• Structural Engineering and Mechanics
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• 제59권2호
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• pp.343-371
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• 2016

In this paper thermo-mechanical vibration analysis of a porous functionally graded (FG) Timoshenko beam in thermal environment with various boundary conditions are performed by employing a semi analytical differential transform method (DTM) and presenting a Navier type solution method for the first time. The temperature-dependent material properties of FG beam are supposed to vary through thickness direction of the constituents according to the power-law distribution which is modified to approximate the material properties with the porosity phases. Also the porous material properties vary through the thickness of the beam with even and uneven distribution. Two types of thermal loadings, namely, uniform and linear temperature rises through thickness direction are considered. Derivation of equations is based on the Timoshenko beam theory in order to consider the effect of both shear deformation and rotary inertia. Hamilton's principle is applied to obtain the governing differential equation of motion and boundary conditions. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of several parameters such as porosity distributions, porosity volume fraction, thermal effect, boundary conditions and power-low exponent on the natural frequencies of the FG beams in detail. It is explicitly shown that the vibration behavior of porous FG beams is significantly influenced by these effects. Numerical results are presented to serve benchmarks for future analyses of FG beams with porosity phases.

• Computers and Concrete
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• 제33권3호
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• pp.241-250
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• 2024

This article investigates the thermal and post-buckling problems of graphene platelets reinforced metal foams (GPLRMF) beams with initial geometric imperfection. Three distribution forms of graphene platelet (GPLs) and foam are employed. This article utilizes the mixing law Halpin Tsai model to estimate the physical parameters of materials. Considering three different boundary conditions, we used the Euler beam theory to establish the governing equations. Afterwards, the Galerkin method is applied to discretize these equations. The correctness of this article is verified through data analysis and comparison with the existing articles. The influences of geometric imperfection, GPL distribution modes, boundary conditions, GPLs weight fraction, foam distribution pattern and foam coefficient on thermal post-buckling are analyzed. The results indicate that, perfect GPLRMF beams do not undergo bifurcation buckling before reaching a certain temperature, and the critical buckling temperature is the highest when both ends are fixed. At the same time, the structural stiffness of the beam under the GPL-A model is the highest, and the buckling response of the beam under the Foam-II mode is the lowest, and the presence of GPLs can effectively improve the buckling strength.

• Computers and Concrete
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• 제33권3호
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• pp.275-284
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• 2024

This work presents a comprehensive investigation of buckling behavior of bidirectional functionally graded imperfect beams exposed to several thermal loading with general boundary conditions. The nonlinear governing equations are derived based on 2D shear deformation theory together with Von Karman strain-displacement relation. The beams are composed of two different materials. Its properties are porosity-dependent and are continuously distributed over the length and thickness of the beams following a defined law. The resulting equations are solved analytically in order to determine the thermal buckling characteristics of BDFG porous beams. The precision of the current solution and its accuracy have been proven by comparison with works previously published. Numerical examples are presented to explore the effects of the thermal loading, the elastic foundation parameters, the porosity distribution, the grading indexes and others factors on the nonlinear thermal buckling of bidirectional FG beam rested on elastic foundation.

• East Asian mathematical journal
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• 제39권3호
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• pp.271-278
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• 2023

We consider a 1-dimensional reaction diffusion equation with the following boundary conditions arising in a theory of the thermal explosion {-u"(t) = λf(u(t)), t ∈ (0, l), -u'(0) + C(0)u(0) = 0, u'(l) + C(l)u(l) = 0, where C : [0, ∞) → (0, ∞) is a continuous and nondecreasing function, λ > 0 is a parameter and f : [0, ∞) → (0, ∞) is a continuous function. We establish the extension of Quadrature method introduced in [8]. Using this extension, we provide numerical results for models with a typical function of f and C in a thermal explosion theory, which verify the existence, uniqueness and multiplicity results proved in [6].

• 대한기계학회논문집
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• 제14권1호
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• pp.119-129
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• 1990

본 연구에서는 선적분화 된 체적력항을 갖는 경계요소법을 이용하여, Griffi- th균열에 대한 열응력세기계수를 구하여 Sumi의 결과와 비교 검토하고, 유무한체내의 대칭 입술형및 대칭 익형 커스프균열들(symmetric lip and airfoil cusp cracks)의 열 응력세기계수를 균열묘면이 단열된 경우와 일정 온도로 유지된 경우에 대해 계산하고 자 한다.

• Nuclear Engineering and Technology
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• 제41권10호
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• pp.1263-1274
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• 2009

Several experimental tests to simulate a reflood phase of a cold-leg LBLOCA of the APR1400 have been performed using the ATLAS facility. This paper describes the related experimental results with respect to the thermal-hydraulic behavior in the core and the system-core interactions during the reflood phase of the cold-leg LBLOCA conditions. The present descriptions will be focused on the LB-CL-09, LB-CL-11, LB-CL-14, and LB-CL-15 tests performed using the ATLAS. The LB-CL-09 is an integral effect test with conservative boundary condition; the LB-CL-11 and -14 are integral effect tests with realistic boundary conditions, and the LB-CL-15 is a separated effect test. The objectives of these tests are to investigate the thermal-hydraulic behavior during an entire reflood phase and to provide reliable experimental data for validating the LBLOCA analysis methodology for the APR1400. The initial and boundary conditions were obtained by applying scaling ratios to the MARS simulation results for the LBLOCA scenario of the APR1400. The ECC water flow rate from the safety injection tanks and the decay heat were simulated from the start of the reflood phase. The simulated core power was controlled to be 1.2 times that of the ANS-73 decay heat curve for LB-CL-09 and 1.02 times that of the ANS-79 decay curve for LB-CL-11, -14, and -15. The simulated ECC water flow rate from the high pressure safety injection pump was 0.32 kg/s. The present experimental data showed that the cladding temperature behavior is closely related to the collapsed water level in the core and the downcomer.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1995년도 춘계학술대회 논문집
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• pp.9-16
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• 1995

The thermal deformation of machine tool spindle influences the performance of the manufacturing systems for precision products. In this research thermal analysis of a high speed machine tool spindle with the rolling bearing and the built-in motor is carried out using Finite Difference Method. The thermal boundary conditions describing the hear generation in the bearing and built-in motor are considered in the simulation. And various convective boundary conditions are assumed with the empirical formula in the references. From the simulation results the characteristics of each element affecting the dynamic thermal behaviour of the machine tool spindle systems have been clarified. This model can be well applied to the future development of the high speed spindle systems.

• 대한기계학회논문집B
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• 제23권1호
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• pp.33-42
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• 1999

The effects of wan thermal boundary condition were investigated for a uniform wall temperature, a uniform wall heat flux, and for coupled heat conduction In the channel wall with transverse rectangular ribs. Numerical investigations for steady laminar flow show behavior similar to that observed experimentally in the separated flow region for flow over a cylinder. Conjugate heat transfer with a low solid-fluid thermal conductivity ratio does not lead to the same results as for the uniform heat flux boundary condition, and heat transfer reversal is found on the back sides of the ribs.

• Steel and Composite Structures
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• 제24권3호
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• pp.359-367
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• 2017

In this work, transient heat transfer analysis of functionally graded (FG) carbon nanotube reinforced nanocomposite (CNTRC) cylinders with various essential and natural boundary conditions is investigated by a mesh-free method. The cylinders are subjected to thermal flux, convection environments and constant temperature faces. The material properties of the nanocomposite are estimated by an extended micro mechanical model in volume fraction form. The distribution of carbon nanotube (CNT) has a linear variation along the radial direction of axisymmetric cylinder. In the mesh-free analysis, moving least squares shape functions are used for approximation of temperature field in the weak form of heat transform equation and the transformation method is used for the imposition of essential boundary conditions. Newmark method is applied for solution time depended problem. The effects of CNT distribution pattern and volume fraction, cylinder thickness and boundary conditions are investigated on the transient temperature field of the nanocomposite cylinders.

• Advances in aircraft and spacecraft science
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• 제8권4호
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• pp.345-372
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• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.