Xiaoting Rui

Automatic Deduction Theorem of Overall Transfer Equation of Multibody System

Transfer matrix method for multibody System (MSTMM) is a new multibody dynamics method developed in recent 20 years. It has been widely used in both science research and engineering for its special features as follows: without global dynamics equations of the system, high programming, low order of system matrix, and high computational speed. Based on MSTMM and its above features, a theorem to deduce automatically the overall transfer equations of multibody systems by handwriting or by computer is proposed in this paper. The theorem is effective for multibody systems with various topological structures, including chain systems, closed-loop systems, tree systems, general systems composed of one tree subsystem, and some closed-loop subsystems. This theorem makes it possible to program large scale software of multibody system dynamics with muchhigher programming, and much higher computational speed because of the above features of MSTMM. Formulations of the proposed method as well as two examples are given to verify this method.

Perturbation Finite Element Transfer Matrix Method for Random Eigenvalue Problems of Uncertain Structures

The rapid computation of random eigenvalue problems of uncertain structures is the key point in structural dynamics, and it is prerequisite to the efficient dynamic analysis and optimal design of structures. In this paper, by combining finite element-transfer matrix method (FE-TMM) with perturbation method, a new method named as perturbation FE-TMM is presented for random eigenvalue problems of uncertain structures. By using the proposed method, the rapid computation of random eigenvalue problems of uncertain structures with complicated shapes and boundaries can be achieved, and the repeated eignvalues and characteristic vectors can be solved conveniently. Compared with stochastic finite element method, this method has the low memory requirement, high computational efficiency and high computational stability. It has more advantages for dynamic design of uncertain structures. Formulations as well as some numerical examples are given to validate the method. [DOI: 10.1115/1.4005574]

Natural Vibrations of Open-Variable Thickness Circular Cylindrical Shells in High Temperature Field

The feasibility of using the transfer matrix method (TMM) to analyze open-variable thickness circular cylindrical shells exposed to a high-temperature field is explored theoretically. In the approach to the problem, the thermal degradation (TG) of thermoelastic characteristics of the material is considered. Natural frequencies and mode shapes for the cylindrical shells are investigated in detail by combining the vibration theory with the TMM. The governing equations of vibration for this system are expressed by the matrix differential equations, and the coefficient matrices are derived. After the relationship between the transfer matrix and the coefficient matrix is established, the fourth-order Runge-Kutta method is used numerically to solve the matrix equation. Once the transfer matrix of single component has been obtained, the product of each component matrix can compose the matrix of the entire structure. The frequency equations and mode shape are formulated in terms of the elements of the structural ...

Modeling and control of a two-axis fast steering mirror with piezoelectric stack actuators for laser beam tracking

This paper outlines an optical beam steering system built using a two-axis fast steering mirror (FSM) with piezoelectric stack actuators to maintain precise pointing control. A novel mathematical model of the FSM is put forward by using a transfer matrix method of a multibody system to describe the dynamics characteristics and a hysteresis model to represent the hysteresis. Based on the proposed model, a model-based hybrid control is applied to force the output angle of the FSM to track the laser beam accurately thereafter. The experimental results are in accordance with the theoretical analysis. The results highlight significantly improved accuracy in the beam tracking control of the FSM.

Static/Dynamic Edge Movability Effect on Non-Linear Aerothermoelastic Behavior of Geometrically Imperfect Curved Skin Panel: Flutter and Post-Flutter Analysis

This paper addresses the problem of the aerothermoelastic modeling behavior and analyses of skin curved panels with static and dynamic edge movability effect in high supersonic flow. Flutter and post-flutter behavior will be analyzed toward determining under which conditions such panels will exhibit a benign instability, that is a stable limit cycle oscillation, or a catastrophic instability, that is an unstable LCO. The aerothermoelastic governing equations are developed from the geometrically non-linear theory of infinitely long two dimensional curved panels. Von Karman non-linear strain-displacement relation in conjunction with the Kirchhoff plate-hypothesis is adopted. A geometrically imperfect curved panel forced by a supersonic/hypersonic unsteady flow is numerically investigated using Galerkin approach. These equations are based on the third-order piston theory aerodynamic for modeling the flow-induced forces. Furthermore, the effects of thermal degradation and Kelvins model of structural damping independent of time and temperature are also considered in this model. Computational analysis and discussion of the finding along with pertinent conclusions are presented.

Modified Finite Element Transfer Matrix Method for Eigenvalue Problem of Flexible Structures

The speedy computation of eigenvalue problems is the key point in structure dynamics. In this paper, by combining transfer matrix method and finite element method, the modified finite element-transfer matrix method and its algorithm for eigenvalue problems are presented. By using this method, the speedy computation of eigenvalue problem of flexible structures can be realized, and the repeated eignvalue problem can be solved simply and conveniently. This method has the low order of system matrix, high computational efficiency, and stability. Formulations of this method, as well as some numerical examples, are given to validate the method.

Controller Parameters Tuning Based on Transfer Matrix Method for Multibody Systems

Transfer matrix method for multibody systems (MS-TMM) is a rife method to multi-rigid-flexible-body systems dynamics model deduction due to that there are no needs to establish the global dynamics equations of the system. Its basic idea is transferring a state vector between the body input(s) and output(s); this idea is close to the linear theories in control analysis and design. In this paper, three controllers’ parameters tuning techniques for the proposed system model using MS-TMM are utilized; one technique is applied to get the stability regions via the frequency response of MS-TMM derived model. Another technique considers a classical PID controller design through the analysis of step input response of the system, and the last technique can be applied in both time and frequency domains if the model has a known mathematical model. A car suspension system is considered to represent modeling and tuning problems. In-depth study of MS-TMM with control techniques and defining the controllers’ parameters stability regions provide an opportunity to formulate a relationship between MS-TMM and control design for novel control applications due to the powerful strength of MS-TMM dealing with more complex problems of the controlled multibody systems.

Free Vibration Characteristic of Multilevel Beam Based on Transfer Matrix Method of Linear Multibody Systems

In this paper, an approach based on transfer matrix method of linear multibody systems (MS-TMM) is developed to analyze the free vibration of a multilevel beam, coupled by spring/dashpot systems attached to them in-span. The Euler-Bernoulli model is used for the transverse vibration of the beams, and the spring/dashpot system represents a simplified model of a viscoelastic material. MS-TMM reduces the dynamic problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundaries are composed of displacements, rotation angles, bending moments, and shear forces, which are partly known and partly unknown, and end up with reduced overall transfer matrix. Nontrivial solution requires the coefficient matrix to be singular to yield the required natural frequencies. This paper implements two novel algorithms based on the methodology by reducing the zero search of the reduced overall transfer matrixs determinate to a minimization problem and demonstrates a simple and robust algorithm being much more efficient than direct enumeration. The proposal method is easy to formulate, systematic to apply, and simple to code and can be extended to complex structures with any boundary conditions. Numerical results are presented to show the validity of the proposal method against the published literature.

Riccati Discrete Time Transfer Matrix Method for Dynamic Modeling and Simulation of an Underwater Towed System

Efficient, precise dynamic modeling and control of complex underwater towed systems has become a research focus in the field of multibody dynamics. In this paper, based on finite segment model of cable, by defining the new state vectors and deducing the new transfer equations of underwater towed systems, a new highly efficient method for dynamic modeling and simulation of underwater towed systems is presented and the pay-out/reel-in process of towed cable is studied. The computational efficiency and numerical stability of the proposed method are discussed. When using the method to study the dynamics of underwater towed systems, it avoids the global dynamic equations of system, and simplifies solving procedure. Irrespective of the degree of freedom of underwater towed system, the matrices involved in the proposed method are always very small, which greatly improve the computational efficiency and avoids the computing difficulties caused by too high matrix orders for complex underwater towed systems. Formulations of the method as well as numerical simulations are given to validate the proposed method.

Dynamics design for multiple launch rocket system using transfer matrix method for multibody system

Dynamics design for complex mechanical systems has become an important research field and development direction at present, capturing attentions of an increasing number of engineers and scientists worldwide. Based on many advantages of the transfer matrix method for multibody system in studying multibody system dynamics, a design problem of a multiple launch rocket system is solved in this paper. Particular attention is addressed to model actions of the exhaust flow on the multiple rocket launcher, which are associated with firing order and firing intervals of rockets. Combined with a genetic algorithm, firing order and firing intervals are optimized to achieve optimum impact point dispersion reduction. The results of numerical simulation and verification tests show good agreement, while the dispersion characteristics of rockets have been improved in a low-cost way.