• Journal of the Korea institute for structural maintenance and inspection
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• v.6 no.1
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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.

• Steel and Composite Structures
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• v.44 no.4
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• pp.557-567
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• 2022

Nonlinear free vibration analysis of a functionally graded beam resting on the nonlinear viscoelastic foundation is studied with uniform temperature rising. The non-linear strain-displacement relationship is considered in the finite strain theory. The governing nonlinear dynamic equation is derived based on the finite strain theory with using of 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 is solved by using of multiple time scale method. The influences of temperature rising, material distribution parameter, nonlinear viscoelastic foundation parameters on the nonlinear free response and phase trajectory are investigated. In this paper, it is aimed that a contribution to the literature for nonlinear thermal vibration solutions of a functionally graded beam resting on the nonlinear viscoelastic foundation by using of multiple time scale method.

• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.193-207
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• 2017

In this study, the vibration of an electrostatically actuated micro cantilever beam is analyzed in which a viscoelastic layer covers a portion of the micro beam length. This proposed model is considered as the main element of mass and pollutant micro sensors. The nonlinear motion equation is extracted by means of Hamilton principle, considering nonlinear shortening effect for Euler-Bernoulli beam. The non-linear effects of electrostatic excitation, geometry and inertia have been taken into account. The viscoelastic model is assumed as Kelvin-Voigt model. The motion equation is discretized by Galerkin approach. The linear free vibration mode shapes of non-uniform micro beam i.e. the linear mode shape of the system by considering the geometric and inertia effects of viscoelastic layer, have been employed as comparison function in the process of the motion equation discretization. The discretized equation of motion is solved by the use of multiple scale method of perturbation theory and the results are compared with the results of numerical Runge-Kutta approach. The frequency response variations for different lengths and thicknesses of the viscoelastic layer have been founded. The results indicate that if a constant volume of viscoelastic layer is to be deposited on the micro beam for mass or gas sensor applications, then a modified configuration may be found by using the analysis of this paper.

• Steel and Composite Structures
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• v.41 no.6
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• pp.821-829
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• 2021

Nonlinear dynamic response of a sandwich beam considering porous core and nano-composite face sheet on nonlinear viscoelastic foundation with temperature-variable material properties is investigated in this research. The Hamilton's principle and beam theory are used to drive the equations of motion. The nonlinear differential equations of sandwich beam respect to time are obtained to solve nonlinear differential equations by Homotopy perturbation method (HPM). The effects of various parameters such as linear and nonlinear damping coefficient, linear and nonlinear spring constant, shear constant of Pasternak type for elastic foundation, temperature variation, volume fraction of carbon nanotube, porosity distribution and porosity coefficient on nonlinear dynamic response of sandwich beam are presented. The results of this paper could be used to analysis of dynamic modeling for a flexible structure in many industries such as automobiles, Shipbuilding, aircrafts and spacecraft with solar easured at current time step and the velocity and displacement were estimated through linear integration.

• Journal of Pharmaceutical Investigation
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• v.36 no.1
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• pp.31-38
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• 2006

Using a Rheometries Dynamic Analyzer (RDA II), the dynamic viscoelastic properties of a semi-solid ointment base (vaseline) in large amplitude oscillatory shear flow fields were measured over a temperature range of $25{\sim}45^{\circ}C$ and the linear viscoelastic behavior in small amplitude oscillatory shear flow fields was investigated over a wide range of angular frequencies. In this article, the nonlinear viscoelastic behavior was reported from the experimentally obtained data and the effect of temperature on this behavior was discussed in detail. In addition, the angular frequency and temperature dependencies of a linear viscoelastic behavior were explained. Finally, the applicability of a time-temperature superposition principle originally developed for polymeric materials was examined using a shift factor. Main results obtained from this study can be summarized as follows : (1) At very small strain amplitude region, vaseline shows a linear viscoelastic behavior independent of the imposed deformation magnitudes. Above a critical strain amplitude $({\gamma}_{0}=0.1{\sim}0.2%)$, however, vaseline exhibits a nonlinear viscoelastic behavior ; indicating that both the storage modulus and dynamic viscosity are sharply decreased with increasing deformation magnitude. (2) In large amplitude oscillatory shear flow fields, an elastic behavior (storage modulus) has a stronger strain amplitude dependence and begins to show a nonlinear behavior at a smaller strain amplitude region than does a viscous behavior (dynamic viscosity). (3) In small amplitude oscillatory shear flow fields, the storage modulus as well as the loss modulus are continuously increased as an increase in angular frequency and an elastic nature is always superior to a viscous behavior over a wide range of angular frequencies. (4) A time-temperature superposition principle can successfully be applicable to vaseline. This finding allows us to estimate the dynamic viscoelastic behavior of vaseline over an extraordinarily extended range (11 decades) of angular frequencies inaccessible from the experimentally measured range (4 decades).

• Geomechanics and Engineering
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• v.32 no.2
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• pp.125-135
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• 2023

Nonlinear vibration analysis of composite beam reinforced by carbon nanotubes resting on the nonlinear viscoelastic foundation is investigated in this study. The material properties of the composite beam is considered as a polymeric matrix by reinforced carbon nanotubes according to different distributions. With using Hamilton's principle, the governing nonlinear partial differential equations are derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Kármán nonlinearity is used. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The nonlinear natural frequency and the nonlinear free response of the system is obtained. In addition, the effects of different patterns of reinforcement, linear and nonlinear damping coefficients of the viscoelastic foundation on the nonlinear vibration responses and phase trajectory of the carbon nanotube reinforced composite beam 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.

• Advances in aircraft and spacecraft science
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• v.11 no.1
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Journal of the Korean Applied Science and Technology
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• v.32 no.4
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• pp.661-668
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• 2015

The surface rheological properties of polymer monolayer show complicated non-linear viscoelastic flow phenomena when they are subjected to spreading flow. These spreading flow properties are controlled by the characteristics of flow units. The kinetics of the formation of an interfacial film obtained after spreading poly(diisobutylene maleic acid) at air-water interface were studied by measuring of the surface pressure with time. The experimental data were analyzed theoretically according to a nonlinear surface viscoelastic model. The values of dynamic modulus, static modulus, surface viscosities and rheological parameters in various area/ monomer were obtained by appling experimental data to the equation of nonlinear surface viscoelastic model.

• Korea-Australia Rheology Journal
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• v.18 no.2
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• pp.67-81
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• 2006

Using a strain-controlled rheometer, the dynamic viscoelastic properties of aqueous xanthan gum solutions with different concentrations were measured over a wide range of strain amplitudes and then the linear viscoelastic behavior in small amplitude oscillatory shear flow fields was investigated over a broad range of angular frequencies. In this article, both the strain amplitude and concentration dependencies of dynamic viscoelastic behavior were reported at full length from the experimental data obtained from strain-sweep tests. In addition, the linear viscoelastic behavior was explained in detail and the effects of angular frequency and concentration on this behavior were discussed using the well-known power-law type equations. Finally, a fractional derivative model originally developed by Ma and Barbosa-Canovas (1996) was employed to make a quantitative description of a linear viscoelastic behavior and then the applicability of this model was examined with a brief comment on its limitations. Main findings obtained from this study can be summarized as follows: (1) At strain amplitude range larger than 10%, the storage modulus shows a nonlinear strain-thinning behavior, indicating a decrease in storage modulus as an increase in strain amplitude. (2) At strain amplitude range larger than 80%, the loss modulus exhibits an exceptional nonlinear strain-overshoot behavior, indicating that the loss modulus is first increased up to a certain strain amplitude(${\gamma}_0{\approx}150%$) beyond which followed by a decrease in loss modulus with an increase in strain amplitude. (3) At sufficiently large strain amplitude range (${\gamma}_0>200%$), a viscous behavior becomes superior to an elastic behavior. (4) An ability to flow without fracture at large strain amplitudes is one of the most important differences between typical strong gel systems and concentrated xanthan gum solutions. (5) The linear viscoelastic behavior of concentrated xanthan gum solutions is dominated by an elastic nature rather than a viscous nature and a gel-like structure is present in these systems. (6) As the polymer concentration is increased, xanthan gum solutions become more elastic and can be characterized by a slower relaxation mechanism. (7) Concentrated xanthan gum solutions do not form a chemically cross-linked stable (strong) gel but exhibit a weak gel-like behavior. (8) A fractional derivative model may be an attractive means for predicting a linear viscoelastic behavior of concentrated xanthan gum solutions but classified as a semi-empirical relationship because there exists no real physical meaning for the model parameters.