• Structural Engineering and Mechanics
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• 제63권2호
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• pp.181-193
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• 2017

An identification method for determination of the parameters of the rheological models of dampers made of viscoelastic material is presented. The models have two, three or four parameters and the model equations of motion contain derivatives of the fractional order. The results of dynamical experiments are approximated using the trigonometric function in the first part of the procedure while the model parameters are determined as the solution to an appropriately defined optimization problem. The particle swarm optimization method is used to solve the optimization problem. The validity and effectiveness of the suggested identification method have been tested using artificial data and a set of real experimental data describing the dynamic behavior of damper and a fluid frequently used in dampers. The influence of a range of excitation frequencies used in experiments on results of identification is also discussed.

• Structural Engineering and Mechanics
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• 제41권1호
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• pp.113-137
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• 2012

Frame structures with viscoelastic (VE) dampers mounted on them are considered in this paper. It is the aim of this paper to compare the dynamic characteristics of frame structures with VE dampers when the dampers are modelled by means of different models. The classical rheological models, the model with the fractional order derivative, and the complex modulus model are used. A relatively large structure with VE dampers is considered in order to make the results of comparison more representative. The formulae for dissipation energy are derived. The finite element method is used to derive the equations of motion of the structure with dampers and such equations are written in terms of both physical and state-space variables. The solution to motion equations in the frequency domain is given and the dynamic properties of the structure with VE dampers are determined as a solution to the appropriately defined eigenvalue problem. Several conclusions concerning the applicability of a family of models of VE dampers are formulated on the basis of results of an extensive numerical analysis.

• Structural Engineering and Mechanics
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• 제52권6호
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• pp.1069-1084
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• 2014

The long-term performance of plates resting on viscoelastic foundations is a major concern in the analysis of soil-structure interaction. As a powerful mathematical tool, fractional calculus may address these plate-on-foundation problems. In this paper, a fractionalized Zener model is proposed to study the time-dependent behavior of a uniformly loaded rectangular thin foundation plate. By use of the viscoelastic-elastic correspondence principle and the Laplace transforms, the analytical solutions were obtained in terms of the Mittag-Leffler function. Through the analysis of a numerical example, the calculated plate deflection, bending moment and foundation reaction were compared to those from ideal elastic and standard viscoelastic models. It is found that the upper and lower bound solutions of the plate response estimated by the proposed model can be determined using the elastic model. Based on a parametric study, the impacts of model parameters on the long-term performance of a foundation plate were systematically investigated. The results show that the two spring stiffnesses govern the upper and lower bound solutions of the plate response. By varying the values of the fractional differential order and the coefficient of viscosity, the time-dependent behavior of a foundation plate can be accurately captured. The fractional differential order seems to be dependent on the mechanical properties of the ground soil. A sandy foundation will have a small fractional differential order while in order to simulate the creeping of clay foundation, a larger fractional differential order value is needed. The fractionalized Zener model is capable of accounting for the primary and secondary consolidation processes of the foundation soil and can be used to predict the plate performance over many decades of time.

• 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.