• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.33-41
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• 2018

In this paper, using modified couple stress theory in place of classical continuum theory, and using shell model in place of beam model, vibrational behavior of nanotubes is investigated via the finite element method. Accordingly classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have taken on great appeal. In the present work the mass-stiffness matrix for cylindrical shell element is developed, and by means of size-dependent finite element formulation is extended to more precisely account for nanotube vibration. In addition to modified couple stress cylindrical shell element, the classical cylindrical shell element can also be defined by setting length scale parameter to zero in the equations. The boundary condition were assumed simply supported at both ends and it is shown that the natural frequency of nano-scale shell using the modified coupled stress theory is larger than that using the classical shell theory and the results of Ansys. The results have indicated using the modified couple stress cylindrical shell element, the rigidity of the nano-shell is greater than that in the classical continuum theory, which results in increase in natural frequencies. Besides, in addition to reducing the number of elements required, the use of this type of element also increases convergence speed and accuracy.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.1
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• pp.174-194
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• 2015

In this paper, an Energy Flow Analysis (EFA) for coplanar coupled Mindlin plates was performed to estimate their dynamic responses at high frequencies. Mindlin plate theory can consider the effects of shear distortion and rotatory inertia, which are very important at high frequencies. For EFA for coplanar coupled Mindlin plates, the wave transmission and reflection relationship for progressing out-of-plane waves (out-of-plane shear wave, bending dominant flexural wave, and shear dominant flexural wave) in coplanar coupled Mindlin plates was newly derived. To verify the validity of the EFA results, numerical analyses were performed for various cases where coplanar coupled Mindlin plates are excited by a harmonic point force, and the energy flow solutions for coplanar coupled Mindlin plates were compared with the classical solutions in the various conditions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.11
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• pp.1119-1125
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• 2009

The coupled fluid-structure interaction problem is analyzed using the theoretical method to investigate the coupled vibration characteristics of functionally graded material(FGM) cylindrical shells conveying an incompressible, inviscid fluid. Material properties are assumed to vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The steady flow of fluid is described by the classical potential flow theory. The motion of shell represented by the first order shear deformation theory(FSDT) to account for rotary inertia and transverse shear strains. The effect of internal fluid can be taken into consideration by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. Numerical examples are presented and compared with exiting results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.6
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• pp.574-580
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• 2013

At high frequencies, the statistical approach such as statistical energy analysis(SEA) and energy flow analysis(EFA) has been applied for estimation of vibroacoustic responses of various built-up structures. The energy coupling relationship between finite coupled structures is required to estimate vibrational energetics of built-up structures. Mindlin plate theory includes the rotatory inertia and shear deformation effects which are dominant as frequency increases. In this paper, the wave transmission analysis is successfully performed for EFA of co-planar coupled Mindlin plates.

• Computers and Concrete
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• v.19 no.6
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• pp.701-710
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• 2017

In this study, the thermoelastic beam in modified couple stress theory due to laser source and heat flux is investigated. The beam are heated by a non-Guassian laser pulse and heat flux. The Euler Bernoulli beam theory and the Laplace transform technique are applied to solve the basic equations for coupled thermoelasticity. The simply-supported and isothermal boundary conditions are assumed for both ends of the beam. A general algorithm of the inverse Laplace transform is developed. The analytical results have been numerically analyzed with the help of MATLAB software. The numerically computed results for lateral deflection, thermal moment and axial stress due to laser source and heat flux have been presented graphically. Some comparisons have been shown in figures to estimate the effects of couple stress on the physical quantities. A particular case of interest is also derived. The study of laser-pulse find many applications in the field of biomedical, imaging processing, material processing and medicine with regard to diagnostics and therapy.

• Earthquakes and Structures
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• v.9 no.1
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• pp.111-126
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• 2015

In this study, the coupled effects of magnetic field, stress and thermal field on gravity waves propagating in a liquid layer over a solid surface are discussed. Due to change in temperature, initial hydrostatic stress and magnetic field, the gravity-sound Rayleigh waves can propagate in the liquid-solid interface. Dispersion properties of waves are derived by using classical dynamical theory of thermoelasticity. The phase velocity of gravity waves influenced quite remarkably in the presence of initial stress parameter, magneto-thermoelastic coupling parameter in the half space. Numerical solutions are also discussed for gravity-Rayleigh waves. In the absence of temperature, stress and magnetic field, the obtained results are in agreement with classical results.

• Coupled systems mechanics
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• v.11 no.2
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• pp.167-198
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• 2022

In this paper we deal with classical instability problems of heterogeneous Euler beam under conservative loading. It is chosen as the model problem to systematically present several possible solution methods from simplest deterministic to more complex stochastic approach, both of which that can handle more complex engineering problems. We first present classical analytic solution along with rigorous definition of the classical Euler buckling problem starting from homogeneous beam with either simplified linearized theory or the most general geometrically exact beam theory. We then present the numerical solution to this problem by using reduced model constructed by discrete approximation based upon the weak form of the instability problem featuring von Karman (virtual) strain combined with the finite element method. We explain how such numerical approach can easily be adapted to solving instability problems much more complex than classical Euler's beam and in particular for heterogeneous beam, where analytic solution is not readily available. We finally present the stochastic approach making use of the Duffing oscillator, as the corresponding reduced model for heterogeneous Euler's beam within the dynamics framework. We show that such an approach allows computing probability density function quantifying all possible solutions to this instability problem. We conclude that increased computational cost of the stochastic framework is more than compensated by its ability to take into account beam material heterogeneities described in terms of fast oscillating stochastic process, which is typical of time evolution of internal variables describing plasticity and damage.

• Smart Structures and Systems
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• v.19 no.5
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• pp.539-551
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• 2017

A mathematical model of electro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with memory-dependent derivative. The governing coupled equations with time-delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to several concrete problems. The exact solutions for all fields are obtained in the Laplace transform domain for each problem. According to the numerical results and its graphs, conclusion about the proposed model has been constructed. The predictions of the theory are discussed and compared with dynamic classical coupled theory. The result provides a motivation to investigate conducting thermoelectric viscoelastic materials as a new class of applicable materials.

• Bulletin of the Korean Chemical Society
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• v.32 no.2
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• pp.439-443
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• 2011

Using the projection operator technique, a reduced density matrix theory for linear absorption spectrum of energy transfer systems is developed for the theoretical absorption line shape of the systems with non-Condon transitions. As an application, we considered a model system of OH vibrations of water. In the present model calculation, the OH vibration modes are coupled to each other via intra-molecular coupling mechanism while their intermolecular couplings are turned off. The time-correlation functions appearing in the formulation are calculated from a mixed quantum/classical mechanics method. The present theory is successful in reproducing the exact absorption line shape. Also the present theory was improved from an existing approximate theory, time-averaged approximation approach.

• Tribology and Lubricants
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• v.8 no.1
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• pp.30-37
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• 1992

The displacement and pressure field of liquid crystals are analyzed numerically and compared with classical Reynolds theory. A plane slider bearing is employed as a simple example considering elasticity, permeability and splay effect which are the inherent characteristics of layered liquid crystals. Due to the geometric constraint of thin wedge and the strong anchoring behavior of the liquid crystals dislocations are inevitable. A finite element method is used to solve five coupled nonlinear equations. The load characteristics based on the pressure distribution along the gap shows that the liquid crystals can carry large load compared to the conventional lubricants.