelastic foundation equation with the buckling equation, Boltzmann’s superposition principle along with the Laplace transform is utilized. Then, the effects of geometry, relaxation modulus of normal and shear layers, viscosity, and time are investigated on the buckling load. The results reveal that the higher viscosity coefficient leads to a slower rate of change in the buckling loads. In addition, the viscoelastic properties have a significant impact on the buckling behavior of the plate. In this regard, the results show that instead of the expected second mode at a constant aspect ratio, the plate experiences the first mode as time passes. The computed results also show that there is a critical threshold. When the foundation stiffness exceeds this threshold, the conventional method of reducing the aspect ratio to prevent buckling not only proves ineffective in reducing the probability of buckling but also, in fact, leads to an increase in buckling occurrences. In addition to the analytical investigation, a finite element (FE) analysis is carried out to study the buckling response of the composite plate. The finite element results also show a reasonably good agreement with those of the analytical method.

Hygrothermomechanical loading-induced vibration study of multilayer piezoelectric nanoplates with functionally graded porous cores resting on a variable viscoelastic substrate

Harnessing vibrations in multifunctional nanostructured plates is pivotal to next-gen microsystems but necessitates understanding scale effects under multifield loading. Investigated in this work are the forced and unforced vibrations of multilayered piezoelectric nanoplates supported on a variable viscoelastic medium and loaded hygrothermo-electromechanically with functionally graded porous (FGP) cores. The viscoelastic foundation is supposed to demonstrate non-linear changes in both stiffness and damping characteristics in the x-coordinate direction. The goal is to improve the accuracy of the results by using the nonlocal strain gradient theory (NSGT) and the third-order shear deformation assumption (TSDA), which include the effects of hardening and softening materials. The FGP core layer considers four states of porosity distribution patterns. These porosity distributions are expected to change in both the in-plane and thickness directions. The governing partial differential equations resulting from Hamilton's principle can be reduced to a system of algebraic equations by applying the Galerkin method. The parametric studies evaluate the effects of several factors, such as the initial electric voltage, viscoelastic medium parameters, moisture rise, temperature changes, porosity distributions, FG index, nonlocal and strain gradient features, and boundary conditions, on the vibration response. The novelty lies in the incorporation of advanced theories, such as the NSGT and TSDT, which capture size-dependent effects and material hardening/softening phenomena. Additionally, the consideration of four distinct porosity distribution patterns in the FGP core layer provides insights into the influence of porosity gradients on the dynamic response. The proposed model can guide the design and optimization of multifunctional nanostructured plates for applications in next-generation microsystems, energy harvesting devices, and smart structures.

Non-linear primary resonance analysis of stiffened FGM conical panels resting on viscoelastic foundation

This article investigates the non-linear forced vibrations and primary resonance analysis of stiffened FGM conical panels (OCPs) resting on a viscoelastic foundation utilizing a semi-analytical method. The classical shells theory and von Kármán nonlinear strain–displacement relations are used to model of OCPs. The equations of motion are derived by applying Hamilton’s principle. Then, the dimensionless equations of motion are established and converted into dimensionless nonlinear ordinary differential equations by applying Galerkin’s method. The solution of the ordinary differential equations is carried out based on the multiple-scale method for analyzing the vibration behavior. In this regard, the necessary relations for the nonlinear primary resonance and internal resonance of stiffened FGM-OCPs are obtained. To validate the suggested methodology, first, the results are verified with various previous research. Second, a numerical method based on the fourth-order Runge-Kutta’s approach is used for verifying the nonlinear vibration analysis. Finally, changes in various parameters such as viscoelastic foundation coefficients, stiffeners, temperature, semi-vertex angle and subtended angle are examined by helping the frequency response plots.

Three-dimensional flutter analysis of a novel circular sandwich plate employing hyperbolic shear deformation theory

Magnetorheological elastomers (MREs) Characterize a category of intelligent materials renowned for their distinct responsiveness to external magnetic fields, demonstrating swift alterations in their mechanical and rheological characteristics. The amalgamation of graphene platelets (GPLs) with MREs, termed GPL-reinforced MRE (GPL-MRE), heralds a novel material category imbued with the adaptive traits of MREs and the structural robustness inherent in GPLs. Such compositional innovation renders this material exceptionally suited for an array of applications across diverse structural frameworks. This research endeavors to scrutinize the flutter boundary of a smart circular sandwich plate featuring a core layer infused with GPL-MRE and variable stiffness composite laminated (VSCL) face layers within the context of supersonic airflow and resting upon a viscoelastic foundation. A novel hyperbolic shear deformation theory is invoked to delineate the displacement field of the sandwich plate. The mechanical properties of the mid-layer are delineated employing the Halpin-Tsai micromechanical methodology. The study probes the effect of supersonic airflow on the structure employing the first-order Piston theory (FPT) in polar coordinates. Hamilton's principle is utilized for deriving the equation of motion governing the structural dynamics in the Finite Element format. Paramount to this investigation is the exploration of assorted parameters and their impact on the flutter occurrence of the structure.

Analytical solutions for joints in an infinite Euler-Bernoulli beam on a viscoelastic foundation subjected to time-lag loads

This paper investigates the analytical method for the infinite beam with joint parts resting on a foundation under time-lag loads. The ground is simulated as a viscoelastic foundation. The existence of joint parts in beams is explained by introducing virtual forces expressed through the Dirac delta function. Integral transformation simplifies the dynamic governing equations for standard beam sections and joint parts into an algebraic equation. The convolution theorem converts the solutions into the time domain. The analytical solutions for dynamic analysis of standard beam sections and joint parts are obtained conveniently in the frequency domain. The proposed analytical method is verified by comparing it with the traditional methods and also validated by numerical examples with time-lag loads. Parametric discussions study the effects on the dynamic response of joint parts and standard beam sections, such as the amplitude and frequency of time-lag loads and coefficient of bending stiffness reduction of joint parts. The parametric analyses emphasize the dramatic effect of critical parameters on the discontinuous deformation of beams. The damage caused by critical values of some factors is emphasized. The severe effects of discontinuous deformation induced by dynamic loads in the safety of beam structures are revealed in this paper. The differences in dynamic responses between the beam and joint part must be monitored to ensure the safety of whole beam structures.

A new higher-order shear deformation theory for flutter instability of a hybrid sandwich panel resting on a viscoelastic foundation

Magnetorheological elastomers (MREs) are smart materials characterized by their ability to adjust mechanical properties through the manipulation of applied magnetic fields, facilitating rapid and reversible tunability. The incorporation of reinforcing fibers introduces distinctive materials termed Magnetorheological Elastomer Composites (MRECs), combining tunability with enhanced rigidity. This study delves into the flutter analysis of a sandwich panel with a mid-layer composed of laminated MRECs and face sheets composed of functionally graded materials (FGMs) featuring porosity. The sandwich panel is situated on a viscoelastic foundation and exposed to a supersonic air current. Employing a higher-order (hyperbolic) shear deformation theory (HSDT), the displacement field of the sandwich plate is estimated. This selection eliminates the requirement for shear correction factors. The mechanical characteristics of the three sheets are determined using the Halpin-Tsai micromechanical method and the rule of mixture. The First-order Piston theory is employed to evaluate the effect of aerodynamic pressure and airflow damping on the sandwich panel. The derivation of the motion equation is achieved through Hamilton's principle. In order to solve the motion equation of the structure, the Finite Element Method (FEM) is utilized. The investigation systematically explores the influence of diverse parameters on the flutter boundary of the sandwich panel.