Summary
On one hand, the new version of transfer matrix method for multibody systems (NV‐MSTMM), has been proposed by formulating transfer equations of elements in acceleration level instead of position level as in the original discrete time transfer matrix method of multibody systems to study multibody system dynamics. This new formulation avoids local linearization and allows using any integration algorithms. On the other hand, sensitivity analysis is an important way to improve the optimization efficiency of multibody system dynamics. In this paper, a totally novel direct differentiation method based on NV‐MSTMM for sensitivity analysis of multibody systems is developed. Based on direct differentiation method, sensitivity analysis matrix for each kind of element is established. By assembling transfer matrices and sensitivity analysis matrices based on differentiation law of multiplication, the sensitivity analysis equation of overall transfer equation is deduced. The computing procedure of the proposed method is also presented. All these improvements as well as three numerical examples show that the direct differentiation method based on NV‐MSTMM is suitable for optimizing the dynamic sensitivity in multi–rigid‐body systems.
Vibration control in launching process is an effective way to improve the dispersion characteristics of Multiple Launch Rocket System (MLRS). In this paper, a novel methodology for MLRS vibration controller design with the application of pulse thrusters and its parameters optimization is introduced. Based on the Transfer Matrix Method for Multibody Systems (MSTMM), the dynamic model of the controlled MLRS with pulse thrusters is established and the launch dynamic simulation system of controlled MLRS is developed. To suppress vibrations of the elevation part using the annularly arranged pulse thrusters, a management scheme based on impulse equivalence approach is presented to adapt the continuous force generated by the PID control law to impulse force. Controller optimization is achieved coupling Particle Swarm Optimization-Genetic Algorithm (PSO-GA) with the established simulation system of controlled MLRS. Finally, the simulation results verify the effectiveness of the proposed controller and demonstrate the engineering practicability value of this methodology.
The initial disturbance of a projectile emerging from the gun muzzle is a major reason for the projectile dispersion. Therefore, measurements of initial disturbances have a great value in improving the understanding. This paper establishes a mathematical model of the measurement system for the projectile's in-bore orientation, by utilizing the theory of ray tracing and kinematics. The layout of the optical apparatuses is attributed to an optimization problem, and the genetic algorithm is implemented to acquire an optimal layout scheme, which is further verified by test. Also, the linear timeinvariant characteristics of the measurement system are numerically verified in the context of spatial ray. These investigations will provide a technical support for the experiment, the optical apparatuses' layout and calibration of the measurement system.
Natural vibration characteristics and dynamics response of multiple launch rocket system (MLRS) are of fundamental importance from the viewpoint of vibration levels, firing dispersion, and stability. In this study, a new launch vehicle-supports-rockets coupling dynamic model for a practical MLRS is established. Rui method, namely the transfer matrix method for multibody systems (MSTMM) is a new and efficient method for multibody system dynamics (MSD) and is used to obtain the vibration characteristics and dynamics response. The dynamics model, the topology figure of dynamics model, the transfer equations of elements, the overall transfer equation, the eigenfrequency equation, the body dynamics equations, the generalized coordinate equations, and the dynamics simulation system for the MLRS are established. Based on the advantages of MSTMM in studying MSD, the vibration characteristics and dynamics response of complex MLRS are computed rapidly. Finally, the new model is validated in three ways: (1) modal experiment of MLRS, (2) launch dynamics experiment of non-full loading rockets, and (3) launch dynamics experiment of full loading rockets. The results show that the proposed model can not only simulate the natural vibration characteristics of the MLRS but also effectively perform dynamic simulations of the MLRS during launching process.
Rui method, namely the transfer matrix method for multibody systems (MSTMM) is a new and efficient method for multibody system dynamics (MSD) for its features as follows: without global dynamics equations of the system, high programming, low order of system matrix and high computational speed. Riccati transfer matrix method for multibody systems was developed by introducing Riccati transformation in MSTMM, for improving numerical stability of MSTMM. In this paper, based on Riccati MSTMM, applying the thought of direct differentiation method, by differentiation of Riccati transfer equations of rigid bodies and joints, generalized acceleration and its differentiation can be obtained. Combined with Backward Euler algorithm, implicit algorithm for Riccati MSTMM is proposed in this paper. The formulation and computing procedure of the method are presented. The numerical examples show that results obtained by first order accurate implicit algorithm proposed in the paper and the fourth order accurate Runge-Kutta method have good agreement, which indicates that this implicit method is more numerical stability than explicit algorithm with the same order accurate. The implicit algorithm for Riccati MSTMM can be used for improving the computational accuracy of multibody system dynamics.
Dynamics characteristics of linear multibidy systems are governed by the eigenfrequencies and the eigenvectors. The study of probabilistic characterization of the eigensolutions is now an important research topic in the field of multibody systems with random parameters. In this paper, by combining transfer matrix method for multibody system (MSTMM) and perturbation approach, a new method named as perturbation MSTMM is presented for random eigenvalue problems of multibody systems. This method has the advantages of, such as low memory storage requirement, high computational efficiency and high computational stability, etc., for dynamic design of multibody systems with random parameters. By using the proposed method, the rapid computation of random eigenvalue problems of general systems with random parameters can be realized, and the problem of repeated eigenvalues can be solved simply and conveniently. Formulations of the proposed method as well as some numerical examples are given to validate the proposed method. The simulation results of the eigenfrequencies are validated by experiment results. All the numerical applications show the merits and efficacy of the proposed method.
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