Effect Of Viscoelastic Damping Research Articles

Two-dimensional viscoelastic beam element for ultra-large space structures based on absolute nodal coordinate formulation

Internal damping is an important factor in the dynamic behaviors of ultra-large space structures in zero damping space environment. To precisely describe the damping, this paper proposes a two-dimensional viscoelastic Euler-Bernoulli beam element based on absolute nodal coordinate formulation and Kelvin-Voigt damping model, where the damping stress is linearly dependent on the stress rate. Firstly, a precise generalized damping force model is developed using the principle of virtual work. A simplified generalized damping force model is then proposed to improve simulation efficiency by neglecting the axial damping force and a part of the transverse damping force. Numerical simulations show that the proposed damping force models will not affect the rigid-body motion of the beam. Then, a simple formula is presented to estimate the damping ratio of the beam for different parameters, which shows good agreement with the logarithmic decrement method in simulations. Finally, the effects of viscoelastic damping on the dynamic behaviors of a Sun-facing beam in space are investigated. Simulation results reveal that the viscoelastic damping can greatly reduce the vibration amplitude of the beam near the resonance frequencies.

Seismic Response of Cable-Stayed Spanning Pipeline Considering Medium-Pipeline Fluid–Solid Coupling Dynamic Effect

With the aim of determining the influence of the fluid–structure coupling dynamic effect of the oil and gas transmission medium and pipeline on the seismic response, an oil pipeline supported by a cable-stayed spanning structure was taken as the study object. Kinetic equations taking into account the action of oil and gas medium were studied, and a finite element model structure considering the additional-mass method and the fluid–structure coupling effect were established separately. In addition, the mechanism of the oil–gas–pipeline coupling action on the seismic response of pipeline structure was analyzed, and the results were obtained. The results show that the pipeline has a minimal seismic response at the abutment location, the seismic response gradually increases along the abutment to the main tower, and the seismic response reach is maximized at about one-fifth of the bridge platform. The seismic response of the oil and gas pipeline model structure using the additional-mass method is generally more significant than that based on the fluid–solid coupled dynamic model; moreover, the maximum displacement response differs by about 24%, and the maximum acceleration response differs by approximately 30%, indicating that the oil and gas medium has a certain viscoelastic damping effect on the seismic response of the oil pipeline, which provides a reference for the seismic response calculation theory and analysis method of cable-stayed spanning oil pipelines.

Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data

Mathematical models are widely recognized as a valuable tool for cardiovascular diagnosis and the study of circulatory diseases, especially to obtain data that require otherwise invasive measurements. To correctly simulate body hemodynamics, the viscoelastic properties of vessels walls are a key aspect to be taken into account as they play an essential role in cardiovascular behavior. The present work aims to apply the augmented fluid-structure interaction system of blood flow to real case studies to assess the validity of the model as a valuable resource to improve cardiovascular diagnostics and the treatment of pathologies. Main contributions of the paper include the evaluation of viscoelastic tube laws, estimation of viscoelastic parameters and comparison of models with literature results and in-vivo experiments. The ability of the model to correctly simulate pulse waveforms in single arterial segments is verified using literature benchmark test cases, designed taking into account a simple elastic behavior of the wall in the upper thoracic aorta and in the common carotid artery. Furthermore, in-vivo pressure waveforms, extracted from tonometric measurements performed on four human common carotid arteries and two common femoral arteries, are compared to numerical solutions. It is highlighted that the viscoelastic damping effect of arterial walls is required to avoid an overestimation of pressure peaks. Finally, an effective procedure to estimate the viscoelastic parameters of the model is herein proposed, which returns hysteresis curves of the common carotid arteries dissipating energy fractions in line with values calculated from literature hysteresis loops in the same vessel.

Dynamic modeling of non-cylindrical curved viscoelastic single-walled carbon nanotubes based on the second gradient theory

This paper is devoted to the theoretical study of the dynamic response of non-cylindrical curved viscoelastic single-walled carbon nanotubes (SWCNTs). The curved nanotubes are largely used in many engineering applications, but it is challenging in understanding mechanically the dynamic response of these curved SWCNTs when considering the influences of the material viscosity. The viscoelastic damping effect on the dynamic response is considered here by using the Kelvin-Voigt viscoelastic model. A modified shear deformation beam theory is here employed to formulate the governing partial differential equations. When the SWCNTs are considered in a small scale model, quantum impacts are important for a correct evaluation of the mechanical response of the nanosystem. This is here investigated by embedding the well-known nonlocal strain gradient approach into the governing equations. The extracted equations are solved by utilizing the Galerkin analytical approach in which the governing partial differential equations are reduced to ordinary differential equations and numerical findings are achieved for various boundary conditions. In order to evaluate the efficiency of the proposed theory, the outcomes in terms of natural frequencies of the vibrating nanotubes are verified with respect to the available literature. It follows a vast systematic study, where several parameters are varied to investigate the influences of geometrical properties involving different polygons of the SWCNTs on the dynamic response.

Viscoelastic Characteristics of Mechanically Assembled Three-Dimensional Structures Formed by Compressive Buckling

Vibrational microplatforms that exploit complex three-dimensional (3D) architectures assembled via the controlled compressive buckling technique represent promising candidates in 3D micro-electromechanical systems (MEMS), with a wide range of applications such as oscillators, actuators, energy harvesters, etc. However, the accuracy and efficiency of such 3D MEMS might be significantly reduced by the viscoelastic damping effect that arises from material viscosity. Therefore, a clear understanding and characterization of such effects are essential to progress in this area. Here, we present a study on the viscoelastic damping effect in complex 3D structures via an analytical model and finite element analysis (FEA). By adopting the Kelvin–Voigt model to characterize the material viscoelasticity, an analytical solution is derived for the vibration of a buckled ribbon. This solution then yields a scaling law for the half-band width or the quality factor of vibration that can be extended to other classes of complex 3D structures, as validated by FEA. The scaling law reveals the dependence of the half-band width on the geometries of 3D structures and the compressive strain. The results could serve as guidelines to design novel 3D vibrational microplatforms for applications in MEMS and other areas of technology.

A non-classical model for an orthotropic Kirchhoff plate embedded in a viscoelastic medium

A non-classical model for an orthotropic Kirchhoff plate embedded in a viscoelastic medium is developed by using an extended version of the modified couple stress theory and a three-parameter foundation model. The equations of motion and the boundary conditions are simultaneously obtained through a variational formulation based on Hamilton’s principle. The new plate model contains three material length scale parameters to capture the microstructure effect, one damping coefficient to account for the viscoelastic damping effect, and two foundation moduli to represent the foundation effect. The current non-classical orthotropic plate model includes the isotropic plate model incorporating the microstructure effect and the classical elasticity-based orthotropic plate model as special cases. To illustrate the new model, the static bending and free vibration problems of a simply supported orthotropic plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate predicted by the current model is smaller than that predicted by the classical model, and the difference is large when the plate thickness is small but diminishes as the thickness becomes large. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. In addition, the damping ratio predicted by the new plate model is lower than that predicted by the classical plate model, and the difference is diminishing as the plate thickness increases. These predicted trends of the size effect at the micron scale agree with those observed experimentally. Furthermore, it is quantitatively shown that the presence of the foundation enlarges the plate natural frequency.

Aero-thermo-elastic stability analysis of sandwich viscoelastic cylindrical shells in supersonic airflow

The aero-thermo-elastic stability of layered cylindrical shells with viscoelstic cores is investigated. The Donnell’s shell theory for the outer layers and the first order shear deformation theory for the viscoelastic layer are employed in conjunction with the von Karman–Donnell kinematic nonlinearity to construct the model. The pre-stresses and pre-deformations arisen from the temperature rise and static aerodynamic pressure are first determined by solving the nonlinear thermo-elastic equilibrium equations using by an exact analytical method. The results are then used in the linear aeroelastic stability equations and analyzed with the Galerkin’s procedure to determine the supersonic flutter boundaries of the structure. Numerical studies are performed to illustrate the effects of viscoelastic damping, geometrical parameters and temperature rise on the flutter stability margins. Special attention is put on the effect of pre-deformation on the aeroelastic stability of the shell. It is found that the pre-deformation could significantly alter the flutter boundaries for sufficiently high temperatures.

Nonlinear response of a resonant viscoelastic microbeam under an electrical actuation

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.

Nonlinear flutter of aerothermally buckled composite shells with damping treatments

Finite element analyses of the aerothermoelastic behavior of aerothermally buckled cylindrical composite shells with various damping treatments were implemented using the theory of layerwise displacement field. The arc-length method and iterative nonlinear scheme were taken up to estimate the post-buckling deformation of composite shells due to aerothermal loads. The complex modulus was adopted to take into account the effects of viscoelastic damping. The post-buckling behaviors and aeroelastic characteristics, under thermal loads, of several damped composite shells were investigated with various damping treatments including free layer and constrained layer and sandwiched damping layers. The results show that the flutter boundary of the cylindrical composite panels with viscoelastic layers can be remarkably affected by the aerothermally buckled shapes and damping treatments. Further, the proper damping treatments, coupled with thermal loads, can improve aerothermoelastic characteristics, resulting in the increase of the flutter boundary.

Air-coupled excitation of rocking motion of individual microspheres on surfaces

In current study, it is demonstrated that the rocking motion of a single microsphere can be excited by means of impulsive acoustic fields generated by air-coupled transduction and the transient response of the particle can be detected optically. Such observation indicates the existence of rolling moment resistance of particle-surface adhesion bonds. A set of experiments were conducted for measuring the rocking resonance frequency of a microsphere on a flat substrate. The waveforms corresponding to the transient out-of-plane displacement of the rocking particle are used to extract the work of adhesion of the bond between the particle and substrate. Some of the frequency responses of the particles exhibited small shifts in their peak frequencies, which are away from their resonance frequencies, when compared to those of the base motion. These shifts are attributed to the viscoelastic damping effect due to capillary water meniscus formation in the adhesion bond of the particle-substrate system.

The hydrodynamic stability of channel flow with compliant boundaries

An asymptotic theory is developed for the hydrodynamic stability of an incompressible fluid flowing in a channel in which one wall is rigid and the other is compliant. We exploit the multideck structure of the flow to investigate theoretically the development of disturbances to the flow in the limit of large Reynolds numbers. A simple spring-plate model is used to describe the motion of the compliant wall, and this study considers the effect of the various wall parameters, such as tension, inertia, and damping, on the stability properties. An amplitude equation for a modulated wavetrain is derived and the properties of this equation are studied for a number of cases including linear and nonlinear theory. It is shown that in general the effect of viscoelastic damping is destabilizing. In particular, for large damping, the analysis points to a fast travelling wave, short-scale instability, which may be related to a flutter instability observed in some experiments. This work also demonstrates that the conclusions obtained by previous investigators in which the effect of tension, inertia, and other parameters is neglected, may be misleading. Finally it is shown that a set of compliant-wall parameters exists for which the Haberman type of critical layer analysis leads to stable equilibrium amplitudes, in contrast to many other stability problems where such equilibrium amplitudes are unstable.

Dynamics of multilayered orthotropic viscoelastic plates of Maxwell solids

This paper is concerned with a simplified dynamical analysis of orthotropic viscoelastic plates that are made up of an arbitrary number of layers each of which is a Maxwell type solid. This study includes the case where some or all the layers are themselves constituted by thinly laminated materials with couple stresses. The recurrence equations for the shear stresses are obtained for an arbitrary number of layers and then applied to plates with two or three layers. The viscoelastic damping effect is determined by the process of linearization and then illustrated by a plate composed of one, two or three layers. It is found that the damping increases with anisotropy and wave number. These results are shown by graphical representations.

Development and evaluation of a pseudo-force approximation applied to nonlinear dynamic contacts and viscoelastic damping

A pseudo-force approximation method is used to study the nonlinear dynamic contacts and the effect of viscoelastic damping of beam-mass-beam systems. A pseudo-contact element with nonlinear stiffness and damping approximated by polynomial functions is defined and evaluated. To improve the system dynamic responses, viscoelastic damping is introduced into the systems using the standard linear model. The nonlinear forces derived from surface elasticity, penetration, instant contact velocity and viscoelastic damper are added to an excitation force vector to avoid reformation of system matrices. The system's equations of motion are directly integrated using the Wilson-θ method with minor modifications to accommodate the dynamic contacts and the viscoelastic damping. A design equation is also proposed to estimate the required viscoelastic dampers.

Influence of Mass Representation on the Equations of Motion for Rotating Structures

Fig. 5 Influence of the viscous damping coefficient on the critical load for several values of the elastic foundation modulus (4 = 0.0044). phenomenon reported in Ref. 1 that the elastic foundation reduces the critical load at which the column will undergo dynamic instability. The effect of viscoelastic damping 77 coupled with the elastic foundation modulus is plotted in Figs. 3 and 4 for Ie = 0.0001 and 0.0044, respectively. The striking phenomenon presented in Figs. 3 and 4 is the sharp reduction in the critical load p for a very lightly damped beam. A similar phenomenon is reported in Ref. 3 for the B-E beam. For shorter beams (higher values of Ie), the reduction in the critical load for very lightly damped beams is more pronounced for higher values of elastic foundation k (see Fig. 4). The results of Fig. 4 show that for lightly damped beams (17 0.025) the elastic foundation has a stabilizing effect. The viscous damping has a stabilizing effect for the B-E beam (small values of Ie), as reported in Ref. 3. Figure 5 shows the influence of the viscous damping coefficient on the critical load for a shorter beam (7^ = 0.0044) for several values of the elastic foundation modulus. The results of Figs. 4 and 5 show that for shorter beams and light damping (viscous and viscoelastic), the elastic foundation has a destabilizing effect. Increasing the damping coefficient beyond a certain value causes the elastic foundation to stabilize the system (a higher critical load for a higher elastic foundation coefficient).

On Standing Waves in Tires

Abstract By using a comprehensive rotating laminated shell model of the tire, the effects of viscoelastic damping on the standing wave phenomenon are investigated in more detail than was previously possible. The shell theory employed is a nonlinear version of Novoshilov's work and the onset of the standing wave is characterized as a small dynamic deformation superposed on a finite deformation. To expand the scope of the model, the viscoelastic constitutive law is treated as either of the differential or hereditary integral type. The solution for the stated model is obtained by the finite element procedure, and the results of several numerical experiments are presented. The substantial role of viscoelastic effects in the development of the standing wave phenomenon of tires is emphasized by the results.