Viscoelastic Boundary Conditions Research Articles

Dynamics of Euler-Bernoulli beams with unknown viscoelastic boundary conditions under a moving load

A new methodology is presented in this work to identify the viscoelastic boundary conditions and dynamical response of Euler-Bernoulli beams under a moving load. A new expression for the transmissibility function of the beam output responses with unknown viscoelastic boundary conditions with Voigt and more generalized four-element models is derived. The proposed identification method uses modal shapes with a pattern search optimization scheme. Finite element simulation was used to demonstrate the validity of the proposed method. The acceleration response from different locations on the beam was utilized in the identification of the boundary conditions considering six optimization cases. The proposed method provided solutions of the boundaries that can satisfy the requirements of the natural frequencies and damping ratios simultaneously. The effects of the number of selected measurement locations, participant modes, and measurement noise on the accuracy of the resulting boundary parameters were investigated. The results showed that the use of three complex modes and eight measurement points provided an accurate estimation of the modal parameters and reduced the relative error effectively in the resulting eight unknown boundary coefficients, under noise-free and corrupted acceleration signals with 5% noise conditions.

Moving load identification on Euler-Bernoulli beams with viscoelastic boundary conditions by Tikhonov regularization

This work presents moving load identification on Euler-Bernoulli beams with viscoelastic boundary conditions based on beam acceleration responses. The Tikhonov regularization and generalized cross validation (GCV) methods are used to investigate the performances of different regularization matrices (L matrices) in terms of their effectiveness in reducing errors in load identification. The effects from noises, inaccurate parameters, arrangements of measurement locations, velocities, and spaces of moving loads are included in the investigations. Simulation results demonstrated that the viscoelastic boundary conditions could play an important role in the performance of these time domain moving load identifications. The use of a higher-order regularization matrix (L matrix) can efficiently reduce the relative errors of the identified loads. In these L matrices, the L 1 matrix could provide a compromised approach to reducing the relative errors more efficiently than higher-order L matrices such as L 2, L 3, and L 4.

A New Computational Approach for Viscoelasticity

Viscoelasticity is the basic content of solid mechanics, which has become an important part of continuum mechanics. It usually includes two aspects: one is the description of viscoelastic properties and the expression of constitutive relationship; the other is the establishment and solution of boundary value problem. In this paper, based on Legendre transformation, a new numerical method which can effectively deal with viscoelastic boundary conditions is established.

An analytical method for the creep and stress relaxation of viscoelastic materials

Based on the properties of symplectic system and the symplectic orthogonal normalization relation between the eigensolutions, the calculation method of viscoelastic boundary condition problem is given, and the computation of stretching and bending problems is carried out. The results show that the creep property of viscoelastic materials.

Identification of the viscoelastic boundary conditions of Euler‐Bernoulli beams using transmissibility

A new method to identify the viscoelastic boundary conditions of Euler‐Bernoulli beams under forced response is here presented. The boundary conditions and transmissibility function with viscoelastic expressions in terms of the Green function are introduced in the identification process. Two distinct identification methods are proposed: the least squares method with singular value decomposition; and the pattern search optimization method. Three examples are reported to demonstrate the efficacy of the proposed methods. The results from the least squares method to provide accurate solutions under noise‐free conditions, but poorly perform with the addition of 1% noise. Conversely, the pattern search optimization method integrates the solutions from different frequencies and provides promising solutions, even with 50% noise. The capability of identifying complex boundary conditions under high levels of noise might open the door for the proposed method to be considered in real‐life applications of structural health monitoring and model updating with boundary conditions of beam‐like structures such as bridges.

General decay for a nonlinear Bresse system with memory conditions on part of the boundary

ABSTRACT In this paper, we study the general decay rate of a nonlinear Bresse system with memory conditions on part of the boundary. Without imposing on , an explicit general decay rate results are established under suitable assumptions of the resolvent kernels. It's worth pointing out that our general decay results are not necessarily of exponential-type or polynomial-type, which are also different from the general decay results obtained in Khemmoudj and Hamadouche [General decay of solutions of a Bresse system with viscoelastic boundary conditions. Discrete Contin Dyn Syst. 2017;37(9):4857–4876]. Moreover, our general decay results allow a wider class of relaxation functions and initial data, and thus generalize some previous results existing in the literature.

A Comparative Study of Cantilever- and Integral-Type Dead Loads on the Seismic Responses of High Arch Dams

The actual dead load of an arch dam should be applied gradually through staged construction and sequenced grouting. However, the cantilever- and integral-type dead loads commonly used in the analysis of arch dams represent simplified versions of the actual loading. In this paper, these two types of dead loads, i.e. cantilever and integral types, are presented based on the Lagrange multiplier method considering the nonlinear behaviors of contraction joints. Based on the finite element method and an appropriate contact model together with artificial viscoelastic boundary conditions, a dynamic analysis model of a dam–foundation–reservoir system is established in consideration of the interactions between the arch dam and foundation, the opening and closing of contraction joints, and the radiation damping effect of the far-field boundary. Taking a 300 m high arch dam in the strong earthquake area of West China as an example, a fine mesh finite element model with a total of approximately 3.5 million degrees of freedom is established. The separate effects of the cantilever and integral dead loads on the static and dynamic responses of the dam are studied. The results demonstrate that the distribution and magnitude of the contraction joint opening width and maximum tensile stress are different under the two different dead load simplifications.

Blow‐up of solution of wave equation with internal and boundary source term and non‐porous viscoelastic acoustic boundary conditions

AbstractIn this paper we study the blow‐up of solution of a mixed problem associated to a nonlinear wave equation with dissipative and source term in a bounded domain of . On a boundary portion of the domain we consider a non‐porous viscoelastic acoustic boundary conditions to a non‐locally reacting boundary.

Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain

Transmitting boundaries are important for modeling the wave propagation in the finite element analysis of dynamic foundation problems. In this study, viscoelastic boundaries for multiple seismic waves or excitations sources were derived for two-dimensional and three-dimensional conditions in the time domain, which were proved to be solid by finite element models. Then, the method for equivalent forces’ input of seismic waves was also described when the proposed artificial boundaries were applied. Comparisons between numerical calculations and analytical results validate this seismic excitation input method. The seismic response of subway station under different seismic loads input methods indicates that asymmetric input seismic loads would cause different deformations from the symmetric input seismic loads, and whether it would increase or decrease the seismic response depends on the parameters of the specific structure and surrounding soil.

Geometrically Nonlinear Transient Response of Laminated Plates with Flexible Supports

Laminated plates are loading-bearing components that are generally connected to flexible pads and exhibit complicated mechanical responses. To investigate the geometrically nonlinear transient responses of a laminated plate with flexible pad supports, a varied constraint reaction model and a systematic numerical procedure are presented in this paper. The flexible pad supports of the plate were treated as viscoelastic boundary conditions, wherein the strip-type pad per unit length was modeled as a cantilever beam. The nonlinear Kelvin–Voigt model was developed to simulate the nonlinear viscoelastic behaviors of the flexible pads. The dynamically varied constraint reactions generated by the viscoelastic supports, which depend upon the displacement and velocity of the nodes along the plate edge, were determined by the deflection and slope equations of the beam theory used, and they were applied on the plate edges by using the nonlinear load functions. Thus, the dynamical responses of the laminated plate with viscoelastic supports were obtained. Numerical results show that the present method can effectively treat the geometrically nonlinear transient response of the laminated plate with viscoelastic supports, and it is essential to consider the effects of non-ideal boundary conditions in the nonlinear transient analysis.

Dynamic stability of FG-CNT-reinforced viscoelastic micro cylindrical shells resting on nonhomogeneous orthotropic viscoelastic medium subjected to harmonic temperature distribution and 2D magnetic field

This paper deals with the dynamic stability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced micro cylindrical shells. The structure is subjected to harmonic non-uniform temperature distribution and 2D magnetic field. The CNT reinforcement is either uniformly distributed or FG along the thickness direction where the effective properties of nano-composite structure are estimated through Mixture low. The viscoelastic properties of structure are captured based on the Kelvin–Voigt theory. The surrounding viscoelastic medium is considered nonhomogeneous with the spring, orthotropic shear and damper constants. The material properties of cylindrical shell and the viscoelastic medium constants are assumed temperature-dependent. The first order shear deformation theory (FSDT) or Mindlin theory in conjunction with Hamilton\'s principle is utilized for deriving the motion equations where the size effects are considered based on Eringen\'s nonlocal theory. Based on differential quadrature (DQ) and Bolotin methods, the dynamic instability region (DIR) of structure is obtained for different boundary conditions. The effects of different parameters such as volume percent and distribution type of CNTs, mode number, viscoelastic medium type, temperature, boundary conditions, magnetic field, nonlocal parameter and structural damping constant are shown on the DIR of system. Numerical results indicate that the FGX distribution of CNTs is better than other considered cases. In addition, considering structural damping of system reduces the resonance frequency.

General decay of solutions of a Bresse system with viscoelastic boundary conditions

In this paper we are concerned with a multi-dimensional Bresse system, in a bounded domain, where the memory-type damping is acting on a portion of the boundary. We establish a general decay results, from which the usual exponential and polynomial decay rates are only special cases.

A micro-nano-rheometer for the mechanics of soft matter at interfaces.

We present a nano-rheometer based on the dynamic drainage flow between a sphere and a plane from bulk regime to highly confined regime. The instrument gives absolute measurements of the viscosity of simple liquids in both regimes. For complex fluids, the measurements involve the viscosity and the elastic modulus. The device operates on distances ranging over four orders of magnitude from 1 nm to 10 μm, bridging rheological properties from the macroscopic to the molecular scale. This allows to measure an hydrodynamic or visco-elastic boundary condition and to explore the causes of the boundary condition at the microscopic level.

Reflection of longitudinal displacement wave at the viscoelastically supported boundary of micropolar half-space

The reflection of elastic waves at the boundary of micropolar half-space with the viscoelastic support is studied in this paper. The spring-dashpot model is used to model the viscoelastic support. The boundary condition includes the force stress, couple stress, the displacements and the micro-rotation and the contribution from the spring and the dashpot on them. The amplitude ratios and phase shifts of reflection waves with respect to the incident wave are obtained from the visco-elastic boundary conditions. Further, the energy flux ratios of the reflection waves to the incident wave are estimated and the energy flux conservation with consideration of the energy dissipation of visco-elastic boundary is used to validate the numerical results. Based on the numerical results, the influences of spring and dashpot are studied respectively. It is found that the elastically supported boundary and the viscously supported boundary have evident different influences on the amplitude ratio and the phase shift. The causes resulting in these deviations are related with the instantaneous elasticity of elastic boundary and the time-delay effects of viscous boundary.

Hybrid material and foundation damping of Timoshenko beams

In this paper, vibration suppression of shear deformable beams with hybrid material-foundation viscoelastic damping is studied. The precise behavior of viscoelastic polymeric structures is taken into consideration by Boltzmann superposition integral and utilizing dynamic mechanical analysis (DMA) results while foundation viscoelasticity is adapted by Kelvin-Voigt model. The integro-partial differential equations of motion are derived based on the Timoshenko theory via Hamilton principle. Assessment of the solution procedure is carried out by comparison with elastic Timoshenko and viscoelastic Euler-Bernoulli cases. Transient response, natural frequency and modal loss factor are attained by Fourier transform, weighted residual method and numerical iterative algorithm. Influences of hybrid viscoelastic damping, foundation properties, geometrical parameters and boundary conditions on vibration characteristics and dynamic response are investigated via comprehensive parametric study. Due to the absence of similar results in the literature, this paper is likely to fill a gap in the state of the art of this problem.

Nonlocal longitudinal vibration of viscoelastic coupled double-nanorod systems

Abstract A theoretical study of the free longitudinal vibration of a nonlocal viscoelastic double-nanorod system (VDNRS) is presented in this paper. It is assumed that a light viscoelastic layer continuously couples two parallel nonlocal viscoelastic nanorods. The model is aimed at representing dynamic interactions in nanocomposite materials. The exact solution for the longitudinal vibration of a double-nanorod system is determined for two types of boundary conditions, Clamped–Clamped (C–C) and Clamped–Free (C–F). D'Alembert's principle is applied to derive the governing equations of motion in terms of the generalized displacements for a nonlocal viscoelastic constitutive equation. The solutions of a set of two homogeneous partial differential equations are obtained by using the classical Bernoulli–Fourier method. Numerical results are presented to show the effect of material length scale parameter, damping from viscoelastic constitutive equations, damping of light viscoelastic layer and boundary conditions for the free longitudinal vibration of a viscoelastic double-nanorod system.

Seismic Response Analysis of Prestressed Concrete Bridge

Using large-scale finite element analysis software ANSYS analyzes seismic respons of prestressed concrete bridge, respectively establish finite element model under viscoelastic boundary conditions and elastic boundary conditions, compare and analyze seismic respons of bridge structure under two kinds of boundary conditions. Compared with elastic boundary conditions, viscoelastic boundary conditions not only can simulate elastic recovery performance of foundation, but also can realize infinite medium radiation damping. The research results provide the basis for the seismic design and protection of bridge.

Seismic Response Analysis of Fuyang River Aqueduct

In this paper, using finite element software ANSYSanalyzes seismic respons of Fuyang river aqueduct, respectively establishfinite element model under viscoelastic boundary conditions and elasticboundary conditions, compare and analyze seismic respons of aqueduct structureunder two kinds of boundary conditions. The results show that, compared withelastic boundary conditions, viscoelastic boundary conditions not only cansimulate elastic recovery performance of foundation, but also can realizeinfinite medium radiation damping, and viscoelastic boundary conditions is moreclose to the actual situation.

Dynamic Response Analysis of Docking Chamber Structure Considering Viscoelastic Boundary Condition

Spring-damper units were set on the boundaries to absorb incident waves and reflected scattering waves to realize viscoelastic artificial boundary (VAB). The equivalent node load input method was used to simulate the VAB and viscoelastic boundary element wave input. Programming is based on APDL secondary development language with ANSYS finite element software. Considering the interaction between chamber structure and the surrounding soil, docking chamber structure dynamic model is established based on the VAB. The linear elastic model was used for concrete structure. The D-P nonlinear model was used for the back soil calculation. Docking chamber structure dynamic analysis under conditions of fixed boundaries and viscoelastic boundaries were conducted. The result indicated that under the viscoelastic boundary conditions, dynamic acceleration response is significant on the top of the lock wall, which is approximately 2.5 times of the value on the bottom of the lock wall. The maximum response stress appears near the cross point of the lock wall and the bottom floor with value of approximately 5620 kPa;.The chamber bottom floor is subjected to tension and maximum stress with the value of approximately 6180 kPa. Usually, the structure response under the fixed boundary conditions is higher than the structure response under the viscoelastic boundary conditions.

Free vibration analysis of a functionally graded viscoelastic supported beam

In this study, the resonance frequency behavior of a functionally graded beam under viscoelastic boundary conditions is investigated. Nondimensional frequency parameters of the beam are analyzed using the finite element method. The system of equations of motion is derived by using Lagrange's equations under the assumption of Euler–Bernoulli beam theory. The material properties of the beam are assumed to vary through thickness according to the power-law distribution. Different boundary conditions are attained by applying various stiffness and damping coefficients to viscoelastic support elements. The model is validated by comparing the results with a previous study. The effects of various material distribution and boundary conditions are discussed in detail.