• Journal of Mechanical Science and Technology
• /
• v.18 no.9
• /
• pp.1549-1558
• /
• 2004

This study is concerned with the general solution of the field intensity factors and energy release rate for a Griffith crack in a piezoelectric ceramic of finite radius under combined anti-plane mechanical and in-plane electrical loading. Both electrically continuous and impermeable crack surface conditions are considered. Employing Mellin transforms and Fourier series, the problem is reduced to dual integral forms. The solution to the resulting expressions is expressed in terms of Fredholm integral equation of the second kind. The solutions are provided to study the influence of the crack length, the crack surface boundary conditions on the intensity factors and the energy release rate.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.7 no.2
• /
• pp.186-192
• /
• 1983

The purpose of this study is to determine the general frequency expression for a rotating shaft of uniform cross section, supported by two bearings, and carrying flywheel at the free end. The bearing spacing and the ratio of the weight of flywheel to the total distributed weight are used as parameters. The data have thus been reduced to dimensionless form so that the results are generally applicable for this type of rotor. Frequencies for the first three modes of vibration are determined. Experimental investigation with rotor/flywheel model confirmed the critical speed frequencies lie between analytical models with simply supported-simply supported boundary conditions and spring supported-spring supported boundary conditions.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.24 no.4
• /
• pp.317-323
• /
• 2014

This study is concerned with the free vibration analysis of an inextensible uniform rope with a spring-mass system at the tip. The rope is hanged vertically in a gravitational field. This problem is related to the free vibration of an elevator rope connected to an elevator cage. The equation of motion and the corresponding boundary conditions are derived by using the Hamilton's principle. The general solution of the governing equation of motion is expressed in terms of Bessel functions. The characteristic equation was derived by applying the boundary conditions. The characteristic values which are in fact non-dimensionalized natural frequencies were obtained numerically. The effects of mass and spring constant were investigated. The numerical results show how the tip mass and spring affect the natural frequencies of the rope.

• Smart Structures and Systems
• /
• v.25 no.4
• /
• pp.501-514
• /
• 2020

This article presents a comprehensive model to investigate a free vibration and resonance frequencies of nanostructure perforated beam element as nano-resonator. Nano-scale size dependency of regular square perforated beam is considered by using nonlocal differential form of Eringen constitutive equation. Equivalent mass, inertia, bending and shear rigidities of perforated beam structure are developed. Kinematic displacement assumptions of both Timoshenko and Euler-Bernoulli are assumed to consider thick and thin beams, respectively. So, this model considers the effect of shear on natural frequencies of perforated nanobeams. Equations of motion for local and nonlocal elastic beam are derived. After that, analytical solutions of frequency equations are deduced as function of nonlocal and perforation parameters. The proposed model is validated and verified with previous works. Parametric studies are performed to illustrate the influence of a long-range atomic interaction, hole perforation size, number of rows of holes and boundary conditions on fundamental frequencies of perforated nanobeams. The proposed model is supportive in designing and production of nanobeam resonator used in nanoelectromechanical systems NEMS.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2011.11a
• /
• pp.178-181
• /
• 2011

Recently, micro shock tube is being extensively used in various fields of engineering applications. The flow characteristics occurring in the micro shock tube may be significantly different from that of conventional macro shock tube due to very low Reynolds number and Knudsen number effects which are, in general, manifested in such flows of rarefied gas, solid-gas two-phase, etc. In these situations, Navier-Stokes equations cannot properly predict the micro shock tube flow. In the present study, a two-dimensional CFD method has been applied to simulate the micro shock tube, with slip velocity and temperature jump boundary conditions. The effects of wall thermal conditions on the unsteady flow in the micro shock tube were also investigated. The unsteady behaviors of shock wave and contact discontinuity were, in detail, analyzed. The results obtained show much more attenuation of shock wave, compared with macro-shock tubes.

• Structural Engineering and Mechanics
• /
• v.65 no.4
• /
• pp.465-476
• /
• 2018

This article investigates buckling behavior of a multi-phase nanocrystalline nanobeam resting on Winkler-Pasternak foundation in the framework of nonlocal couple stress elasticity and a higher order refined beam model. In this model, the essential measures to describe the real material structure of nanocrystalline nanobeams and the size effects were incorporated. This non-classical nanobeam model contains couple stress effect to capture grains micro-rotations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, and couple stress effects are omitted. Hamilton's principle is employed to derive the governing equations and the related boundary conditions which are solved applying an analytical approach. The buckling loads are compared with those of nonlocal couple stress-based beams. It is showed that buckling loads of a nanocrystalline nanobeam depend on the grain size, grain rotations, porosities, interface, elastic foundation, shear deformation, surface effect, nonlocality and boundary conditions.

• Ocean and Polar Research
• /
• v.31 no.4
• /
• pp.297-304
• /
• 2009

We investigated the response of the westerly winds over the Southern Ocean (SO) to glacial boundary conditions for the Last Glacial Maximum using the CCM3 atmospheric general circulation model. In response to glacial boundary conditions, the zonally averaged maximum SO westerly winds weakened 20-35% and were displaced toward the equator by 3-4 degrees. This weakening of the SO westerly winds arose from a substantial increase in mean sea level pressure (MSLP) in the southern part of the SO around Antarctica relative to the northern part. The increase in MSLP around Antarctica is associated with a marked temperature reduction caused by an increase in sea ice cover and ice albedo feedback during the glacial time. The weakened westerly winds in the SO and their equator-ward displacement might play a role in reducing the atmospheric $CO_2$ concentration by reducing upwelling of the carbon rich deep water during the glacial time.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2003.11a
• /
• pp.802-807
• /
• 2003

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and tip masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the translational spring parameter, the rotational spring parameter, the mass ratio and the dimensionless mass moment of inertia.

• Structural Engineering and Mechanics
• /
• v.15 no.6
• /
• pp.705-716
• /
• 2003

Gradient elastic flexural beams are dynamically analysed by analytic means. The governing equation of flexural beam motion is obtained by combining the Bernoulli-Euler beam theory and the simple gradient elasticity theory due to Aifantis. All possible boundary conditions (classical and non-classical or gradient type) are obtained with the aid of a variational statement. A wave propagation analysis reveals the existence of wave dispersion in gradient elastic beams. Free vibrations of gradient elastic beams are analysed and natural frequencies and modal shapes are obtained. Forced vibrations of these beams are also analysed with the aid of the Laplace transform with respect to time and their response to loads with any time variation is obtained. Numerical examples are presented for both free and forced vibrations of a simply supported and a cantilever beam, respectively, in order to assess the gradient effect on the natural frequencies, modal shapes and beam response.

• Structural Engineering and Mechanics
• /
• v.24 no.6
• /
• pp.699-707
• /
• 2006

In the paper, a direct method of solution of the Navier equation is presented. An orthotropic thick hollow cylinder under a one-dimensional steady-state temperature distribution and a uniform magnetic field with general types of thermal and mechanical boundary conditions is considered. The Navier equation in terms of displacement is derived and solved analytically by the direct method, and magnetothermoelastic responses and perturbation of the magnetic field vector in the orthotropic thick hollow cylinder is described. The present method is suitable for orthotropic thick hollow cylinders placed in an axial magnetic field with arbitrary thermal and mechanical boundary conditions. Finally, numerical examples are carried out and discussed.