• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1433-1448
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• 2021

In the present work, we investigate a viscoelastic equation involving a logarithmic nonlinear source term. After proving the existence of solutions, we establish a general decay estimate of the solution using energy estimates and theory of convex functions. This result extends and complements some previous results of [9, 21].

• Interaction and multiscale mechanics
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• v.6 no.1
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• pp.31-50
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• 2013

A five parameter viscoelastic model is developed to study harmonic waves propagating in the non-homogeneous viscoelastic filaments of varying density. The constitutive relation for five parameter model is first developed and then it is applied for harmonic waves in the specimen. In this study, it is assumed that density, rigidity and viscosity of the specimen i.e., rod are space dependent. The specimen is non-homogeneous, initially unstressed and at rest. The method of non-linear partial differential equation has been used for finding the dispersion equation of harmonic waves in the rods. A simple method is presented for reflections at the free end of the finite non-homogeneous viscoelastic rods. The harmonic wave propagation in viscoelastic rod is also presented numerically with MATLAB.

• International Journal of Aeronautical and Space Sciences
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• v.13 no.4
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.4
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• pp.619-628
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• 2001

A viscoelastic constitutive equation of rubber is proposed under small oscillatory load superimposed on large static deformation. The proposed model is derived through linearization of Simos nonlinear viscoelastic constitutive model and reference configuration transformation. Statically pre-deformed state is used as reference configuration. The model is extended to a generalized viscoelastic constitutive equation including widely-used Mormans model. Static deformation correction factor is introduced to consider the influence of pre-strain on the relaxation function. The model is tested for dynamic behavior of rubbers with different carbon black fractions. It is shown that the constitutive equation with static deformation correction factor agrees well with test results.

• Journal of KSNVE
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• v.4 no.4
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• pp.487-496
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• 1994

Recently, the application of viscoelastic material in the field of vibration isolation has gradually increased due to its achievement in structural damping capacity, and many of the theoretical and experimental study has been carried out. In this study, the dynamic characteristics of the visoelastically supported cantilever beam, of which govering equation is based on the Bernoulli- Euler equation, is analyzed theoretically and experimentally. Expression for stiffness of multi-layered viscoelastic materal has been developed using variables such as frequency and number of layers, and further, based on this expression, damping characteristic of the beam is investigated with experimental verification.

• Steel and Composite Structures
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• v.45 no.3
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• pp.349-367
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• 2022

In this research, an approach combining a semi-analytical method and an analytical method is presented to investigate the static and dynamic post-buckling behavior of the sandwich functionally graded (FG) porous cylindrical shells exposed to external pressure. The sandwich cylindrical shell considered is composed of a viscoelastic core and two FG porous (FGP) face layers. The viscoelastic core is made of Kelvin-Voigt-type material. The material properties of the FG porous face layer are considered continuous through each face thickness according to a porosity coefficient and a volume fraction index. Two types of sandwich FG porous viscoelastic cylindrical shells named Type A and Type B are considered in the research. Type A shell has the porosity evenly distributed across the thickness direction, and Type B has the porosity unevenly distributes across the thickness direction. The FG face layers are considered in two cases: outside metal surface, inside ceramic surface (OMS-ICS), and inside metal surface, outside ceramic surface (IMS-OCS). According to Donnell shell theory, von-Karman equation, and Galerkin's method, a discretized nonlinear governing equation is derived for analyzing the behavior of the shells. The explicit expressions for static and dynamic critical buckling loading are thus developed. To study the dynamic buckling of the shells, the governing equation is examined via a numerical approach implementing the fourth-order Runge-Kutta method. With a procedure presented by Budiansky-Roth, the critical load for dynamic post-buckling is obtained. The effects of various parameters, such as material and geometrical parameters, on the post-buckling behaviors are investigated.

• Structural Engineering and Mechanics
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• v.81 no.6
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• pp.705-714
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• 2022

The aim of this paper is to investigate nonlinear dynamic responses of functionally graded composite beam resting on the nonlinear viscoelastic foundation subjected to moving mass with temperature rising. The non-linear strain-displacement relationship is considered in the finite strain theory and the governing nonlinear dynamic equation is obtained by using the Hamilton's principle. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then the governing equation is solved by using of multiple time scale method. The influences of temperature rising, material distribution parameter, nonlinear viscoelastic foundation parameters, magnitude and velocity of the moving mass on the nonlinear dynamic responses are investigated. Also, the buckling temperatures of the functionally graded beams based on the finite strain theory are obtained.

• Elastomers and Composites
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• v.45 no.4
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• pp.250-255
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• 2010

From the three element non-Newtonian model of one non-Newtonian viscoelastic Maxwell elements and a elastic spring, the stress relaxation equation was derived. The various model parameters of this equation were evaluated by appling the experimental results of stress relaxation to the stress relaxation equation. The theoretical curves calculated from this model parameters agreed with the experimental stress relaxation curves. From the parameters of nonlinear viscoelastic model, the hole volume, fine structure, viscoelastic properties and mechanical properties of polymer fibers were studied. The experiments of stress relaxation were carried out using the tensile tester with the solvent chamber. The stress relaxation curves of the two types polyacrylonitrile-polyvinylchloride copolymer and another two types PVC monofilament fibers were obtained in air and water of various temperatures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.12
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• pp.2072-2078
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• 2003

In this paper, the boundary element analysis of viscoelastic strain energy release rate G(t) for the cracked linear viscoelastic solids has been attempted. This study proposes the G(t) equation and the calculating method of G(t) by time-domain boundary element analysis for the viscoelastic solids. The G(t) is defined as the derivative of the viscoelastic potential energy II(t) with respect to crack length a. Two example problems are presented to show the applicability of the proposed method to the analysis of the cracked linear viscoelastic solids. Numerical results of example problems show the accuracy and effectiveness of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.907-914
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• 2015

In this paper, we consider a viscoelastic plate equation with p-Laplacian $u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both ${\sigma}$ and g.