• Steel and Composite Structures
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• v.48 no.3
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• pp.293-303
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• 2023

In this paper, geometrically nonlinear free vibration analysis of Mindlin viscoelastic plates with various geometrical and material properties is studied based on the Von-Karman assumptions. A novel solution is proposed in which the nonlinear frequencies of time-dependent plates are predicted according to the nonlinear frequencies of plates not dependent on time. This method greatly reduces the cost of calculations. The viscoelastic properties obey the Boltzmann integral law with constant bulk modulus. The SHPC meshfree method is employed for spatial discretization. The Laplace transformation is used to convert equations from the time domain to the Laplace domain and vice versa. Solving the nonlinear complex eigenvalue problem in the Laplace-Carson domain numerically, the nonlinear frequencies, the nonlinear viscous damping frequencies, and the nonlinear damping ratios are verified and calculated for rectangular, skew, trapezoidal and circular plates with different boundary conditions and different material properties.

• Smart Structures and Systems
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• v.30 no.3
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• pp.239-243
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• 2022

We investigate the influence of nonlinear viscoelastic damping on the response of a cantilever sensor covered by piezoelectric layers in a symmetric or asymmetric configuration. We formulate an initial-boundary-value problem which consistently incorporates both geometric and material nonlinearities including the effect of viscoelastic damping which cannot be ignored for micro- and nano-mechanical sensor operation in a vacuum environment. We employ an asymptotic multiple-scales methodology to yield the system nonlinear frequency response near its primary resonance and employ a model-based estimation procedure to deduce the system damping backone curve from controlled experiments in vacuum. We discuss the effect of nonlinear damping on sensor applications for scanning probe microscopy.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1999.10a
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• pp.228-235
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• 1999

As a seismic damper the viscoelastic damper is known the effective method to control the drift of the flexible building. As the viscoelastic damper has the characteristics of both damping and stiffness specially when the rubber material used hysteretic damping. The behavior of the hysteretic damping is quite different from that of the viscous damping. For the evaluation of the viscoelastic damper for the seismic purpose the nonlinear response spectrum was generated based on the dynamic test of the viscoelastic damper and the results is compared to that of the typical linear response spectrum,

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.137-147
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• 2022

In this paper, we considered the Dirichlet initial boundary value problem of a nonlinear viscoelastic wave equation with nonlinear damping and source terms, and investigated finite time blow-up phenomena of the solutions to the equation with arbitrary positive initial data, under suitable conditions.

• 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.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.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.387-407
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• 2010

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.

• 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.

• Steel and Composite Structures
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• v.44 no.1
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• pp.91-104
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• 2022

The purpose of the present work is to study the parametric nonlinear vibration behavior of three layered symmetric laminated plate. In the analytical formulation; both normal and shear deformations are considered in the core layer by means of the refined higher-order zig-zag theory. Harmonic balance method in conjunction with Galerkin procedure is adopted for simply supported laminate plate, to obtain its natural and damping properties. For these aims, a set of complex amplitude equations governed by complex parameters are written accounting for the geometric nonlinearity and viscoelastic damping factor. The frequency response curves are presented and discussed by varying the material and geometric properties of the core layer.

• Structural Engineering and Mechanics
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• v.75 no.1
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• pp.87-100
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• 2020

The present paper investigates the combination resonance behavior of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal and external functionally graded stiffeners under two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. With regard to classical plate theory of shells, von-Kármán equation and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The combination resonance is obtained by using the multiple scales method. Finally, the influences of the stiffeners angles, foundation type, the nonlinear elastic foundation coefficients, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.