• Wind and Structures
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• v.28 no.6
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.25 no.2
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• pp.109-118
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• 2013

The absence of a simple and general analytical model has been a problem in the design and analysis of desiccant-assisted air-conditioning systems. In this study, such an analytical model has been developed based on the approximate integral solution of the coupled transient ordinary differential equations for the heat and mass transfer processes in a desiccant wheel. It turned out that the initial conditions should be determined by the solution of four linear algebraic equations including the heat and mass transfer equations for the air flow as well as the energy and mass conservation equations for the desiccant bed. It is also shown that time-averaged exit air temperature and humidity relations could be given in terms of the heat and mass transfer effectiveness.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.3
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• pp.163-177
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• 2018

This paper successfully applies the modified Adomian decomposition method to find the approximate solutions of the Caputo fractional integro-differential equations. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also, the behavior of the solution can be formally determined by analytical approximation. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.

• Structural Engineering and Mechanics
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• v.20 no.4
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• pp.465-476
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• 2005

Free vibration of orthotropic functionally graded beams, whose material properties can vary arbitrarily along the thickness direction, is investigated based on the two-dimensional theory of elasticity. A hybrid state-space/differential quadrature method is employed along with an approximate laminate model, which allows us to obtain the semi-analytical solution easily. With the introduction of continuity conditions at each fictitious interface and boundary conditions at the top and bottom surfaces, the frequency equation for an inhomogeneous beam is derived. A completely exact solution of an FGM beam with material constants varying in exponential way through the thickness is also presented, which serves a benchmark to verify the present method. Numerical results are performed and discussed.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.331-337
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• 2020

This paper proposes a new approximate analytical solution for highly nonlinear vibration of mechanical systems called Hamiltonian Approach (HA) that can be widely use for structural health monitoring systems. The complete procedure of the HA approach is studied, and the precise application of the presented approach is surveyed by two familiar nonlinear partial differential problems. The nonlinear frequency of the considered systems is obtained. The results of the HA are verified with the numerical solution using Runge-Kutta's [RK] algorithm. It is established the only one iteration of the HA leads us to the high accurateness of the solution.

• Smart Structures and Systems
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• v.1 no.3
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• pp.309-324
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• 2005

This paper presents an efficient and accurate coupled beam model for piezoelectric bimorphs based on improved first-order shear deformation theory (FSDT). The model combines the equivalent single layer approach for the mechanical displacements and a layerwise modeling for the electric potential. General electric field function is proposed to reasonably approximate the through-the-thickness distribution of the applied and induced electric potentials. Layerwise defined shear correction factor (k) accounting for nonlinear shear strain distribution is introduced into both the shear stress resultant and the electric displacement integration. Analytical solutions for free vibrations and forced response under electromechanical loads are obtained for the simply supported piezoelectric bimorphs with series or parallel arrangement, and the numerical results for various length-to-thickness ratios are compared with the exact two-dimensional piezoelasticity solution. Excellent predictions with low error estimates of local and global responses as well as the modal frequencies are observed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.4
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• pp.787-794
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• 1992

To predict performances of Stirling Engines, a second-order analysis method has been developed. The present method which is based on the approximate analytical solution to the Ideal Adiabatic Model includes major loss mechanisms due to finite heat transfer and flow friction. Comparison of calculated results with previously reported study for a specific engine shows reasonable agreements and a possibility of being used for basic designs. Also, predicted performances with repect to engine speeds are consistent with experimental data in trend. To improve the prediction capability of this method, it is needed that not only additional losses should be taken into account, but also fundamental characteristics of oscillating flow and heat transfer should be better understood.

• Steel and Composite Structures
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• v.17 no.1
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• pp.133-143
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• 2014

In this paper, we try to prepare an accurate analytical solution for solving nonlinear vibration of thin circular sector cylinder. A new approximate solution called variational approach is presented and correctly applied to the governing equation of thin circular sector cylinder. The effect of important parameters on the response of the problem is considered. Some comparisons have been presented between the numerical solution and the present approach. The results show an excellent agreement between these methods. It has been illustrated that the variational approach can be a useful method to solve nonlinear problems by considering the effects of important parameters.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.9
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• pp.1441-1451
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• 1997

This paper addresses method which can be used for analyzing thermal stresses of a functionally graded material(FGM) using semi-analytical approach. FGM is a nonhomogeneous material whose composition changes continuously from a metal surface to a ceramic surface. An infinite one dimensional FGM plate is considered. The temperature distribution in the FGM is obtained by approximate Green's function solution. To expedite the convergence of the solutions, alternative Green's function solution is derived and shows good agreement with results from finite difference method. Thermal stresses are calculated using temperature distribution of the plate.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.10a
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• pp.850-854
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• 2009

Approximate analysis for a building installed with a friction damper is revisited to get insight of its dynamic behavior. Energy balance equation is used to have a closed analytical form solution of dynamic magnification factor (DMF) for the building with combined viscous and friction damping. It is found out that DMF is dependent on friction force ratio and resonance frequency. Linear transfer function from input external force to output building displacement is obtained by simplifying DMF equation. Root mean square of building displacement is derived under earthquake-like random excitation. Finally, design of friction damper is proposed by processing target control ratio, damping ratio factor, and friction force in sequence.