Jianshu Zhang

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.

Study on the Natural Vibration Characteristics of Flexible Missile With Thrust by Using Riccati Transfer Matrix Method

Due to the mass consumption and engine thrust of a flexible missile during the powered phase flight, its natural vibration characteristics may be changed significantly. The calculation of natural frequencies and mode shapes plays an important role in the structural design of the missile. Aiming at calculating the natural vibration characteristics of the missile rapidly and accurately, a nonuniform beam subjected to an engine thrust is used to model the free vibration of the missile and Riccati transfer matrix method (RTMM) is adopted in this paper. Numerical results show that the natural frequencies of a typical single stage flexible missile are increased unceasingly in its powered phase, and its mode shapes are changed a lot. When the presented methodology is used to study the natural vibration characteristics of flexible missiles, not only the mass, stiffness, and axial compressive force distributions are described realistically but also numerical stability, high computation speed, and accuracy are achieved.

Study on the Dynamics of Laser Gyro Strapdown Inertial Measurement Unit System Based on Transfer Matrix Method for Multibody System

The dynamic test precision of the strapdown inertial measurement unit (SIMU) is the basis of estimating accurate motion of various vehicles such as warships, airplanes, spacecrafts, and missiles. So, it is paid great attention in the above fields to increase the dynamic precision of SIMU by decreasing the vibration of the vehicles acting on the SIMU. In this paper, based on the transfer matrix method for multibody system (MSTMM), the multibody system dynamics model of laser gyro strapdown inertial measurement unit (LGSIMU) is developed; the overall transfer equation of the system is deduced automatically. The computational results show that the frequency response function of the LGSIMU got by the proposed method and Newton-Euler method have good agreements. Further, the vibration reduction performance and the attitude error responses under harmonic and random excitations are analyzed. The proposed method provides a powerful technique for studying dynamics of LGSIMU because of using MSTMM and its following features: without the global dynamics equations of the system, high programming, low order of system matrix, and high computational speed.

Study on the Stress-Stiffening Effect and Modal Synthesis Methods for the Dynamics of a Spatial Curved Beam

In this paper, based on the nonlinear strain–deformation relationship, the dynamics equation of a spatial curved beam undergoing large displacement and small deformation is deduced using the finite-element method of floating frame of reference (FEMFFR) and Hamiltonian variation principle. The stress-stiffening effect, which is also called geometric stiffening effect, is accounted for in the dynamics equation, which makes it possible for the dynamics simulation of the spatial curved beam with high rotational speed. A numerical example is carried out by using the deduced dynamics equation to analyze the stress-stiffening effect of the curved beam and then verified by abaqus software. Then, the modal synthesis methods, which result in much fewer numbers of coordinates, are employed to improve the computational efficiency.

Study on automatic deduction method of overall transfer equation for branch multibody system

The transfer matrix method for multibody system is a new method developed in recent 20 years for studying multibody system dynamics. The new version of transfer matrix method for multibody system and automatic deduction theorem of system overall transfer equation have been formed in 2012. The overall transfer equation plays one of the key roles for transfer matrix method for multibody system. In order to study branch system dynamics with new version of transfer matrix method for multibody system, the automatic deduction theorem of overall transfer equation has been expanded in this article, which made it practicable to deduce automatically the overall transfer equation for branch system with new version of transfer matrix method for multibody system. The transfer equations and transfer matrices of typical elements are developed for the automatic deduction theorem of overall transfer equation. Thereby new version of transfer matrix method for multibody system owns the following features: there is no need to establish the global dynamics equation of system, by which the study on multibody system dynamics will be simplified greatly; the automatic deduction of overall transfer equation for multibody system is realized, consequently the algorithm is simple and highly programmable; moreover, the order of system matrix is always low, which result in high computational speed. The branch multibody system dynamics has been computed with the automatic deduction theorem of overall transfer equation as well as ordinary multibody system dynamics method. The computational results obtained by the two methods have good agreements, which validate the automatic deduction theorem of overall transfer equation for branch multibody system.

Visualized simulation and design method of mechanical system dynamics based on transfer matrix method for multibody systems

The transfer matrix method for multibody systems is a new method with very high computational speed developed in recent 20 years for studying multibody system dynamics. By combining transfer matrix method for multibody systems, computer graphics, and open-source software, this article puts forward an approach and software MSTMMSim for visualized simulation and design of mechanical system dynamics. The approach includes the following procedures in sequence: design of functional model, design of three-dimensional solid model, design of dynamics model, automated formation of dynamics equations, and software MSTMMSim for visualized simulation and design of mechanical system dynamics. The proposed method and software provide a platform to realize the simulation and design of complex mechanical systems with the following characteristics: (1) automatic deduction of the overall transfer equation, (2) high computational speed, and (3) high visualization and programming of dynamics simulation and design process. The proposed method and software are verified by the practical example of simulation and design of a tank system dynamics using this platform.