• International Journal of Aeronautical and Space Sciences
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• 제13권4호
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• pp.458-467
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• 2012

In this study, the linear viscoelastic response of a rectangular laminated plate is investigated. The viscoelastic properties, expressed by two basic spring-dashpot models, that is Kelvin and Maxwell models, is assumed in the range to investigate the influence of viscoelastic coefficients to mechanical behavior. In the present study, viscoelastic responses are performed for two popular equivalent single-layered theories, such as the first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT). Compliance and relaxation modulus of time-dependent viscoelastic behavior are approximately determined by Prony series. The constitutive equation for linear viscoelastic material as the Boltzmann superposition integral equation is simplified by the convolution theorem of Laplace transformation to avoid direct time integration as well as to improve both accuracy and computational efficiency. The viscoelastic responses of composite laminates in the real time domain are obtained by applying the inverse Laplace transformation. The numerical results of viscoelastic phenomena such as creep, cyclic creep and recovery creep are presented.

• 한국구조물진단유지관리공학회 논문집
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• 제6권1호
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• pp.171-177
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• 2002

The viscoelastic dampers are considered to be one of the most efficient means of upgrading existing structures against seismic loads. Generally in the dynamic analysis of a structure with added viscoelastic dampers the internal forces of the dampers are represented by constants that are linearly proportional to displacement and velocity. The purpose of this study is to verify the validity of the linear Kelvin model by comparing the results from the linear analysis with those obtained from the more rigorous nonlinear model such as fractional derivative model. According to the results the structural responses of 1-DOF structure obtained using the linear model are very close to those obtained from nonlinear model. However for multi-D0F structure the difference between the results from both models is enlarged as a results of the assumptions associated with the linear modeling of the viscoelastic dampers.

• Geomechanics and Engineering
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• 제39권3호
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• pp.257-271
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• 2024

In this study, free and forced vibration behaviour of viscoelastic porous functionally graded (VPFG) plates resting on elastic foundations are investigated. Differential equations are obtained via higher order shear deformation theory. Equations of motion are obtained through energy formulations and Hamilton's principle. Navier's method based on double Fourier series is employed for the solution. Damping effect is implemented into the analysis by means of Kelvin and linear standard viscoelastic models. Viscoelastic material properties are used instead of elastic properties by means of the correspondence principle. Displacements of the plates are determined in Laplace domain and transformed into time domain by using Durbin's Modified Inverse Laplace transform method. The proposed algorithm's accuracy is validated through free and damped vibration analyses on VPFG plate, with results compared to existing studies in the literature. The study examines the influence of viscoelastic damping parameters, porosity volume fraction indexes, foundation characteristics, porosity distribution patterns and material property variations on the damped forced vibration response.

• Journal of Pharmaceutical Investigation
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• 제39권3호
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• pp.185-199
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• 2009

Using a strain-controlled rheometer [Advanced Rheometric Expansion System (ARES)], the steady shear flow properties and the dynamic viscoelastic properties of $Antiphlamine-S^{(R)}$ lotion have been measured at $20^{\circ}C$ (storage temperature) and $37^{\circ}C$ (body temperature). In this article, the temperature dependence of the linear viscoelastic behavior was firstly reported from the experimental data obtained from a temperature-sweep test. The steady shear flow behavior was secondly reported and then the effect of shear rate on this behavior was discussed in detail. In addition, several inelastic-viscoplastic flow models including a yield stress parameter were employed to make a quantitative evaluation of the steady shear flow behavior, and then the applicability of these models was examined by calculating the various material parameters. The angular frequency dependence of the linear viscoelastic behavior was nextly explained and quantitatively predicted using a fractional derivative model. Finally, the strain amplitude dependence of the dynamic viscoelastic behavior was discussed in full to elucidate a nonlinear rheological behavior in large amplitude oscillatory shear flow fields. Main findings obtained from this study can be summarized as follows : (1) The linear viscoelastic behavior is almostly independent of temperature over a temperature range of $15{\sim}40^{circ}C$. (2) The steady shear viscosity is sharply decreased as an increase in shear rate, demonstrating a pronounced Non-Newtonian shear-thinning flow behavior. (3) The shear stress tends to approach a limiting constant value as a decrease in shear rate, exhibiting an existence of a yield stress. (4) The Herschel-Bulkley, Mizrahi-Berk and Heinz-Casson models are all applicable and have an equivalent validity to quantitatively describe the steady shear flow behavior of $Antiphlamine-S^{(R)}$ lotion whereas both the Bingham and Casson models do not give a good applicability. (5) In small amplitude oscillatory shear flow fields, the storage modulus is always greater than the loss modulus over an entire range of angular frequencies tested and both moduli show a slight dependence on angular frequency. This means that the linear viscoelastic behavior of $Antiphlamine-S^{(R)}$ lotion is dominated by an elastic nature rather than a viscous feature and that a gel-like structure is present in this system. (6) In large amplitude oscillatory shear flow fields, the storage modulus shows a nonlinear strain-thinning behavior at strain amplitude range larger than 10 % while the loss modulus exhibits a weak strain-overshoot behavior up to a strain amplitude of 50 % beyond which followed by a decrease in loss modulus with an increase in strain amplitude. (7) At sufficiently large strain amplitude range (${\gamma}_0$>100 %), the loss modulus is found to be greater than the storage modulus, indicating that a viscous property becomes superior to an elastic character in large shear deformations.

• Elastomers and Composites
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• 제53권4호
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• pp.207-212
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• 2018

Taylor rod impact tests have been the subject of many theoretical and experimental investigations. This paper discusses the numerical methods for simulating the Taylor impact test, which is widely used to obtain constitutive equations and failure conditions under high-velocity collisions of materials. With this in mind, a particle-based MPM (material point method) for linear viscoelastic solid materials was implemented, and MPM simulations for viscoelastic deformation behavior were numerically verified and confirmed by comparing the MPM and FEM results. In addition, this modeling and numerical approach could be extended to more complex viscoelastic models for basic understanding and to analyze the deformation and fracture behavior of more complicated viscoelastic material systems.

• Structural Engineering and Mechanics
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• 제73권3호
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• pp.319-330
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• 2020

This paper investigates the free vibrations of cylindrical shells made of time-dependent materials for different viscoelastic models under various boundary conditions. During the extraction of equations, the displacement field is estimated through the first-order shear deformation theory taking into account the transverse normal strain effect. The constitutive equations follow Hooke's Law, and the kinematic relations are linear. The assumption of axisymmetric is included in the problem. The governing equations of thick viscoelastic cylindrical shell are determined for Maxwell, Kelvin-Voigt and the first and second types of Zener's models based on Hamilton's principle. The motion equations involve four coupled partial differential equations and an analytical method based on the elementary theory of differential equations is used for its solution. Relying on the results, the natural frequencies and mode shapes of viscoelastic shells are identified. Conducting a parametric study, we examine the effects of geometric and mechanical properties and boundary conditions, as well as the effect of transverse normal strain on natural frequencies. The results in this paper are compared against the results obtained from the finite elements analysis. The results suggest that solutions achieved from the two methods are ideally consistent in a special range.

• Structural Engineering and Mechanics
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• 제11권1호
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• pp.71-87
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• 2001

A frequency domain response analysis is presented for building frames passively controlled by viscoelastic dampers, under harmonic ground excitation. Three different models are used to represent the linear dynamic force-deformation characteristics of viscoelastic dampers namely, Kelvin model, Linear hysteretic model and Maxwell model. The frequency domain solution is obtained by (i) an iterative pseudo-force method, which uses undamped mode shapes and frequencies of the system, (ii) an approximate modal strain energy method, which uses an equivalent modal damping of the system in each mode of vibration, and (iii) an exact method which uses complex frequency response function of the system. The responses obtained by three different methods are compared for different combinations of viscoelastic dampers giving rise to both classically and non-classically damped cases. In addition, the effect of the modelling of viscoelastic dampers on the response is investigated for a certain frequency range of interest. The results of the study are useful in appropriate modelling of viscoelastic dampers and in understanding the implication of using modal analysis procedure for building frames which are passively controlled by viscoelastic dampers against base excitation.

• 한국전산구조공학회논문집
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• 제18권3호
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• pp.321-332
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• 2005

본 논문에서는 축대칭 형상의 점탄성 구조물이 정적 하중을 받을 때에 대한 시간영역에서의 유한요소해법의 정식화 과정을 제시한다. 또한, 여러 가지 경계조건을 갖는 점탄성 중공구나 원통 문제들의 변위나 응력 이론해들을 탄성-점탄성 상응원리를 이용하여 유도하고 제시한다. 이때 점탄성 재료는 부피변형이 탄성적이고 전단변형은 3요소로 구성된 표준선형 고체처럼 거동한다고 가정한다. 구대칭, 축대칭 및 평면변형률 유한요소모텔을 이용한 수치결과들을 유도된 이론해들과 비교하여 제시된 유한요소해법과 이론해들의 타당성과 정확성을 보인다.

• Korea-Australia Rheology Journal
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• 제13권4호
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• pp.205-217
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• 2001

This review article summarizes results of recent viscoelastic and dielectric studies for entangled cis-polyisoprene (PI) chains. The PI chains have the so-called type-A dipoles parallel along the chain backbone, and their slow viscoelastic and dielectric relaxation processes reflect the same global chain motion. However, this motion is differently averaged in the viscoelastic and dielectric properties, the former representing the isochronal orientational anisotropy of individual entanglement segments while the latter detecting the orientational correlation of the segments at two separate times (0 and t). On the basis of this difference, the viscoelastic and dielectric data of the entangled PI chains were compared to elucidate detailed features of the chain dynamics. Specifically, the molecular picture of dynamic tube dilation (DTD) incorporated in recent models was tested for linear and star PI chain. The comparison revealed that the DTD picture was valid for linear PI chains but failed for the star PI chains in the dominant part of the terminal relaxation. The failure for the star chains was related to the pre-requisite for the DTD process, rapid equilibration of successive entanglement segments through their constraint release (CR) motion: For the star chains, the dilated tube diameter expected in the terminal regime was considerably large because of a broad distribution of motional modes of the chains, so that the CR-equilibration required for DTD could not occur in time. The terminal relaxation of the star chain appeared to occur through the CR process before the expected DTD process was completed. The situation was different for the linear chain exhibiting narrowly distributed motional modes. The dilated tube expected for the linear chain was rather thin and the required CR-equilibration occurred in time, resulting in the success of the DTD picture. These detailed features of the chain dynamics was revealed only when the viscoelastic and dielectric properties were compared, demonstrating the importance of this comparison.

• Earthquakes and Structures
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• 제1권1호
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• pp.43-67
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• 2010

A gradient-based evolutionary optimization methodology is presented for finding the optimal design of both the added dampers and their supporting members to minimize an objective function of a linear multi-storey structure subjected to the critical ground acceleration. The objective function is taken as the sum of the stochastic interstorey drifts. A frequency-dependent viscoelastic damper and the supporting member are treated as a vibration control device. Due to the added stiffness by the supplemental viscoelastic damper, the variable critical excitation needs to be updated simultaneously within the evolutionary phase of the optimal damper placement. Two different models of the entire damper unit are investigated. The first model is a detailed model referred to as "the 3N model" where the relative displacement in each component (i.e., the spring and the dashpot) of the damper unit is defined. The second model is a simpler model referred to as "the N model" where the entire damper unit is converted into an equivalent frequency-dependent Kelvin-Voigt model. Numerical analyses for 3 and 10-storey building models are conducted to investigate the characters of the optimal design using these models and to examine the validity of the proposed technique.