• 한국소음진동공학회논문집
• /
• 제26권5호
• /
• pp.602-608
• /
• 2016

The paper proposes a practical meshless method for the free vibration analysis of clamped plates having arbitrary shapes by extending the non-dimensional dynamic influence function (NDIF) method, which was developed by the author in 1999. In the proposed method, the domain and boundary of the plate of interest are discretized using only nodes without elements unlike FEM and the system matrices are obtained by making domain nodes and boundary nodes satisfy the governing differential equation and boundary conditions, respectively. However, since the above system matrices are not square ones, the problem of free vibrations of clamped plates is not reduced to an algebraic eigenvalue problem. An additional theoretical treatment is considered to produce an algebraic eigenvalue problem. It is revealed from case studies that the proposed method is valid and accurate.

• Coupled systems mechanics
• /
• 제12권6호
• /
• pp.519-530
• /
• 2023

This paper presents a mathematical model suitable for the calculation of laminated glass, i.e. glass plates combined with an interlayer material. The model is based on a beam differential equation for each glass plate and a separate differential equation for the slip in the interlayer. In addition to slip, the model takes into account prestressing force in the interlayer. It is possible to combine the two contributions arbitrarily, which is important because the glass sheet fabrication process changes the stiffness of the interlayer in ways that are not easily predictable and could introduce prestressing of varying magnitude. The model is suitable for reformulation into an inverse procedure for calculation of the relevant parameters. Model consisting of a system of differential-algebraic equations, proved too stiff for cases with the thin interlayer. This novel approach covers the full range of possible stiffnesses of layered glass sheets, i.e., from zero to infinite stiffness of the interlayer. The comparison of numerical and experimental results contributes to the validation of the model.

• International Journal of Control, Automation, and Systems
• /
• 제4권6호
• /
• pp.714-724
• /
• 2006

In this note a method of designing optimal vibration control based on Haar functions to control of bounce and pitch vibrations in engine-body vibration structure is presented. Utilizing properties of Haar functions, a computational method to find optimal vibration control for the engine-body system is developed. It is shown that the optimal state trajectories and optimal vibration control are calculated approximately by solving only algebraic equations instead of solving the Riccati differential equation. Simulation results are included to demonstrate the validity and applicability of the technique.

• Journal of Mechanical Science and Technology
• /
• 제14권1호
• /
• pp.103-112
• /
• 2000

Numerical simulations of unsteady opposed-flow flames are performed using an adaptive time integration method designed for differential-algebraic systems. The compressibility effect is considered in deriving the system of equations, such that the numerical difficulties associated with a high-index system are alleviated. The numerical method is implemented for systems with detailed chemical mechanisms and transport properties by utilizing the Chemkin software. Two test simulations are performeds hydrogen/air diffusion flames with an oscillatory strain rate and transient ignition of methane against heated air. Both results show that the rapid transient behavior is successfully captured by the numerical method.

• Journal of applied mathematics & informatics
• /
• 제20권1_2호
• /
• pp.293-303
• /
• 2006

This paper describes a numerical scheme for optimal control of a time-dependent linear system to a moving final state. Discretization of the corresponding differential equations gives rise to a linear algebraic system. Defining some binary variables, we approximate the original problem by a mixed integer linear programming (MILP) problem. Numerical examples show that the resulting method is highly efficient.

• 대한수학회보
• /
• 제53권2호
• /
• pp.507-518
• /
• 2016

In this paper, using forms of conjugations, we give some algebraic properties of bicomplex numbers. We research differential operators, elementary functions and the analogous Cauchy-Riemann system in bicomplex number systems. Also, we investigate the definition and properties of regular functions with values in bicomplex settings in Clifford analysis.

• Structural Engineering and Mechanics
• /
• 제48권5호
• /
• pp.697-709
• /
• 2013

A simulation method called modified differential transform is studied to solve the free vibration problems of uniform Euler-Bernoulli beam. First of all, the modified differential transform method is derived. Secondly, the modified differential transformation is applied to uniform Euler-Bernoulli beam free-free vibration. And then a set of differential equations are established. Through algebraic operations on these equations, we can get any natural frequency and normalized mode shape. Thirdly, the FEM is applied to obtain the numerical solutions. Finally, mode experimental method (MEM) is conducted to obtain experimental data for analysis by signal processing with LMS Test.lab Vibration testing and analysis system. Experimental data and simulation results are illustrated to be in comparison with the analytical solutions. The results show that the modified differential transform method can achieve good results in predicting the solution of such problems.

• Steel and Composite Structures
• /
• 제35권5호
• /
• pp.671-685
• /
• 2020

This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic-metal-ceramic (CMC) and metal-ceramic-metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton's principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1991년도 하계학술대회 논문집
• /
• pp.695-698
• /
• 1991

In this paper tried the estimation of parameter using of Cal-Sal functions. System equation given by the linear differential equation is converted into the integral equation, operation matrix for integral of Cal-Sal functions is used to find the estimation of parameter on the given system. Converting linear differential equation to linear algebraic equation, the method presented here computing time and required memory size can be reduced. Therefore real time data process can be possible.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2000년도 하계학술대회 논문집 D
• /
• pp.2611-2613
• /
• 2000

This paper deals with a novel approach to unknown inputs observer(UIO) design for linear time-invariant dynamical systems using a fast Walsh transform and Walsh function's differential operation. Generally, UIO has a derivation of system outputs which is not available from the measurement directly. And it is an obstacle to estimate the unknown inputs properly when unexpected measurement noises are presented. Therefore, this paper propose an algebraic approach to eliminate such problems by using a Walsh function's differential operation.