• Journal of Mechanical Science and Technology
• /
• v.16 no.10
• /
• pp.1346-1354
• /
• 2002

The purpose of this work is to study the effects of specularly reflecting wall under the combined radiative and laminar free convective heat transfer in an infinite square duct. An absorbing and emitting gray medium is enclosed by the opaque and diffusely emitting walls. The walls may reflect diffusely or specularly. Boussinesq approximation is used for the buoyancy term. The radiative heat transfer is evaluated using the direct discrete ordinates method. The parameters under considerations are Rayleigh number, conduction to radiation parameter, optical thickness, wall emissivity and reflection mode. The differences caused by the reflection mode on the stream line, and temperature distribution and wall heat fluxes are studied. Some differences are observed for the categories mentioned above if the order of the conduction to radiation parameter is less than order of 10$\^$-3/ fer the range of Rayleigh number studied. The differences at the side wall heat flux distributions are observed as long as the medium is optically thin. As the top wall emissivity decreases, the differences between these two modes are increased. As the optical thickness decreases at the fixed wall emissivity, the differences also increase. The difference of the streamlines or the temperature contours is not as distinct as the side wall heat flux distributions. The specular reflection may alter the fluid motion.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.971-976
• /
• 2002

The differential equations governing free vibrations of the elastic arches with unsymmetric axis are derived in rectangular coordinates rather than in polar coordinates, in which the effect of rotatory inertia is included. Frequencies and mode shapes are computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Rectangular coordinates. The lowest four natural frequency parameters are reported, with and without the rotatory inertia, as functions of three non-dimensional system parameters: the rise to chord length ratio, the span length to chord length ratio, and the slenderness ratio. Also typical mode shapes of vibrating arches are presented.

• Earthquakes and Structures
• /
• v.10 no.5
• /
• pp.1033-1048
• /
• 2016

An analytical solution based on the neutral surface concept is developed to study the free vibration behavior of simply supported functionally graded plate reposed on the elastic foundation by taking into account the effect of transverse shear deformations. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain obtained by using a new refined shear deformation theory. The foundation is described by the Winkler-Pasternak model. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power law formulation, and the Poisson ratio is held constant. The equation of motion for FG rectangular plates resting on elastic foundation is obtained through Hamilton's principle. Numerical examples are provided to show the effect of foundation stiffness parameters presented for thick to thin plates and for various values of the gradient index, aspect and side to thickness ratio. It was found that the proposed theory predicts the fundamental frequencies very well with the ones available in literature.

• Structural Engineering and Mechanics
• /
• v.62 no.3
• /
• pp.345-355
• /
• 2017

The aim of the present study is to develop an elemental approach based on the differential quadrature method for free vibration analysis of cracked thin plate structures. For this purpose, the equations of motion are established using the classical plate theory. The well-known Generalized Differential Quadrature Method (GDQM) is utilized to discretize the governing equations on each computational subdomain or element. In this method, the differential terms of a quantity field at a specific computational point should be expressed in a series form of the related quantity at all other sampling points along the domain. However, the existence of any geometric discontinuity, such as a crack, in a computational domain causes some problems in the calculation of differential terms. In order to resolve this problem, the multi-block or elemental strategy is implemented to divide such geometry into several subdomains. By constructing the appropriate continuity conditions at each interface between adjacent elements and a crack tip, the whole discretized governing equations of the structure can be established. Therefore, the free vibration analysis of a cracked thin plate will be provided via the achieved eigenvalue problem. The obtained results show a good agreement in comparison with those found by finite element method.

• Advances in materials Research
• /
• v.5 no.4
• /
• pp.223-244
• /
• 2016

In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi- three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

• Steel and Composite Structures
• /
• v.22 no.2
• /
• pp.257-276
• /
• 2016

In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Smart Structures and Systems
• /
• v.19 no.6
• /
• pp.601-614
• /
• 2017

In this work, free vibration analysis of size-dependent functionally graded (FG) nanoplates resting on two-parameter elastic foundation is investigated based on a novel nonlocal refined trigonometric shear deformation theory for the first time. This theory includes undetermined integral variables and contains only four unknowns, with is even less than the conventional first shear deformation theory (FSDT). Mori-Tanaka model is employed to describe gradually distribution of material properties along the plate thickness. Size-dependency of nanosize FG plate is captured via the nonlocal elasticity theory of Eringen. By implementing Hamilton's principle the equations of motion are obtained for a refined four-variable shear deformation plate theory and then solved analytically. To show the accuracy of the present theory, our research results in specific cases are compared with available results in the literature and a good agreement will be demonstrated. Finally, the influence of various parameters such as nonlocal parameter, power law indexes, elastic foundation parameters, aspect ratio, and the thickness ratio on the non-dimensional frequency of rectangular FG nanoscale plates are presented and discussed in detail.

• Structural Engineering and Mechanics
• /
• v.62 no.5
• /
• pp.607-618
• /
• 2017

In this paper, an analytical procedure based on the perturbation technique is presented to study the free vibrations of annular viscoelastic plates by considering the first order shear deformation theory as the displacement field. The viscoelastic properties obey the standard linear solid model. The equations of motion are extracted for small deflection assumption using the Hamilton's principle. These equations which are a system of partial differential equations with variable coefficients are solved analytically with the perturbation technique. By using a new variable change, the governing equations are converted to equations with constant coefficients which have the analytical solution and they are appropriate especially to study the sensitivity analysis. Also the natural frequencies are calculated using the classical plate theory and finite elements method. A parametric study is performed and the effects of geometry, material and boundary conditions are investigated on the vibrational behavior of the plate. The results show that the first order shear deformation theory results is more closer than to the finite elements with respect to the classical plate theory for viscoelastic plate. The more results are summarized in conclusion section.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.23 no.4
• /
• pp.337-344
• /
• 2014

While implicit integration methods such as Newton's method have excellent stability for the analysis of stiff and constrained mechanical systems, they have the drawback that the evaluation and LU-factorization of the system Jacobian matrix required at every time step are time-consuming. This paper proposes a Jacobian update-free Newton's method in order to overcome these defects. Because the motions of all bodies in a vehicle model are limited with respect to the chassis body, the equations are formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. This makes the system Jacobian remain nearly constant, and thus allows the Newton's method to be free from the Jacobian update. Consequently, the proposed method significantly decreases the computational cost of the vehicle dynamic simulation. This paper provides detailed generalized formulation procedures for the equations of motion, constraint equations, and generalized forces of the proposed method.

• Archives of Reconstructive Microsurgery
• /
• v.9 no.1
• /
• pp.56-61
• /
• 2000

Recommendable reconstructive surgery in the patient with thumb amputation through base of the first metacarpal bone is pollicization. Some patients who do not agree with harvest sound finger as a new thumb, we can consider other options as toe transplantation or osteoplastic thumb reconstruction for creating thumb. Toe transplantation to the thumb is effective procedure in the amputation of distal to metacarpal shaft, it is rarely indicated in the cases of proximal to base of the first metacarpal bone. We performed three cases of modified osteoplastic thumb reconstruction with free vascularized rib that combined with scapular free flap or radial forearm flap. The length of transplanted rib ranged from 7~11cm, the donor vessels are posterior intercostal artery and vein which anastomosed to radial artery. The grafted rib wrapped with additional free flap for creating new thumb. Result of that procedure was not much encouraging, aesthetic appearance and mobility of thumb were not so satisfactory but reconstructed thumb gave improvement of the hand function without sacrificing toe or other digit. That gave reasonable stability for powerful side pinch and three pod pinch and opposable thumb with normal carpo-metacarpal joint motion that can give much function to the thumb absent hand. In spite of those disadvantages, thumb reconstruction with rib transfer can be useful for patients who do not want to lose another part of the body for creating thumb in basal amputation of the thumb metacarpal.