Stability analyses on dynamic control for a moving body levitated magnetically over elastic guideways

Based on the Floquet theory on ordinary differential equations with periodically variable coefficients and the bifurcation approach to nonlinear equations, a numerical approach to determining the stability region of control parameters is established for a dynamic control system composed of a moving body levitated magnetically over flexible guideways. The system is nonlinearly coupled among the elastic deformation of guideways, disturbance the levitation position of the body and electromagnetic control forces. The numerical simulation is given for the system in the case in which the control parameters are taken within and out of the stability region respectively. Results show that this approach is reliable. This project is supported by NSFC(No. 19725207), the Pre-research Project of the Committee of Science and Technology for Defence of China and the Science Foundation of Education Ministry of China for Ph. D. Programmes.     

Dynamics of a Cubic Nonlinear Vibration Absorber

We study the dynamics of a nonlinear active vibration absorber. We consider a plant model possessing curvature and inertia nonlinearities and introduce a second-order absorber that is coupled with the plant through user-defined cubic nonlinearities. When the plant is excited at primary resonance and the absorber frequency is approximately equal to the plant natural frequency, we show the existence of a saturation phenomenon. As the forcing amplitude is increased beyond a certain threshold, the response amplitude of the directly excited mode (plant) remains constant, while the response amplitude of the indirectly excited mode (absorber) increases. We obtain an approximate solution to the governing equations using the method of multiple scales and show that the system possesses two possible saturation values. Using numerical techniques, we perform stability analyses and demonstrate that the system exhibits complicated dynamics, such as Hopf bifurcations, intermittency, and chaotic responses.     

ON THE FREE VIBRATION OF A SUBMERGED FGM HOLLOW SPHERE

The free vibration of a functionally graded material hollow sphere submerged in a compressible fluid medium is exactly analyzed. The sphere is assumed to be spherically isotropic with material constants being inhomogeneous along the radial direction. By employing a separation technique as well as the spherical harmonics expansion method, the governing equations are simplified to an uncoupled second-order ordinary differential equation, and a coupled system of two such equations. Solutions to these equations are given when the elastic constants and the mass density are power functions of the radial coordinate. Numerical examples are finally given to show the effect of the material gradient on the natural frequencies. The project is supported by the National Natural Sciences Foundation of China(No. 19872060).     

Application of the sequential gradient-restoration algorithm to thermal convective instability problems

The problem of the thermal stability of a horizontal incompressible fluid layer with linear and nonlinear temperature distributions is solved by using the sequential gradient-restoration algorithm developed for optimal control problems. The hydrodynamic boundary conditions for the layer include a rigid or free upper surface and a rigid lower surface. The resulting disturbing equations are solved as a Bolza problem in the calculus of variations. The results of the study are compared with the existing works in the literature.The authors acknowledge valuable discussions with Dr. A. Miele.     

Numerical examples of the behavior of REQP on nonlinear programming problems involving linear dependence among the constraint normals

This report illustrates, by means of numerical examples, the behavior of the constrained minimization algorithm REQP in situations where the active constraint normals are not linearly independent. The examples are intended to demonstrate that the presence of the penalty parameter in the equations for calculating the Lagrange multiplier estimates enables a useful search direction to be computed. This is shown to be true, whether the dependence among the constraint normals occurs at the solution or in some other region.     

人造金刚石生长中的温度控制

 本文讨论了与腔体组装方法、温度梯度和边界条件等有关的温度控制问题及其对金刚石生长的影响。     

Hybrid passive/active absorbers for flow ducts

A new type of acoustic liner developed for broadband noise reduction in flow ducts is considered in this paper. It combines passive absorbent properties of a porous layer and active control at its rear face. The complete design procedure of this hybrid passive/active liner is developed here. The passive part is first considered with the determination of a suitable porous material and the cut-off frequency separating the active low frequency regime from the passive high frequency one. The control system is then presented: a digital adaptive feedback control is performed independently cell by cell, allowing an easy subsequent increase of the liner surface. The entire optimization process has been successfully applied to a laboratory flow duct: both predictions and measurements show the interest of the hybrid liner to reduce the noise radiation.     

关于年龄相关的种群扩散系统的最优边界控制计算的惩罚移位法

研究了惩罚移位法应用于一类种群扩散系统最优边界控制的计算,构造了其逼近程序,并证明了这种方法的收敛性.     

Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm

In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.     

Optimal harvesting for an age-dependent <Emphasis Type="Italic">n</Emphasis>-dimensional food chain model

This paper is concerned with optimal harvesting policy for an age-dependent n-dimensional food chain model. The existence and uniqueness of non-negative solution of the system are proved using the fixed point theorem. By Mazur＇s theorem, the existence of optimal control strategy is demonstrated and optimality conditions derived by means of normal cone.