• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.5
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• pp.187-197
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• 2004

This paper presents the effects of cylinder shell elasticity on effective bulk modulus of oil $K_e$ in automotive hydraulic dampers. A theoretical model of cylinder shell bulk modulus $K_c$ based on the elasticity theory of thick-walled cylinder incorporating not only radial but longitudinal deformation is proposed. In a cylinder, values of $K_c$ by the new model and traditional models are computed and the discrepancies among them are discussed. In a twin-tube type automotive damper, the variation of $K_e$ under different pressure values in chambers of the damper cylinder, based on different theoretical models for $K_c$ is computed. Through these computations, it is shown that remarkable discrepancies in computed values of $K_e$ might occur according to the $K_e$ models in connection with $K_c$ models.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.1
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• pp.436-444
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• 2013

This article presents the dynamic response of nano-scale plates using the nonlocal continuum theory and higher-order shear deformation theory. The nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. The relations between nonlocal and local theories are discussed by numerical results. Also, the effects of nonlocal parameters, aspect ratio, side-to-thickness ratio, size of nano-scale plate and time step on dynamic response are investigated and discussed. The amplitude and cycle increase when nonlocal parameter increase. In order to validate the present solutions, the reference solutions are used and discussed. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the transient dynamic analysis of nano-scale structures.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.37-52
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• 2020

This paper investigates the free and forced longitudinal vibration of a double nanorod system using doublet mechanics theory. The doublet mechanics theory is a multiscale theory spanning between lattice dynamics and continuum mechanics. Equations of motion and boundary conditions for the double nanorod system are obtained using Hamilton's principle. Clamped-clamped and clamped-free boundary conditions are considered. Frequencies and dynamic displacements are determined to demonstrate the effects of length scale parameter of considered material and geometry of the nanorods. It is shown that frequencies obtained by the doublet mechanics theory are bounded from above (van Hove singularity) and unlike classical elasticity theory doublet mechanics theory predicts finite number of modes depending on the length of the nanotube. The present doublet mechanics results have been compared to molecular dynamics, experimental and nonlocal theory results and good agreement is observed between the present and other mentioned results. The difference between wave frequencies of graphite is less than 10% between doublet mechanics and experimental results near to the end of the first Brillouin zone.

• Structural Engineering and Mechanics
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• v.78 no.1
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• pp.15-22
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• 2021

An investigation of the nonlinear thermal buckling behavior of a nano-sized beam constructed from intelligent materials called piezo-magnetic materials has been presented in this article. The nano-sized beam geometry has been considered based on two assumptions: an ideal straight beam and an imperfect beam. For incorporating nano-size impacts, the nano-sized beam formulation has been presented according to nonlocal elasticity. After establishing the governing equations based on classic beam theory and nonlocal elasticity, the nonlinear buckling path has been obtained via Galerkin's method together with an analytical trend. The dependency of buckling path to piezo-magnetic material composition, electro-magnetic fields and geometry imperfectness has been studied in detail.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.11
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• pp.5930-5938
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• 2013

The sigmoid functionally graded mateiral(S-FGM) theory is reformulated using the nonlocal elatictiry of Erigen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical solutions of biaxial buckling of nano-scale plates are presented using this theory to illustrate the effects of nonlocal theory and power law index of sigmoid function on buckling load. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index, (ii) length, (iii) nonlocal parameter, (iv) aspect ratio and (v) mode number on nondimensional biaxial buckling load are studied. To validate the present solutions, the reference solutions are discussed.

• Journal of Biomedical Engineering Research
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• v.28 no.1
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• pp.75-83
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• 2007

Elasticity is an important physical property of biological tissues. Differences in elasticity can help facilitate the diagnosis of tumors and their extent. Magnetic Resonance Elastography (MRE) tries to visualize images of tissue elasticity by externally applying shear stress on the surface of an imaging object. Applied shear stress induces internal displacements that can be measured from MR phase images. In order to conduct MRE imaging experiments, we need to first develop a vibrator. We found that there does not exist enough technical information to design the MRE vibrator. In this paper, we describe the theory, design and construction of an MRE vibrator. We report the performance of the developed vibrator using two different test methods. We found that the vibrator successfully induces enough internal displacements that can be imaged using an MRI scanner. We suggest future studies of numerous MRE imaging experiments using the vibrator.

• Interaction and multiscale mechanics
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• v.4 no.2
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• pp.85-105
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• 2011

The influence of surface elasticity and surface residual stress on the elastic field of an isotropic nanoscale elastic layer of finite thickness bonded to a rigid material base is considered by employing the Gurtin-Murdoch continuum theory of elastic material surfaces. The fundamental solutions corresponding to buried vertical and horizontal line loads are obtained by using Fourier integral transform techniques. Selected numerical results are presented for the cases of a finite elastic layer and a semi-infinite elastic medium to portray the influence of surface elasticity and residual surface stress on the bulk stress field. It is found that the bulk stress field depends significantly on both surface elastic constants and residual surface stress. The consideration of out-of-plane terms of the surface stress yields significantly different solutions compared to previous studies. The solutions presented in this study can be used to examine a variety of practical problems involving nanoscale/soft material systems and to develop boundary integral equations methods for such systems.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.181-202
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• 1999

Dynamic response of axisymmetric arbitrary laminated composite cylindrical shell of finite length, using three-dimensional elasticity equations are studied. The shell is simply supported at both ends. The highly coupled partial differential equations are reduced to ordinary differential equations (ODE) with variable coefficients by means of trigonometric function expansion in axial direction. For cylindrical shell under dynamic load, the resulting differential equations are solved by Galerkin finite element method, In this solution, the continuity conditions between any two layer is satisfied. It is found that the difference between elasticity solution (ES) and higher order shear deformation theory (HSD) become higher for a symmetric laminations than their unsymmetric counterpart. That is due to the effect of bending-streching coupling. It is also found that due to the discontinuity of inplane stresses at the interface of the laminate, the slope of transverse normal and shear stresses aren't continuous across the interface. For free vibration analysis, through dividing each layer into thin laminas, the variable coefficients in ODE become constants and the resulting equations can be solved exactly. It is shown that the natural frequency of symmetric angle-ply are generally higher than their antisymmetric counterpart. Also the results are in good agreement with similar results found in literatures.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.2
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• pp.1109-1117
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• 2014

We study free vibration analysis of sigmoid functionally graded materials(S-FGM) nano-scale plates, using a nonlocal elasticity theory of Eringen in this paper. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Numerical solutions of S-FGM nano-scale plate are presented using this theory to illustrate the effect of nonlocal theory on natural frequency of the S-FGM nano-scale plates. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index (ii) nonlocal parameters, (iii) elastic modulus ratio and (iv) thickness and aspect ratios on nondimensional frequencies are investigated. In order to validate the present solutions, the reference solutions are compared and discussed. The results of S-FGM nano-scale plates using the nonlocal theory may be the benchmark test for the free vibration analysis.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.411-427
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• 2015

Based on linear elastic theory of quasicrystals, various equations and solutions for quasicrystal beams are deduced systematically and directly from plane problem of two-dimensional quasicrystals. Without employing ad hoc stress or deformation assumptions, the refined theory of beams is explicitly established from the general solution of quasicrystals and the Lur'e symbolic method. In the case of homogeneous boundary conditions, the exact equations and exact solutions for beams are derived, which consist of the fourth-order part and transcendental part. In the case of non-homogeneous boundary conditions, the exact governing differential equations and solutions under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively. In two illustrative examples of quasicrystal beams, it is shown that the exact or accurate analytical solutions can be obtained in use of the refined theory.