Viscoelastic Damping Coefficient Research Articles

Modified couple stress theory for wave propagation in viscoelastic sandwich microplates with FG-GPLRC core and piezoelectric face sheets as sensor and actuator

In the present investigation, wave propagation of the viscoelastic sandwich microplates with functionally graded graphene nanoplatelets’ reinforced composite (FG-GPLRC) core and piezoelectric face sheets as sensor and actuator has been analyzed by the refined zigzag theory (RZT). Electromagnetic field is exposed to core and piezoelectric layers. Young's modulus, mass density, and Poisson's ratio are calculated based on the modified Halpin–Tsai model and rule of mixtures because FG-GPLs are arranged as uniform, parabolic, and linear patterns along the thickness of core. In addition, viscoelastic properties of the structure are simulated by the Kelvin–Voigt model. The system is located on an orthotropic visco Pasternak medium. The modified couple stress theory (MCST) is applied to simulate the microscale effects of the structure. Hamilton's principle is utilized for deriving the motion equations. Phase velocity, cut-off, and escape frequencies are computed with an analytical solution. The influence of valuable parameters, such as geometrical dimensions of the system, magnetic field, external voltage, small scale parameter, viscoelastic structural damping coefficient, various foundation types, weight fraction, and different distributions of GPLs on phase velocity, will be studied. The results of this study have a significant effect on the design and fabrication of sandwich micro-structures used in various industrial equipment.

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.

Asymptotic Stability of Energy for a Weak Viscoelastic Plate Equation with Complementary Frictional Damping

We are concerned with asymptotic stability of energy for plate equations with vanishing viscoelastic dampings and complementary frictional dampings, where the internal viscoelastic dampings are assumed to be time-dependent. In terms of the relaxation function $$\theta (t)$$ and the coefficient $$\gamma (t)$$ of viscoelastic term, we obtain the decay rates for the plate equations’ energies. Since we do not need the viscoelastic damping coefficient to be bigger than a fixed positive number, which is required in previous investigations of the asymptotic stability of the plate equations’ energies, our decay theorems extend and improve essentially the existing decay results for the plate equations in both viscoelastic damping case and mixed-type damping case.

Digital light processing in a hybrid atomic force microscope: In Situ, nanoscale characterization of the printing process.

Stereolithography (SLA) and digital light processing (DLP) are powerful additive manufacturing techniques that address a wide range of applications including regenerative medicine, prototyping, and manufacturing. Unfortunately, these printing processes introduce micrometer-scale anisotropic inhomogeneities due to the resin absorptivity, diffusivity, reaction kinetics, and swelling during the requisite photoexposure. Previously, it has not been possible to characterize high-resolution mechanical heterogeneity as it develops during the printing process. By combining DLP 3D printing with atomic force microscopy in a hybrid instrument, heterogeneity of a single, in situ printed voxel is characterized. Here, we describe the instrument and demonstrate three modalities for characterizing voxels during and after printing. Sensing Modality I maps the mechanical properties of just-printed, resin-immersed voxels, providing the framework to study the relationships between voxel sizes, print exposure parameters, and voxel-voxel interactions. Modality II captures the nanometric, in situ working curve and is the first demonstration of in situ cure depth measurement. Modality III dynamically senses local rheological changes in the resin by monitoring the viscoelastic damping coefficient of the resin during patterning. Overall, this instrument equips researchers with a tool to develop rich insight into resin development, process optimization, and fundamental printing limits.

Controlled motion of viscoelastic fiber-reinforced magnetostrictive sandwich plates resting on visco-Pasternak foundation

This article presents a controlled motion investigation of viscoelastic/fiber-reinforced/magnetostrictive/sandwich plates supported via visco-Pasternak foundations. The core of the plate is modeled as a Kelvin-Voigt viscoelastic model. The governing dynamic system is derived using Hamilton’s principle according to simple sinusoidal shear deformation plate theory. A simple feedback control system is utilized to control the structural vibration. Navier’s type solution of the system is obtained to study the influence of significant parameters, especially, the effect of the general thickness ratios, aspect ratio, the thickness ratio of the magnetostrictive layer to viscoelastic layer, sequence staking, foundations, viscoelastic structural damping coefficient, the magnitude of the feedback coefficient, and location of magnetostrictive layers on the vibrational behavior of studied sandwich plate. A comparison with previous studies is performed for validation of the corresponding numerical results and present formulation. Numerical outcomes indicate that increasing the thickness ratio of the viscoelastic layer to the magnetostrictive layer leads to improvement of the system vibration control, as well as the damping coefficient, grows and the damped natural frequency decreases with the increase of viscoelastic structural damping coefficient. The study maybe helps the designers and engineers in development of structural control systems in several applied fields.

Hygrothermal effect on vibration of magnetostrictive viscoelastic sandwich plates supported by Pasternak's foundations

In hygrothermal environment, vibration study of a simply supported smart sandwich plate embedded in an elastic substrate medium is presented in the present article. The sandwich plate contains layers of fiber-reinforced and magnetostrictive materials and core of viscoelastic material. The kinematic equations system is derived via employing Hamilton's principle with considering the transverse shear strains with and without the normal strains effect. Various numerical examples are carried out to study the effects of temperature rise, degree of moisture concentration, elastic foundations parameters, thickness ratio, aspect ratio, thickness ratio of magnetostrictive layer to viscoelastic layer, modes, lamination schemes, magnitude of the feedback coefficient, position of the magnetostrictive layers and viscoelastic structural damping coefficient on controlled motion and vibration characteristics of plate. Some observation about influences of the temperature and humidity concentrations on vibration characteristics of studied plate are presented in detail. The outcomes indicate that the hygrothermal environments have negative effects on vibration suppression of advanced composite structures especially the uniform hygrothermal distribution. The frequencies increase with increasing the viscoelastic structural damping coefficient and the foundation constants.

Nonlinear Primary Frequency Response Analysis of Self-Sustaining Nanobeam Considering Surface Elasticity

This paper is focused to investigate the effects of nonlinear sources, including viscoelastic foundation and geometrical nonlinearity along with the surface elasticity and residual surface stress effects on the primary frequency response of a harmonically excited nanoscale Bernoulli-Euler beam. Due to large surface-area-to-volume ratio, the theory of surface elasticity as well as residual surface stress effects are taken into account within the beam models. The Galerkin approach accompanied by trigonometric shape functions is utilized to reduce the governing PDEs of the system to ODEs. The multiple scales perturbation method theory is applied to compute the nonlinear frequency response of nanobeam. The effects of linear and nonlinear viscoelastic damping coefficient of the medium, crystallographic directions of [100] and [111] of anodic alumina, geometrical nonlinear term and geometrical property on the nonlinear primary frequency response of nanoscale beam are investigated. The results show that theses parameters have a significant effect on the nonlinear frequency response of nanobeams in the case of primary resonance.

Flow-induced vibration attenuation of a viscoelastic pipe conveying fluid under sinusoidal flow using a nonlinear absorber

In this paper, the dynamics of a viscoelastic pipe conveying fluid attached to a nonlinear energy sink (NES) subjected to a sinusoidal flow is studied, aiming at performance improvement of such fluid-interaction systems. The NES has an essentially nonlinear cubic stiffness and a nonlinear cubic damping. Complexification-averaging and fourth-order Runge-Kutta methods are applied to solve the equations of the motion. The conditions of flow-induced instability, the weak modulated response (WMR), and the strongly modulated response (SMR) are investigated. The influence of the internal fluid velocity, the external flow velocity, the viscoelastic damping coefficient, the NES stiffness, location, and damping on the system efficiency is elucidated. The Poincare-Bendixson theorem implies that there are no closed trajectories in the phase diagram of the system response. The results revealed that the occurrence probability of the SMR and jump phenomenon in the system response increases by ascending the internal fluid velocity. Besides, it is shown that at high external fluid velocities or low viscoelastic damping coefficients, the detached resonance curve (DRC) emerges in the frequency-response curves, and simultaneously the unstable regions expand. Furthermore, by approaching the NES installation location to the pipe supports, the occurrence probability of the SMR, DRC, and WMR descends, the divergence regions are enlarged and the transient response lasts longer.

Analysis of Viscoelastic Functionally Graded Sandwich Plates with CNT Reinforced Composite Face Sheets on Viscoelastic Foundation

In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown’s parameters and governing equations are reduced and also the using of shear correction factor is not necessary because the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. The governing equations obtained using Hamilton’s principle is solved for a rectangular viscoelastic sandwich plate. The effects of the main parameters on the vibration characteristics of the viscoelastic sandwich plates are also elucidated. The results show that the frequency significantly decreases with using foundation and increasing the viscoelastic structural damping coefficient as well as the damping coefficient of materials and foundation.

Nonlocal Thermal and Mechanical Buckling of Nonlinear Orthotropic Viscoelastic Nanoplates Embedded in a Visco-Pasternak Medium

This paper discusses the thermal and mechanical buckling of simply supported and clamped orthotropic viscoelastic graphene sheets (nanoplates) embedded in a visco-Pasternak elastic medium. For this purpose, the nonlocal continuum mechanical model is employed with two-variable plate theory. The material of the present nanoplate is assumed to be orthotropic and viscoelastic. The modified nonlinear Kelvin–Voigt viscoelastic model is utilized to formulate the constitutive relations depending on the viscoelastic structural damping coefficient. Moreover, the visco-Pasternak elastic medium is composed of both viscoelastic and shear layers. The viscoelastic layer includes a set of dashpots and elastic springs connected in parallel. In accordance with the two-variable theory, two governing equations are derived via Hamilton’s principle. These equations are analytically solved for various boundary conditions to obtain the explicit solution for critical buckling temperature and buckling load. The present buckling load and buckling temperature both are compared well with the published ones in the literature. In addition, various numerical studies are thoroughly carried out, concentrating on the influences of the plate geometric, nonlocal parameter, structural damping coefficient, elastic foundation parameters, foundation damping parameter and boundary conditions on the critical buckling load and temperature of the nanoplates. The results show that the involvement of the viscidity of the nanoplate and viscoelastic foundation enhances the strength of the nanoplates and therefore increases the resistance of them to external loads.

Nonlocal piezo-hygrothermal analysis for vibration characteristics of a piezoelectric Kelvin–Voigt viscoelastic nanoplate embedded in a viscoelastic medium

This article presents vibration characteristics of a piezoelectric viscoelastic nanoplate under various boundary conditions embedded in a visco-Pasternak’s medium using nonlocal plate theory. The piezo-hygrothermal effects are all included. The hygrothermal piezoelectric nanoplate is made of orthotropic viscoelastic material. Also, the visco-Pasternak’s medium is modeled according to a Kelvin–Voigt foundation. A Two-variable sinusoidal shear deformation plate theory is presented. The imaginary and real parts of the eigenfrequency of piezoelectric viscoelastic nanoplates which are associated with viscoelastic foundation, nonlocal parameter, as well as the viscoelastic structural damping coefficient, are obtained. The effects of other parameters such as aspect ratio, side-to-thickness ratio, temperature change, and moisture concentration are all investigated. The predicted results are compared with the corresponding ones in the literature to check their validation. Additional results are presented and suitable discussions are made.

Size-Dependent Vibration of Axially Moving Viscoelastic Micro-Plates Based on Sinusoidal Shear Deformation Theory

In the present research, vibration and instability of axially moving viscoelastic micro-plate is investigated. Sinusoidal shear deformation theory (SSDT) is utilized due to its accuracy of polynomial functions than other plate theories. Based on Kelvin’s model, the viscoelastic structural properties of micro-plate are taken into consideration. The modified couple stress theory (MCST) is employed because of its capability to interpret the size effect. Using Hamilton’s principle, equations of motion are obtained and solved by hybrid analytical–numerical solution at different boundary conditions. Influences of various parameters such as size effect, axially moving speed, viscoelastic structural damping coefficient, thickness and aspect ratio on the vibration characteristics of moving viscoelastic micro-plate are discussed in detail. The results indicated that the critical speed of moving micro-plate is strongly dependent on the aspect ratio, therefore, the low aspect ratio should be considered for optimum design of this kind of moving micro-devices. The results of this investigation can be used in design and manufacturing of axially moving systems at the micro-scale such as micro-magnetic tapes.

Dynamic pull-in and pull-out analysis of viscoelastic nanoplates under electrostatic and Casimir forces via sinusoidal shear deformation theory

In the present research, dynamic pull-in and pull-out analysis of viscoelastic nanoplate switch under electrostatic and intermolecular Casimir forces are studied. The Viscoelastic properties of the nanoplate are considered using Kelvin-Voigt model. Sinusoidal shear deformation theory is utilized for mathematical modeling of the structure due to its accuracy of polynomial function than other plate theories. The surface effects are considered based on Gurtin-Murdoch theory to enhance the accuracy of results. Considering size effects based on Eringen's nonlocal theory, motion equations are derived using Hamilton's principle and solved by Galerkin's method. Considering two boundary conditions of clamped in all edges (CCCC) and clamped in two edges and free in tow another edges (CCFF), the influences of various parameters such as small scale effect, surface layer, viscoelastic damping coefficient and applied voltage on the pull-in voltage, pull-in time, pull-in deflection and pull-out voltage are discussed in details. Numerical results indicate that considering small scale effects, the pull-in time and voltage as well as pull-out voltage are increased and decreased, respectively, for CCFF and CCCC boundary conditions. In addition, as the effective gap distance increases, the pull-out voltage tends toward the pull-out voltage. The results of this investigation can be used in control and optimum design of smart nano-electrical devices in advanced applications as smart controller.

Combined viscoelastic and elastic wave dissipation mechanism at low velocity impact

The understanding of effects occurring during low velocity normal particle impact on a hard elastic plate is important for the description of different processes occurring during pneumatic conveying, in jet mills, mixers, or fluidized bed apparatuses. In this study, a suitable semi-empiric method is proposed to calculate the coefficient of restitution. This coefficient of restitution is modelled by means of combination of two different approaches. The first approach is based on dissipation of impact energy due to bending wave excitation in the plate described only by one inelasticity parameter. The second approach is based on viscoelastic mechanism of energy dissipation, represented by an additional viscoelastic damping coefficient. Thus, these two coefficients are responsible for bending and viscoelastic energy dissipation and are calculated independently from each other. The summarized energy dissipation is used to determine both material parameters and coefficients. A good agreement between calculated and measured coefficient of restitution was observed. In this way, the interaction between steel spheres impacting on glass plates with a thickness comparable to the diameter of the sphere was calculated as an example.

Responses and energy transmissibility of a viscoelastic isolation system with a power-form restoring force under delayed feedback control

In this paper, combination of cubic nonlinearity and time delay is designed to improve the performance of a viscoelastic isolation system with a power-form restoring force. By the method of multiple scales, the amplitude-frequency response, stability, backbone curve and energy transmissibility are considered. More specifically, three nonlinear cubic delayed feedback control methodologies are examined: position, velocity and acceleration delayed feedback. It is found that the viscoelastic damping coefficient can induce multi-valued response, especially frequency island phenomenon. In this regard, the isolation system indicates the softening behavior for under-linear restoring force and hardening behavior for over-linear restoring force. And equivalent damping and jump avoidance condition are first proposed to interpret the effect of feedback control loop on dynamical behaviors. Furthermore, with the purpose of improving the stability and reducing the vibration, suitable feedback parameter pairs are determined by the frequency response together with stability conditions. Finally, the vibration isolation property is predicted based on energy transmissibility in different cases. Results show that the strategy proposed in this paper is practicable and feedback control parameters are significant factors to alter dynamical behaviors, and more importantly, to improve the isolation effectiveness for the viscoelastic isolation system.

Tunable active vibration attenuation using highly deformable dielectric elastomers

Subject to a voltage, dielectric elastomers (DEs) undergo large deformations, resulting in a wide array of applications in actuators and energy generators. In this paper, a novel potential application of DEs is presented that employs a DE as a vibration damper to achieve the vibration attenuation of a spring oscillator. Based on the developed model, the passive vibration control of the spring oscillator is investigated by utilizing the viscoelastic damping of the DE itself. Subsequently, the active vibration attenuation is studied by applying alternating oppositely-phased voltages at different frequencies, which applies to DEs with a relatively lower viscoelastic damping coefficient. In order to obtain a tunable and controllable vibration attenuation process, the corresponding desired voltage is calculated through the prescribed trend of stretch. The results indicate that the vibration attenuation can be tuned and specified by applying the calculated voltage.

Large amplitude vibration of fractionally damped viscoelastic CNTs/fiber/polymer multiscale composite beams

An analytical formulation combined with a fractional-order time derivative damping model has been developed to conduct a comprehensive study on the large amplitude free and forced vibration response of carbon nanotubes (CNTs)/fiber/polymer laminated multiscale composite beams. The Caputo fractional derivative of order α is employed to incorporate the viscoelastic material having nonlinear behavior. The governing equations of CNTs/fiber/polymer composite (CNTFPC) beams are coupled second order nonlinear partial FDEs (fractional differential equations) which are derived based on Euler–Bernoulli beam theory and von Kármán geometric nonlinearity. Halpin–Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale nanocomposite. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. Discretized by the Galerkin approximation, the perturbation method of multiple time scales is employed to obtain the nonlinear natural frequencies, amplitude–frequency equation and time history of the beams with hinged–hinged boundary conditions. The effects of the Caputo fractional derivative order, beam geometry, volume fraction of fibers and weight percentage of SWCNTs and MWCNTs on the nonlinear oscillation of the CNTFPC beams are investigated through a detailed parametric study. It is found that nonlinear natural frequencies, amplitude–frequency relationship and time history are characterized by viscoelastic damping coefficient which are connected with the natural frequency by the exponential relationship with a negative fractional exponent.

Nonlocal Vibration Behavior of a Viscoelastic SLGS Embedded on Visco- Pasternak Foundation Under Magnetic Field

This paper is concerned with the surface and small scale effects on transverse vibration of a viscoelastic single-layered graphene sheet (SLGS) subjected to an in-plane magnetic field. The SLGS is surrounded by an elastic medium which is simulated as Visco-Pasternak foundation. In order to investigate the small scale effects, the nonlocal elasticity theory is employed due to its simplicity and accuracy. The effect of structural damping of SLGS is taken into account based on Kelvin’s model on elastic materials. An analytical method is used to obtain the natural frequency of the system. A detailed parametric study is conducted to elucidate the effects of the surface layers, nonlocal parameter, magnetic field, Visco-Pasternak elastic medium, viscoelastic structural damping coefficient and aspect ratio of graphene sheet. The findings indicate that enhancing the magnetic field and the density of surface layers leads to an increase in the natural frequency of SLGS.

Dynamic response of partially sealed circular tunnel in viscoelastic saturated soil

Based on Biot's wave equation, dynamic response of a circular tunnel with partially sealed liner in viscoelastic saturated soil is investigated. By introducing two scalar potential functions, the analytical solutions of stresses, displacements and pore pressure induced by axisymmetric gradually applied step load are derived in Laplace transform domain. Numerical results are obtained by inverting Laplace transform presented by Durbin and used to analyze the influences of partial permeable property of boundary and viscoelastic damping coefficient of soil on dynamic response of the tunnel. It is shown that the attenuation of radial displacement appeared with the increase of viscoelastic damping coefficient of soil, and relative rigidity of liner and soil, and the influence of partial sealing property of boundary on stresses, displacements and pore pressure is remarkable. The available solutions of permeable and impermeable boundary conditions are only two extreme cases of this paper.

The psychomechanics of simulated sound sources: material properties of impacted bars.

Sound can convey information about the materials composing an object that are often not directly available to the visual system. Material and geometric properties of synthesized impacted bars with a tube resonator were varied, their perceptual structure was inferred from multidimensional scaling of dissimilarity judgments, and the psychophysical relations between the two were quantified. Constant cross-section bars varying in mass density and viscoelastic damping coefficient were synthesized with a physical model in experiment 1. A two-dimensional perceptual space resulted, and the dimensions were correlated with the mechanical parameters after applying a power-law transformation. Variable cross-section bars varying in length and viscoelastic damping coefficient were synthesized in experiment 2 with two sets of lengths creating high- and low-pitched bars. In the low-pitched bars, there was a coupling between the bar and the resonator that modified the decay characteristics. Perceptual dimensions again corresponded to the mechanical parameters. A set of potential temporal, spectral, and spectrotemporal correlates of the auditory representation were derived from the signal. The dimensions related to mass density and bar length were correlated with the frequency of the lowest partial and are related to pitch perception. The correlate most likely to represent the viscoelastic damping coefficient across all three stimulus sets is a linear combination of a decay constant derived from the temporal envelope and the spectral center of gravity derived from a cochlear representation of the signal. These results attest to the perceptual salience of energy-loss phenomena in sound source behavior.