• Wind and Structures
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• v.7 no.2
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• pp.89-106
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• 2004

The response of tall buildings to gust buffeting is usually evaluated assuming that the structural damping is of a viscous nature. In addition, when dampers are incorporated in the design to mitigate the response, their effect is allowed for increasing the building modal damping ratios by a quantity corresponding to the additional energy dissipation arising from the presence of the devices. Even though straightforward, this procedure has some degree of inaccuracy due to the existence of a memory effect, associated with the damping mechanism, which is neglected by a viscous model. In this paper a more realistic viscoelastic model is used to evaluate the response to gust buffeting of tall buildings provided with energy dissipation devices. Both cases of viscous and hysteretic inherent damping are considered, while for the dampers a generic viscoelastic behaviour is assumed. The Laguerre Polynomial Approximation is used to write the equations of motion and find the frequency response functions. The procedure is applied to a 25-story building to quantify the memory effects, and the inaccuracy arising when the latter is neglected.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.37-52
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• 2005

We consider the existence of solutions of viscoelastic degenerate problem of Kirchhoff type with nonlinear boundary damping and memory term. Moreover, we consider the uniform decay of the energy for the problem.

• Steel and Composite Structures
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• v.45 no.4
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• pp.535-546
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• 2022

The memory response of nonlocal systematical formulation size-dependent coupling of viscoelastic deformation and thermal fields for piezoelectric materials with dual-phase lag heat conduction law is constructed. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern control theory, is applied to the non-dimensional equations. The resulting formulation together with the Laplace transform technique is applied to solve a problem of a semi-infinite piezoelectric rod subjected to a continuous heat flux with constant time rates. The inversion of the Laplace transforms is carried out using a numerical approach. Some comparisons of the impacts of nonlocal parameters and time-delay constants for various forms of kernel functions on thermal spreads and thermo-viscoelastic response are illustrated graphically.

• East Asian mathematical journal
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• v.34 no.1
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• pp.69-84
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• 2018

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source for each independent kernels h and g with respect to Volterra terms. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Smart Structures and Systems
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• v.19 no.5
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• pp.539-551
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• 2017

A mathematical model of electro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with memory-dependent derivative. The governing coupled equations with time-delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to several concrete problems. The exact solutions for all fields are obtained in the Laplace transform domain for each problem. According to the numerical results and its graphs, conclusion about the proposed model has been constructed. The predictions of the theory are discussed and compared with dynamic classical coupled theory. The result provides a motivation to investigate conducting thermoelectric viscoelastic materials as a new class of applicable materials.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.943-966
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• 2023

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan-Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with g satisfying some general growth at infinity.

• Proceedings of the Korean Society of Rheology Conference
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• 2001.09a
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• pp.162.3-162
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• 2001

• Computational Structural Engineering
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• v.6 no.2
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• pp.103-114
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• 1993

An advanced time-domain finite element formulation is presented for the displacement and stress analysis of isotropic, linear viscoelastic problems of a hereditary-type constitutive law. The semidiscrete finite element method with linear time-stepping scheme and an elastic-viscoelastic correspondence principle are used in the theoretical development. An efficient treatment of hereditary integral is introduced to improve the numerical accuracy, to reduce the computation time, and to avoid the use of large memory storage. Two-dimensional numerical examples of plane strain and plane stress are solved under the assumption on the material property of being elastic in dilatation and like three-element Voigt model in distorsion, and compared with the analytical solutions and the past numerical results to show the versatility and efficiency of the proposed method.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.727-734
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• 2004

An uncoupled computational model for analyzing the hygrothermal dynamic response of composite laminates has been developed. The constitutive equations, expressed in an integral form, and involving relaxation moduli are adopted, to describe the non-aging hygrothermorheologically simple materials. A Prony series represents the relaxation moduli is exploited in order to derive a recursive relationship, and thereby eliminate the storage problem that arises when dealing with material possessing memory. The problem is formulated in a descritized variational form. Mindlin and higher order finite elements are employed for spatial descretization, while the Newmark average acceleration scheme is exploited for temporal descritization. The adopted recursive formula uses only the details of the previous event to compute the details of the current one. Numerical results of the displacement fields of both thin and thick viscoelastic laminates problems are discussed to show up the effectiveness of Mindlin and higher-order shear theories.

• Journal of Aerospace System Engineering
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• v.18 no.1
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• pp.1-10
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• 2024

In a previous study, a structure of a superplastic yoke consisting of a thin FR4 layer laminated with viscoelastic tape on both sides of a shape memory alloy (SMA) was proposed to reduce residual vibration generated by a deployable solar panel during high motion of a satellite. Damping properties of viscoelastic tapes will change with temperature, which can directly affect vibration reduction performance of the yoke. To check damping performance of the yoke at different temperatures, free damping tests were performed under various temperature conditions to identify the temperature range where the damping performance was maximized. Based on above temperature test results, this paper predicts temperature of the yoke through orbital thermal analysis so that the yoke can have effective damping performance even if it is exposed to an orbital thermal environment. In addition, the thermal design method was described so that the yoke could have optimal vibration reduction performance.