Viscoelastic Beam Research Articles

Multi-scale analysis for dynamic stability of an axially accelerating viscoelastic beam subjected to combination parametric resonance

Multi-scale analysis for dynamic stability of an axially accelerating viscoelastic beam subjected to combination parametric resonance

A viscoelastic metamaterial beam for integrated vibration isolation and energy harvesting

Locally resonant metamaterials have low-frequency band gaps and the capability of converging vibratory energy in the band gaps at resonant cells. It has been demonstrated by several researchers that the dissipatioin of vibratory energy within the band gap can be improved by using viscoelastic materials. This paper designs an integrated viscoelastic metamaterial for energy harvesting and vibration isolation. The viscoelastic metamaterial is achieved by a viscoelastic beam periodically arrayed with spatial ball-pendulum nonlinear energy harvesters. The nonlinear resonator with an energy harvesting function is achieved by placing a free-rolling magnetic ball in a spherical cavity with an additional induction coil. The dynamic equations of viscoelastic metamaterials under transverse excitation are established, and the energy harvesting and vibration isolation characteristics within the dispersion relation of viscoelastic metamaterials are analyzed. The results show that the vibrations of the main body of the viscoelastic metamaterial beam are significantly suppressed in the frequency range of the local resonance band gap. At the same time, the elastic waves are limited in the nonlinear resonator with an energy harvesting function, which improves the energy output. Finally, an experimental platform of viscoelastic metamaterial vibration is established for validation purposes.

Investigation on parametric excitation vibration and piezoelectric active control of axially moving viscoelastic beams

The nonlinear dynamics equation governing the behavior of axially moving viscoelastic beams is established in this paper, based on Hamilton’s principles. The Galerkin method is employed to discretize the equation for numerical analysis. Nonlinear parametric vibration control for axially moving viscoelastic beams is explored using piezoelectric laminated actuators based on LQR optimal linear control and SMC sliding mode control strategies. The stability of the moving beam is examined in respect of moving speed and active control. The influence of actuator position and control schemes on vibration control performance for the moving beam is also examined. In respect to linear and nonlinear equations, two control strategies of LQR are given to illustrate the control performances. The sliding mode control (SMC) is also given to reduce the vibration of the moving viscoelastic beam and exhibit the control performance and its robustness.

Bernstein polynomials in analyzing nonlinear forced vibration of curved fractional viscoelastic beam with viscoelastic boundaries

Bernstein polynomials in analyzing nonlinear forced vibration of curved fractional viscoelastic beam with viscoelastic boundaries

Nonlinear dynamics and forced vibrations of simply-supported fractional viscoelastic microbeams using a fractional differential quadrature method

In this paper, free and forced nonlinear vibrations of fractional viscoelastic microbeams are modeled based on Euler-Bernoulli theory, the Von Karman’s nonlinear strain relations, the modified couple stress theory (MCST), and the fractional Kelvin-Voigt viscoelastic model. In the present work, the nonlinear-fractional order governing equations are discretized in the space domain by Galerkin’s method. Two different approaches are introduced to solve the resulting nonlinear fractional-order Duffing equation in the time domain. In the first approach, a time marching fractional finite difference method is presented to compute the transient time response starting from the initial conditions. This approach is time consuming if the frequency-amplitude curves of steady state response are required since it provides just one point on the frequency-amplitude curve. More importantly, this approach usually converges only for the stable branch with smallest amplitude of frequency-amplitude curve. In the second approach, we introduce a novel fractional differential quadrature method (FDQM) to discretize the fractional Duffing equation and apply a pseudo-arc length algorithm to directly construct the frequency-amplitude curves. Effects of the fractional-order, linear and nonlinear viscoelasticity coefficients, viscous damping parameter, microstructure parameters, and the micro-beam thickness on the nonlinear dynamics of the viscoelastic micro-beam are analyzed numerically. Numerical results show that each of these parameters can change natural frequency and/or the damping behavior of the structure. The present model can be used for designing and analyzing the nonlinear microstructure viscoelastic beam under dynamic loads.

An analytical approach for shock response of fractional viscoelastic beams with tip mass

This paper specifically analyzes the behavior of a beam with fractional viscoelastic properties and a tip mass under shock. The shock is applied longitudinally to the beam, and a fractional Kelvin–Voigt model is employed to describe the viscoelastic properties. Additionally, the paper examines the fractional viscoelastic power as a function of time during the shock. The equation of motion for the fractional viscoelastic beam with a tip mass is derived using Hamilton’s principle. In order to ensure accurate analysis of the results, the graphs are carefully analyzed in both the time and frequency domains. To solve the equations, the special technique provided for differential equations of variable order (VO) is used. Two distinct methods, namely, absolute method and square root of the sum of squares method, are thoroughly examined to calculate the absolute acceleration. Subsequently, the most suitable method is selected based on the evaluation results. The study’s results demonstrate that the damping parameters of the viscoelastic beam have a significant impact on shock transmissibility. Additionally, the findings demonstrate that the ability to transfer shocks can be manipulated by modifying the system’s geometry and mass.

Analysis of energy dissipation in non-linear viscoelastic beam in skew bending

This paper deals with the problem of analyzing the energy dissipation in a non-linear viscoelastic beam structural component made of a functionally graded material. The beam is in skew bending. The viscoelastic model used for dealing with the beam mechanical behaviour is set-up by combining of linear as well as non-linear springs and dashpots. The viscoelastic model is under strains which change in time on sinusoidal law. The material properties of the viscoelastic model are distributed smoothly along the thickness of the beam structure. The energy dissipation in the beam is due to dashpots which are parts of the viscoelastic model. Therefore, the strain energy dissipation density is derived by analyzing the stresses and strains in the dashpots. Then the strain energy dissipation density is integrated in the volume of the beam in order to obtain solution of the dissipated energy. The solution is applied for investigating the change of the dissipated energy due to variation of the properties of the model and the loading conditions of the beam.

Stabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delay

An approach is implemented in this article to analyze the decay rate of nonlinear beams according to the Euler-Bernoulli equation in the context of rheological viscoelastic damping deformations taking into account the neutral type delay. The interaction between viscoelastic and neutral type delays is discussed as our main aim to support a rapidly developing literature. Using the energy method and constructing an appropriate Lyapunov functional, under certain conditions on the kernel and neutral delay terms, we show that despite the destructive nature of delays in general, a very general decaying energy for the problem was obtained.

Numerical analysis of the dynamic characteristics of a fractional-order viscoelastic beam with fixed supports at both ends

In this paper, we present a generalized model of a viscoelastic beam, which takes into account the influence of axial forces and incorporates a fractional constitutive relationship. In addition, we propose a novel numerical calculation method for analyzing fractional-order viscoelastic beams. This method takes the transverse displacement and bending moment of the beam as state variables, transforms the beam model into a discrete state space equation through the application of the central difference method, and utilizes an improved precise integration algorithm to solve the equation. To evaluate the performance of the method, the responses of the beam under two types of excitations, namely uniformly distributed transverse load and the motion of the support at both ends, are calculated under fixed hinge conditions. The results demonstrate that the present method has excellent accuracy and convergence, and also reveal some nonlinear phenomena of the system.

Random Vibration Analysis of an Axially Moving Viscoelastic Beams based on Complex mode and Pseudo Excitation

Axially Moving Beams can serve as simplified models for many engineering systems, such as aerial cable trams, power conveyor belts, magnetic tapes, textile fibers, aerospace vehicles, etc. They often work in open environments in the wild, with random excitations. In engineering practice, viscoelastic materials are widely used in various engineering fields. This article studies the lateral random response of axially moving viscoelastic beams under various random excitations. Under the random external excitation of concentrated and distributed loading, analytical expressions of the mean function, correlation function, power spectral density, and mean square function of the random response of an axially moving viscoelastic beam are derived. They prove the correctness and simplicity of the Pseudo-excitation method for solving the power spectral density of the random displacement response of axially moving viscoelastic beams.

Multilayered inhomogeneous beam under relaxation: an analytical delamination investigation

Delamination in a multilayered inhomogeneous viscoelastic beam structure under relaxation is analyzed. The moduli of elasticity of beam layers change with time. A linear viscoelastic model with two springs and a dashpot is used for describing the relaxation behaviour. The response of the model is obtained by considering the equilibrium of its components. The material properties vary continuously along the width of layers. Besides, the modulus of elasticity of one of the springs changes with time. Time-dependent strain energy release rate (TDSERR) for the delamination is found by using the time-dependent strain energy (TDSE) in the beam. The TDSERR is found also by analyzing the compliance. The results are identical. The influence of different factors and parameters on the delamination is evaluated.

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.

Исследование коэффициентных обратных задач с учетом реологии для функционально-градиентных стержней

The problems of determining the variable rheological properties of functionally gradient beams from some additional information about displacements are considered. Vibrations of a cantilevered inhomogeneous viscoelastic beam are studied in the framework of two models - Euler-Bernoulli and Timoshenko. The oscillations are caused by a moment concentrated at the end of the beam, oscillating in time. Within the framework of the concept of complex modules, operator relations linking the given and desired functions are obtained. Functions reflecting the laws of change of long-term and instantaneous modules have been restored. The results of computational experiments on the restoration of functions of various types are presented.

An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams

We propose a novel approach to the linear viscoelastic problem of shear-deformable geometrically exact beams. The generalized Maxwell model for one-dimensional solids is here efficiently extended to the case of arbitrarily curved beams undergoing finite displacement and rotations. High efficiency is achieved by combining a series of distinguishing features, that are: (i) the formulation is displacement-based, therefore no additional unknowns, other than incremental displacements and rotations, are needed for the internal variables associated with the rate-dependent material; (ii) the governing equations are discretized in space using the isogeometric collocation method, meaning that elements integration is totally bypassed; (iii) finite rotations are updated using the incremental rotation vector, leading to two main benefits: minimum number of rotation unknowns (the three components of the incremental rotation vector) and no singularity problems; (iv) the same SO(3)-consistent linearization of the governing equations and update procedures as for non-rate-dependent linear elastic material can be used; (v) a standard second-order accurate time integration scheme is made consistent with the underlying geometric structure of the kinematic problem. Moreover, taking full advantage of the isogeometric analysis features, the formulation permits accurately representing beams and beam structures with highly complex initial shape and topology, paving the way for a large number of potential applications in the field of architectured materials, meta-materials, morphing/programmable objects, topological optimizations, etc. Numerical applications are finally presented in order to demonstrate attributes and potentialities of the proposed formulation.

Vibration Characteristics Analysis of Immersed Tunnel Structures Based on a Viscoelastic Beam Model Embedded in a Fluid-Saturated Soil System Due to a Moving Load

Vibration Characteristics Analysis of Immersed Tunnel Structures Based on a Viscoelastic Beam Model Embedded in a Fluid-Saturated Soil System Due to a Moving Load

Auto-parametric resonance of flexible viscoelastic beams under interaction between longitudinal and transverse modes

For a system encompassing subsystems, dynamic modal interaction may experience unanticipated vibrations among subsystems that are excited indirectly. This paper focuses attention to a nonlinear auto-parametric resonance phenomenon of a flexible beam introduced via modal coupling of longitudinal forced resonance and transverse parametric resonance under longitudinal pulsatile excitation. The coupled resonance equations are first modeled based on the Euler-Bernoulli beam theory by incorporating nonlinear curvature, von Kármán's nonlinear strain-displacement relationship and the flexible beam model characterizing nonlinear inertia and displacement interaction. The Galerkin truncation-incremental harmonic balance method (IHBM) is then introduced to obtain both the stability boundary and amplitude-frequency bifurcation maps. Through the corresponding relationship between stability boundary and bifurcation diagram, the energy exchange between two modes is identified as well as the instability region and bifurcation topology can be tuned. It is found that the modal interaction greatly widens the instability region with at most two resonance bands of lateral resonance. By tuning structural and foundation damping, resonance can be controlled to occur only in one frequency band of the pair as desired. This research provides guidance to design broadband energy harvesting or vibration suppression equipment with tunable working frequency band for using the strategy of auto-parametric resonance.

Nonlinear Analysis of a Viscoelastic Beam Moving with Variable Axial Tension and Time-Dependent Speed

Nonlinear Analysis of a Viscoelastic Beam Moving with Variable Axial Tension and Time-Dependent Speed

Vibrations of porous functionally graded CNT reinforced viscoelastic beams connected via a viscoelastic layer

This work analyses the vibrational response of porous viscoelastic functionally graded (FG) carbon nanotube (CNT) reinforced double beams. The beams are simply supported, connected through a viscoelastic layer, where four functionally graded patterns of CNT in the thickness directions (uniformly distributed (UD), FG-V, FG-O, and FG-X) are considered. The porosity models considered are UD, PO-V and PO-X. After formulating the coupled equations of motion via an energy-based method, and incorporating the effects of the viscoelastic beams and viscoelastic layers, the equations are solved using an assumed series expansion technique. The equations and solution methodology are verified utilising simplified models from existing literature and also through development of a finite element method (FEM) based simplified model; very good agreement has been achieved. Effects of the stiffness and viscous coefficients of the viscoelastic layer, the structural viscosity parameter of the porous CNT reinforced double beams, the porosity coefficient, and porosity models are examined. Overall, the results indicate that the stiffness and viscous coefficients of the viscoelastic layer have increasing effects on the real and imaginary components of second series fundamental transverse natural frequency of the double beam system, respectively. An increase in the structural viscosity parameter of the porous CNT reinforced double beams leads to an increase in the imaginary components of the fundamental frequencies of both the series. Moreover, a range of different effects on the real and imaginary components of the natural frequencies were noted while varying the porosity coefficient and models. The FG-X CNT porous reinforced viscoelastic double beams with a viscoelastic layer have the highest natural frequencies of all the cases. The study demonstrates the importance of the porosity, viscoelastic layer and viscoelastic material properties on the dynamics of the system.

On-demand heart valve manufacturing using focused rotary jet spinning

On-demand heart valve manufacturing using focused rotary jet spinning

General decay of the solution to a nonlinear viscoelastic beam with delay

General decay of the solution to a nonlinear viscoelastic beam with delay