• Advances in nano research
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• v.14 no.1
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• pp.45-65
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• 2023

This paper aimed to investigate the nonclassical size dependent free vibration behavior of regularly squared cutout viscoelastic nanobeams. The nonlocal strain gradient elasticity theory is modified and adopted to incorporate the viscoelasticity effect. The Kelvin Voigt viscoelastic model is adopted to model the linear viscoelastic constitutive response. To explore the influence of shear deformation effect due to cutout, both Euler Bernoulli and Timoshenko beams theories are considered. The Hamilton principle is utilized to derive the dynamic equations of motion incorporating viscoelasticity and size dependent effects. Closed form solutions for the resonant frequencies for both perforated Euler Bernoulli nanobeams (PEBNB) and perforated Timoshenko nanobeams (PTNB) are derived considering different boundary conditions. The developed procedure is verified by comparing the obtained results with the available results in the literature. Parametric studies are conducted to show the influence of the material damping, the perforation, the material and the geometrical parameters as well as the boundary and loading conditions on the dynamic behavior of viscoelastic perforated nanobeams. The proposed procedure and the obtained results are supportive in the analysis and design of perforated viscoelastic NEMS structures.

• Journal of KSNVE
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• v.10 no.3
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• pp.531-535
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• 2000

A three-parameter model of viscoelastic damper which has a non-linear spring as an element is incorporated into an oscillator. The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by get analytic solutions of the system. The frequency-response curves show that multiple solutions co-exist and that the jump phenomena can occur. In addition it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurences of such non-linear phenomena. A direct time intergration of the original equation of motion validifies the use of the harmonic balance method to this sort of 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.

• Advances in nano research
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• v.6 no.4
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• pp.399-422
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• 2018

Unwanted vibration is an issue in many industrial systems, especially in nano-devices. There are many ways to compensate these unwanted vibrations based on the results of the past researches. Elastic medium and smart material etc. are effective methods to restrain unnecessary vibration. In this manuscript, dynamic analysis of viscoelastic nanosensor which is made of functionally graded (FGM) nanobeams is investigated. It is assumed that, the shaft is flexible. The system is modeled based on Timoshenko beam theory and also environmental condition, external linear varying loads and thermal loading effect are considered. The equations of motion are extracted by using energy method and Hamilton principle to describe the translational and shear deformation's behavior of the system. Governing equations of motion are extracted by supplementing Eringen's nonlocal theory. Finally vibration behavior of system especially the frequency of system is developed by implementation Semi-analytical differential transformed method (DTM). The results are validated in the researches that have been done in the past and shows good agreement with them.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.543-546
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• 2000

Static and dynamic experiments were done to study on the restitution behaviors of strings. The elastic and viscoelastic model were compared. To apply a linear viscoelastic model (Kelvin model) to longitudinal behaviors of strings, static and dynamic tensile tests were done. Using their results, it should be intended to acquire damped stress (Stress related to velocity), and to calculate the viscoelastic coefficient. Fixing both ends, string was pushed by the loadcell attached to the tensile tester. The experimental results were in accordance with the calculated results using the Kelvin model acquired from the results of longitudinal tensile test. But the results of falling mass experiments, the behaviors of strings were near to elastic model. The clamping condition of strings in both sides has an effected on the value of COR. The smaller contact area, the grower the value of COR.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.04a
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• pp.744-749
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• 2011

Silicon oil in viscous fluid damper has a viscoelastic feature that show stiffness besides damping. These properties depend on frequency and are non-linear. A lot of research has been conducted in order to identify viscoelastic damper with mathematical model. Fractional Derivative Maxwell Model has been widely used, but this model did not explain the effect of damper size change on the damper performance. In this paper, the experimental study was conducted to validate damper's dynamic behaviors when total damper's size is changed while maintaining same aspect ratio and orifice size.

• Journal of KSNVE
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• v.10 no.1
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• pp.64-73
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• 2000

We present finite element equations in the Laplace-domain for linear viscoelastic and viscoelstically damped structures governed by a constitutive equation involving factional order derivative opeartors. These equations yield a nonstandard eigenproblem consisted of frequency dependent stiffness matrix. To solve this nonstandard eigenproblem we suggest an eigenvalue iteration procedure in the Laplace-domain. Improved Zenor and GHM material function type constitutive equations in the Laplace-domain are also available for this procedure. From above equations, complex eigenvalues and complex eigenvectors are obtained. Using obtained eigenvalues and eigenvectors, time domain analysis is performed by means of mode superposition. Finally, finite element solutions of viscoelastic and viscoeleastically damped sandwich beam are presented as an example.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.2
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• pp.186-191
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• 2008

A lot of equipments installed in ships must be isolated for relaxing the shock, vibration and noise using the elastic mounts. Most of the elastic mounts are made of the rubber, however it is not easy to design the effective rubber mount. Because, in general, the rubber has a non-linear constitutive characteristics especially for a large deformation. So, there are many difficulties to estimate the accurate structural response of rubber which is the basis of the shape design of the mounts. In this study, the detailed non-linear viscoelastic large deformation finite element analysis method was dealt with. And to verify validity of the present analysis scheme, the results were compared with experiments.

• Advances in nano research
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• v.16 no.4
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• pp.413-426
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• 2024

This paper investigates the dynamic behavior of a simply supported viscoelastic plate made of functionally graded carbon nanotube reinforced composite under dynamic loading. Carbon nanotubes are distributed in 5 different shapes: U, V, A, O and X, depending on the shape they form through the thickness of the plate. The displacement fields are derived in the Laplace domain using a higher-order shear deformation theory. Equations of motion are obtained through the application of the energy method and Hamilton's principle. The resulting equations of motion are solved using Navier's method. Transforming the Laplace domain displacements into the time domain involves Durbin's modified inverse Laplace transform. To validate the accuracy of the developed algorithm, a free vibration analysis is conducted for simply supported plate made of functionally graded carbon nanotube reinforced composite and compared against existing literature. Subsequently, a parametric forced vibration analysis considers the influence of various parameters: volume fractions of carbon nanotubes, their distributions, and ratios of instantaneous value to retardation time in the relaxation function, using a linear standard viscoelastic model. In the forced vibration analysis, the dynamic distributed load applied to functionally graded carbon nanotube reinforced composite viscoelastic plate is obtained in terms of double trigonometric series. The study culminates in an examination of maximum displacement, exploring the effects of different carbon nanotube distributions, volume fractions, and ratios of instantaneous value to retardation times in the relaxation function on the amplitudes of maximum displacements.

• Proceedings of the Korean Fiber Society Conference
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• 1996.10a
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• pp.195-199
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• 1996