• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.3
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• pp.450-458
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• 2000

This study deals with the unsteady close-contact melting of solid blocks on a flat surface subject to convective heating. Normalizing the model equations in reference to the steady solution successfully leads them to cover constant heat flux and isothermal limits at small and large extremes of the Biot number, respectively. The resulting equations admit a compactly expressed analytical solution, which includes the previous solutions as a subset. Based on the steady solution, the characteristics of close-contact melting can be categorized into constant heat flux, transition, and isothermal regimes, the boundaries of which appear to be nearly independent of the contact force. The unsteady solutions corresponding to Biot numbers in the transition regime show intermediate behaviors between those of the two limits. With a proper approximation, the present solution procedure can cope with the case of variable fluid temperature and heat transfer coefficient. Regardless of imposed conditions, the mean normalized Nusselt number during the unsteady process asymptotically approaches to a constant value as the Biot number comes close to each limit.

• Geomechanics and Engineering
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• v.10 no.2
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• pp.189-205
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• 2016

Soils are subjected to additional stresses due to the loads transferred by the foundations of the buildings. The distribution of stress in soil has great importance in geotechnical engineering projects such as stress, settlement and liquefaction analyses. The purpose of this study is to examine the shear stresses on horizontal plane below the rectangular foundations subjected to biaxial bending on an elastic soil. In this study, closed-form analytical solutions for shear stresses in x and y directions were obtained from Boussinesq's stress equations. The expressions of analytical solutions were simplified by defining the shear stress influence values ($I_1$, $I_2$, $I_3$), and solution charts were presented for obtaining these values. For some special loading conditions, the expressions for shear stresses in the soil below the corners of a rectangular foundation were also given. In addition, a computer program was developed to calculate the shear stress increment at any point below the rectangular foundations. A numerical example for illustrating the use of the presented solution charts was given and, finally, shear stress isobars were obtained for the same example by a developed computer program. The shear stress expressions obtained in this work can be used to determine monotonic and cyclic behavior of soils below rectangular foundations subjected to biaxial bending.

• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.325-336
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• 2020

In this study, the continuous and discontinuous contact problems of functionally graded (FG) layer resting on a rigid foundation were considered. The top of the FG layer was loaded by a distributed load. It was assumed that the shear modulus and the density of the layer varied according to exponential functions along the depth whereas the the Poisson ratio remained constant. The problem first was solved analytically and the results were verified with the ones obtained from finite element (FE) solution. In analytical solution, the stress and displacement components for FG layer were obtained by the help of Fourier integral transform. Critical load expression and integral equation for continuous and discontinuous contact, respectively, using corresponding boundary conditions in each case. The finite element solution of the problem was carried out using ANSYS software program. In continuous contact case, initial separation distance and contact stresses along the contact surface between the FG layer and the rigid foundation were examined. Separation distances and contact stresses were obtained in case of discontinuous contact. The effect of material properties and loading were investigated using both analytical and FE solutions. It was shown that obtained results were compatible with each other.

• Smart Structures and Systems
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• v.5 no.6
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• pp.613-632
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• 2009

The present paper is concerned with the design of a proper patch actuator network in order to track a desired displacement of the sidewalls of a one-storey frame structure; both, for the static and the dynamic case. Weights for each patch of the actuator network found in our previous work were based on beam theory; in the present paper a refinement of these weights by modeling the sidewalls of the frame structure as thin plates is presented. For the sake of calculating the refined weights approximate solutions of the plate equations are calculated by an extended Galerkin method. The solutions based on the analytical plate model are compared with three-dimensional Finite Element results computed in the commercially available code ANSYS. The patch actuator network is put into practice by means of four piezoelectric patches attached to each of the two sidewalls of the frame structures, to which electric voltages proportional to the analytically refined patch weights are applied. Analytical and numerical results coincide very well over a broad frequency range.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.535-549
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• 2019

This study aimed to develop a high-order shear deformation theory to predict the free vibration of hybrid cross-ply laminated plates under different boundary conditions. The equations of motion for laminated hybrid rectangular plates are derived and obtained by using Hamilton's principle. The closed-form solutions of anti-symmetric cross-ply and angle-ply laminates are obtained by using Navier's solution. To assess the validity of our method, we used the finite element method. Firstly, the analytical and the numerical implementations were validated for an antisymmetric cross-ply square laminated with available results in the literature. Then, the effects of side-to-thickness ratio, aspect ratio, lamination schemes, and material properties on the fundamental frequencies for different combinations of boundary conditions of hybrid composite plates are investigated. The comparison of the analytical solutions with the corresponding finite element simulations shows the good accuracy of the proposed analytical closed form solution in predicting the fundamental frequencies of hybrid cross-ply laminated plates under different boundary conditions.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.833-847
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• 2021

The horizontal porous baffle and its effect as an anti-slosh device have been investigated intensively in a swaying and rolling rectangular tank. To accurately assess the level at which porous baffles reduce liquid sloshing, the Matched Eigenfunction Expansion Method (MEEM) has been utilized as an analytical tool. The velocity potentials in the horizontal baffle-covered fluid region are expressed by the sum of the homogeneous and particular solutions to avoid solving the complex dispersion equation. By applying an equivalent linearized quadratic loss model, the nonlinear algebraic equation is derived and solved by implementing the Newton-Raphson iterative scheme. To prove the validity of the present theoretical model, a series of experiments have been conducted with different centered horizontal porous baffles with varying porosities and submerged depths in a swaying and rolling rectangular tank. Reasonably good agreements are obtained regarding the analytical solutions and the experiment's findings. The influence of porosity, submerged depth, and length of a centered horizontal porous baffle on anti-slosh performance have been analyzed, especially at resonance modes. The developed predictive tool can potentially provide guidelines for optimal design of the horizontal porous baffle.

• Steel and Composite Structures
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• v.44 no.4
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• pp.531-543
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• 2022

An exact dynamic analytical method for free vibrations of continuous partial-interaction composite beams is proposed based on the Timoshenko beam theory. The main advantage of this method is that the independent shear deformations and rotary inertia of sub-beams are considered, which is more in line with the reality. Therefore, the accuracy of eigenfrequencies obtained by this method is significantly improved, especially for higher order modes, compared to the existing methods where the rotary angles of both sub-beams are assumed to be equal irrespective of the differences in the shear stiffness of each sub-beam. Furthermore, the solutions obtained by the proposed method are exact owing to no introduction of approximated displacement and force fields in the derivation. In addition, an exact analytical solution for the case of simply supported is obtained. Based on this, an approximate expression for the fundamental frequency of continuous partial-interaction composite beams is also proposed, which is useful for practical engineering applications. Finally, the practicability and effectiveness of the proposed method and the approximate expression are explored using numerical and experimental examples; The influence factors including the interfacial interaction, shear modulus ratio, span-to-depth ratio, and side-to-main span length ratio on the eigenfrequencies are presented and discussed in detail.

• Structural Engineering and Mechanics
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• v.50 no.4
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• pp.487-500
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• 2014

An analytical solution for the nonlinear in-plane free oscillations of the suspended cable which contains the quadratic and cubic nonlinearities is investigated via the homotopy analysis method (HAM). Different from the existing analytical technique, the HAM is indeed independent of the small parameter assumption in the nonlinear vibration equation. The nonlinear equation is established by using the extended Hamilton's principle, which takes into account the effects of the geometric nonlinearity and quasi-static stretching. A non-zero equilibrium position term is introduced due to the quadratic nonlinearity in order to guarantee the rule of the solution expression. Therefore, the mth-order analytic solutions of the corresponding equation are explicitly obtained via the HAM. Numerical results show that the approximate solutions obtained by using the HAM are in good agreement with the numerical integrations (i.e., Runge-Kutta method). Moreover, the HAM provides a simple way to adjust and control the convergent regions of the series solutions by means of an auxiliary parameter. Finally, the effects of initial conditions on the linear and nonlinear frequency ratio are investigated.

• Aerospace Engineering and Technology
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• v.3 no.2
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• pp.42-49
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• 2004

Analytical solutions are developed to predict temperature of a satellite box during launch stage under the assumption of worst hot condition. The considered time period is from fairing jettison to separation of satellite during launch stage. After fairing jettison, a box mounted on outer surface of satellite are exposed to space environments such as direct solar flux, Earth IR, Albedo, and free molecular heating. The thermal governing equation is simplified to 1st order ordinary differential equation such that analytic solutions are acquired after the box is assumed as a single lumped mass. The analytical solutions are also available for mass varying box. Finally, the practical application is performed for the case of STSAT-1 launch scenario.

• Smart Structures and Systems
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• v.23 no.6
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• pp.669-682
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• 2019

Vibration mitigation of cables or hangers is one of the crucial problems for cable supported bridges. Previous research focused on the behaviors of cable with dampers or crossties, which could help engineering community apply these mitigation devices more efficiently. However, less studies are available for hybrid applied cross-ties and dampers, especially lack of both analytical and experimental verifications. This paper studied damping and frequency of two parallel identical cables with a connection cross-tie and an attached damper. The characteristic equation of system was derived based on transfer matrix method. The complex characteristic equation was numerically solved to find the solutions. Effects of non-dimensional spring stiffness and location on the maximum cable damping, the corresponding optimum damper constant and the corresponding frequency of lower vibration mode were further addressed. System with twin small-scale cables with a cross-link and a viscous damper were tested. The damping and frequency from the test were very close to the analytical ones. The two branches of solutions: in-phase modes and the out-of-phase modes, were identified; and the two branches of solutions were different for damping and frequency behaviors.