• Steel and Composite Structures
• /
• 제22권1호
• /
• pp.161-182
• /
• 2016

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) axisymmetric circular plates with simply-supported and clamped edges. The strong formulation of this 3D elasticity axisymmetric problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler-Lagrange equations of this problem and its associated boundary conditions. The primary field variables are naturally independent of the circumferential coordinate, then interpolated in the radial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions can then be obtained by means of the transfer matrix method. The accuracy and convergence of this method are examined by comparing their solutions with the accurate ones available in the literature.

• Steel and Composite Structures
• /
• 제52권5호
• /
• pp.525-541
• /
• 2024

This study uses the state-space approach to study the bending behavior of Levy-type functionally graded (FG) plates sandwiched between two piezoelectric layers. The coupled governing equations are obtained using Hamilton's principle and Maxwell's equation based on the efficient four-variable refined plate theory. The partial differential equations (PDEs) are converted using Levy's solution technique to ordinary differential equations (ODEs). In the context of the state-space method, the higher-order ODEs are simplified to a system of first-order equations and then solved. The results are compared with those reported in available references and those obtained from Abaqus FE simulations, and good agreements between results confirm the accuracy and efficiency of the approach. Also, the effect of different parameters such as power-law index, aspect ratio, type of boundary conditions, thickness-to-side ratio, and piezoelectric thickness are studied.

• Structural Engineering and Mechanics
• /
• 제23권2호
• /
• pp.115-127
• /
• 2006

The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.

• 대한산업공학회지
• /
• 제8권2호
• /
• pp.15-21
• /
• 1982

This paper offers an alternative to the common probability generating function approach to the solution of steady state equations when a Markovian queue has a multivariate state space. Identifying states and substates and grouping them into vectors appropriately, we formulate a two - dimensional Markovian queue as a Markov chain. Solving the resulting matrix equations the transition point steady state probabilities (SSPs) are obtained. These are then converted into arbitrary time SSPs. The procedure uses only probabilistic arguments and thus avoids a large and cumbersome state space which often poses difficulties in the solution of steady state equations. For the purpose of numerical illustration of the approach we solve a Markovian queue with one server and two classes of customers.

• 한국소음진동공학회논문집
• /
• 제14권5호
• /
• pp.424-431
• /
• 2004

An implicit direct-time integration method for obtaining transient responses of general dynamic systems is described. The conventional Newmark method cannot be directly applied to state-space first-order differential equations, which contain no explicit acceleration terms. The method proposed here is the state-space Newmark method that incorporates the average velocity concept, and can be applied to an analysis of general dynamic systems that are expressed by state-space first-order differential equations. It is also readily coded into a program. Stability and accuracy analyses indicate that the method is numerically unconditionally stable like the conventional Newmark method, and has a period error of 2nd-order accuracy for small damping and 4th-order for large damping and an amplitude error of 2nd-order, regardless of damping. In addition, its utility and validity are confirmed by two application examples. The results suggest that the proposed state-space Newmark method based on average velocity be generally applied to the analysis of transient responses of general dynamic systems with a high degree of reliability with respect to stability and accuracy.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2003년도 추계학술대회논문집
• /
• pp.465-470
• /
• 2003

In this study, the state-space Newmark method based on average velocity is presented to analyse the transient dynamic response for general dynamic system. The conventional Newmark method based on average acceleration cannot he directly to the first-order state-space differential equations introducing the state-space vector. To overcome this problem, the time-step integration algorithm, based on average velocity concept, suitable for the first-order state-space differential equations is proposed In results, the proposed method has %he numerical stability and order of accuracy, which is proved analytically, equal to those of the conventional Newmark method based on average acceleration. Also, the formulation for numerical solution is very simple and the calculation time Is nearly equal to that of the conventional Newmark method based on average acceleration in spite of an increase of two times over matrix size. This method will be look forward to applying the general dynamic system to calculate the transient dynamic response.

• Advances in nano research
• /
• 제14권2호
• /
• pp.127-139
• /
• 2023

This paper studies the free vibration behavior of bi-dimensional functionally graded (BFG) nanobeams subjected to arbitrary boundary conditions. According to Eringen's nonlocal theory and Hamilton's principle, the underlying equations of motion have been obtained for BFG nanobeams. Moreover, the variable substitution method is utilized to establish the structure's state-space differential equations, followed by forming the dynamic stiffness matrix based on state-space differential equations. In order to compute the natural frequencies, the current study utilizes the Wittrick-Williams algorithm as a solution technique. Moreover, the nonlinear vibration frequencies calculated by employing the proposed method are compared to the frequencies obtained in previous studies to evaluate the proposed method's performance. Some illustrative numerical examples are also given in order to study the impacts of the nonlocal parameters, material property gradient indices, nanobeam length, and boundary conditions on the BFG nanobeam's frequency. It is found that reducing the nonlocal parameter will usually result in increased vibration frequencies.

• 대한전기학회논문지
• /
• 제45권3호
• /
• pp.399-406
• /
• 1996

This paper presents a method of hierarchical state estimation of the time-varying linear systems via Block-pulse function(BPF). When we estimate the state of the systems where noise is considered, it is very difficult to obtain the solutions because minimum error variance matrix having a form of matrix nonlinear differential equations is included in the filter gain calculation. Therefore, hierarchical approach is adapted to transpose matrix nonlinear differential equations to a sum of low order state space equation from and Block-pulse functions are used for solving each low order state space equation in the form of simple and recursive algebraic equation. We believe that presented methods are very attractive nd proper for state estimation of time-varying linear systems on account of its simplicity and computational convenience. (author). 13 refs., 10 figs.

• 전력전자학회:학술대회논문집
• /
• 전력전자학회 2019년도 전력전자학술대회
• /
• pp.483-484
• /
• 2019

This paper proposes a harmonic state space (HSS) modeling of DC microgrid. In the HSS model, nonlinear equations for the switched circuit model are transformed into multiple linear equations. The simulation results have shown the HSS modeling is comparable with PSIM simulation.

• 대한전기학회논문지:전력기술부문A
• /
• 제54권2호
• /
• pp.67-72
• /
• 2005

In conventional small signal stability analysis, system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of state matrix. However, when a system contains switching elements such as FACTS devices, it becomes non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is by means of eigenvalue analysis of the system periodic transition matrix based on discrete system analysis method. In this paper, RCF(Resistive Companion Form) method is used to analyse small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of power system, generator, controllers and FACTS devices including switching elements should be modeled in the form of state transition equations. From this state transition matrix eigenvalues which are mapped to unit circle can be calculated.