• 동력기계공학회지
• /
• 제19권5호
• /
• pp.52-59
• /
• 2015

This paper is presented for the free vibration of a conical shell with annular plates or circular plate using the transfer of influence coefficient. The governing equations of vibration of a conical shell, including annular plate, are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix of a single component has been determined, the entire structure matrix is obtained by the product of each component matrix and the joining matrix. The natural frequencies and the modes of vibration were calculated numerically for joined conical-annular plates. The validity of the present method is demonstrated through simple numerical examples, and through comparison with the results of finite element method, transfer matrix method and ANSYS. The conclusion show that the present method can accurately obtain natural vibration characteristics of the conical shell with annular or circle end plates.

• Structural Engineering and Mechanics
• /
• 제63권1호
• /
• pp.65-76
• /
• 2017

This research investigated the vibration frequency of sandwich plate made of piezoelectric fiber reinforced composite core (PFRC) and face sheets of piezomagnetic materials. The effective electroelastic constants for PFRC materials are obtained by the micromechanical approach. The resting medium of sandwich plate is modeled by Pasternak foundation including normal and shear modulus. Besides, sandwich plate is subjected to linearly varying normal stresses that change by load factor. The coupled equations of motion are derived using first order shear deformation theory (FSDT) and energy method. These equations are solved by differential quadrature method (DQM) for simply supported boundary condition. A detailed numerical study is carried out based on piezoelectricity theory to indicate the significant effect of load factor, volume fraction of fibers, modulus of elastic foundation, core-to-face sheet thickness ratio and composite materials on dimensionless frequency of sandwich plate. These findings can be used to aerospace, building and automotive industries.

• 동력기계공학회지
• /
• 제17권1호
• /
• pp.50-57
• /
• 2013

This describes the formulation for the free vibration of joined conical-cylindrical shells with uniform thickness using the transfer of influence coefficient. This method was developed based on successive transmission of dynamic influence coefficients, which were defined as the relationships between the displacement and the force vectors at arbitrary nodal circles of the system. The two edges of the shell having arbitrary boundary conditions are supported by several elastic springs with meridional/axial, circumferential, radial and rotational stiffness, respectively. The governing equations of vibration of a conical shell, including a cylindrical shell, are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix of a single component has been determined, the entire structure matrix is obtained by the product of each component matrix and the joining matrix. The natural frequencies and the modes of vibration were calculated numerically for joined conical-cylindrical shells. The validity of the present method is demonstrated through simple numerical examples, and through comparison with the results of previous researchers.

• Structural Engineering and Mechanics
• /
• 제28권6호
• /
• pp.749-765
• /
• 2008

Free axisymmetric vibrations of layered cylindrical shells of variable thickness are studied using spline function approximation techniques. Three different types of thickness variations are considered namely linear, exponential and sinusoidal. The equations of axisymmetric motion of layered cylindrical shells, on the longitudinal and transverse displacement components are obtained using Love's first approximation theory. A system of coupled differential equations on displacement functions are obtained by assuming the displacements in a separable form. Then the displacements are approximated using Bickley-spline approximation. The vibrations of two-layered cylindrical shells, made up of several types of layered materials and different boundary conditions are considered. Parametric studies have been made on the variation of frequency parameter with respect to the relative layer thickness, length ratio and type of thickness variation parameter.

• Coupled systems mechanics
• /
• 제7권6호
• /
• pp.707-729
• /
• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• Coupled systems mechanics
• /
• 제10권1호
• /
• pp.39-60
• /
• 2021

The present paper is concerned with the study of nonlinear ultrasonic waves in a magneto thermo (MT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix. The analytical formulation is developed based on Eringen's nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analyzed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations. Parametric work is carried out to scrutinize the influence of the non local scaling, magneto-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter, and tube geometrical parameters have significant effects on dimensionless frequency of nano tubes. The results presented in this study can provide mechanism for the study and design of the nano devices like component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro- magneto-mechanical systems (NEMMS) that make use of the wave propagation properties of armchair single-walled carbon nanotubes embedded on polymer matrix.

• Kyungpook Mathematical Journal
• /
• 제61권4호
• /
• pp.831-843
• /
• 2021

In this paper we look at the three dimensional stagnation point flow problem over a rough rotating disk. We study the theoretical behaviour of the stagnation point flow, or forced flow, in the presence of a slip factor in which convective instability stationary modes appear. We make a numerical investigation of the effects of slip on the behaviour of the flow components of the stagnation point flow where the disk is rough. We provide, for the first time in the literature, a complete convective instability analysis and an energy analysis. Suitable similarity transformations are used to reduce the Navier-Stokes equations and the continuity equation into a system of highly non-linear coupled ordinary differential equations, and these are solved numerically subject to suitable boundary conditions using the bvp4c function of MATLAB. The convective instability analysis and the energy analysis are performed using the Chebyshev spectral method in order to obtain the neutral curves and the energy bars. We observe that the roughness of the disk has a destabilising effect on both Type-I and Type-II instability modes. The results obtained will be prominently treated as benchmarks for our future studies on stagnation flow.

• Steel and Composite Structures
• /
• 제46권1호
• /
• pp.15-31
• /
• 2023

Organic solar cells utilized natural polymers to convert solar energy to electricity. The demands for green energy production and less disposal of toxic materials make them one of the interesting candidates for replacing conventional solar cells. However, the different aspects of their properties including mechanical strength and stability are not well recognized. Therefore, in the present study, we aim to explore the chaotic responses of these organic solar cells. In doing so, a specific type of organic solar cell constructed from layers of material with different thicknesses is considered to obtain vibrational and chaotic responses under different boundaries and initial conditions. A square plate structure is examined with first-order shear deformation theory to acquire the displacement field in the laminated structure. The bounding between different layers is considered to be perfect with no sliding and separation. On the other hand, nonlocal elasticity theory is engaged in incorporating the structural effects of the organic material into calculations. Hamilton's principle is adopted to obtain governing equations with regard to boundary conditions and mechanical loadings. The extracted equations of motion were solved using the perturbation method and differential quadrature approach. The results demonstrated the significant effect of relative glass layer thickness on the chaotic behavior of the structure with higher relative thickness leading to less chaotic responses. Moreover, a comprehensive parameter study is presented to examine the effects of nonlocality and relative thicknesses on the natural frequency of square organic solar cell structure.

• 청정기술
• /
• 제10권1호
• /
• pp.9-17
• /
• 2004

수소이온 교환 막을 가진 직접 메탄올 연료전지(DMFC)는 기존의 전력원에 비해 많은 장점을 가지고 있다. 그러나 직접메탄올 연료전지는 메탄올 crossover, 음극의 과전압, limiting current density 등 해결해야할 문제들이 있다. 직접메탄올 연료전지의 물리화학적 현상은 여러 편미분방정식들로 표현 가능하다. 본 연구에서는 이러한 편미분방정식을 풀기위해 FEMLAB를 이용하였다. FEMLAB은 PDE를 기초로 문제를 정의하고 1, 2, 3D, 비선형, 그리고 시간의 함수 형태의 편미분방정식들로 정의된 시스템을 전산모사하기위해 디자인되었다. 시스템의 메탄올 농도 분포를 알아보기 위해 촉매층에서 전기화학적반응식으로 Tafel식을 적용하여 전산모사를 수행하였다. 전산모사를 통해 음극의 촉매층에서 메탄올 농도의 급격한 감소는 직접 메탄올 연료전지의 성능저해의 요인임을 확인하였다.

• 한국지반공학회논문집
• /
• 제19권4호
• /
• pp.55-64
• /
• 2003

흙의 건조현상은 기상조건에 지배받는 evaporativity와 지반의 물 전달 능력에 지배받는 evaporability의 영향을 받는다. 지표면증발은 점토로 매립된 지반에서 건설장비의 주행성을 확보하기 위해서는 필요불가결한 요소이다. 본 논문에서는 준설 점토 지반에서의 증발현상을 규명할 수 있는 모델을 제시하였다. 이 모델은 포화토 및 불포화토에서의 수분과 물의 이동 및 열전달에 대한 식으로 구성되어 있다. 흙수분 특성곡선을 구하기 위하여 압력판추출시험(pressure plate extractor test)과 데시케이터실험이 수행되었으며 일차원 증발현상을 규명하기 위하여 컬럼증발실험을 수행하였다. 체적이 변하는 흙에서의 물, 증기 및 열전달 비선형 미분방정식을 풀기 위하여 유한차분프로그램을 개발하였으며 실험결과와 이론해를 비교하였다.