2015 Vol. 36, No. 5

Display Method:
Symplectic Eigenspace Expansion for the Random Vibration Analysis of Gyroscopic Systems
ZHAO Yan, LI Ming-wu, LIN Jia-hao, ZHONG Wan-xie
2015, 36(5): 449-459. doi: 10.3879/j.issn.1000-0887.2015.05.001
Abstract(1226) PDF(1199)
The random dynamic responses of the damped gyroscopic system were investigated under random loads. The pseudo-excitation method, as a highly efficient and accurate method for random vibration analysis, had been widely used in the fields of structural seismic and wind engineering. In the Lagrange framework based on a single physics variable the method of modal superposition is effective to reduce the degrees of freedom for complex structures in the numerical random vibration analysis. However, for the random analysis of gyroscopic systems, given the existing gyroscopic effects, application of the modal superposition method based on the Rayleigh quotient eigenvalues will be quite limited. Therefore, the general description of the symplectic eigenvalue problem was introduced firstly. Furthermore, for the damped gyroscopic system subjected to stationary random loads, the pseudo-excitation method was used and the solution formulae were derived based on the symplectic eigenspace expansion. For the conservative gyroscopic system, the solution expression was in an explicit form. In the numerical examples, the stationary random responses of a gyroscopic system were computed with the present method, of which the accuracy and efficiency were verified through comparison of the results with those out of other methods. The present method is of significance for the random vibration problems about mechanical engineering equipments with gyroscopic systems.
Dynamic Analysis of the 4-DOF Vehicle-Road Coupling System Under Random Excitation
LI Qian, LIU Jun-qing, CHEN Cheng-cheng
2015, 36(5): 460-473. doi: 10.3879/j.issn.1000-0887.2015.05.002
Abstract(1092) PDF(916)
The Gauss stationary random process was adopted to simulate pavement roughness, and a MATLAB program was compiled to obtain the values of pavement roughness. A 4-DOF vehicle model was built, and the vehicle and road were seen as a holistic coupling system. Then the dynamic equilibrium equations for the vehicle-road coupling system were established. In order to simplify the analysis work, the traditional method which used the theory of random vibration to determine the dynamic tire force was avoided and the values of pavement roughness were directly input in the form of vectors into the dynamic equilibrium equations, which were solved with the MATLAB program developed based on the incremental Newmark-βmethod. The reliability of the model was verified with a test. Then how the dynamic load coefficient and vertical vehicle acceleration were influenced by the vehicle speed and pavement roughness grade was parametrically analyzed in an example. At last, the effects of the roadbed elastic modulus on the vehicle vibration characteristics were investigated. The results show that, the vehicle dynamic load coefficient increases with the driving speed and the pavement roughness grade as well, meanwhile the vehicle body vibration acceleration rises with the driving speed but converges or even slightly falls after a peak value, and that acceleration goes up always with the roughness grade; furthermore, the dynamic load coefficient decreases with the roadbed elastic modulus and converges down to a constant value.
Feedback Linearization and Congestion Control for a Discrete Traffic Flow Model
FANG Ya-ling, SHI Zhong-ke
2015, 36(5): 474-481. doi: 10.3879/j.issn.1000-0887.2015.05.003
Abstract(1092) PDF(904)
A new method for controlling the macro discrete traffic flow model was presented in the automated freeway system. The non-linear model of traffic flow was transformed to an easily tractable linear system model with the precise state feedback linearization method, and the design of the traffic density controller was simplified. For the linearized system model, the control law was designed according to the feedback tracking control strategy with input transformation, to stabilize the dynamic property of the system. Then the system state variables were controlled to indirectly stabilize the traffic flow density and further alleviate the traffic congestion. The controller designing procedure was also given. The simulation results show that the control method is effective and practicable.
Analysis of Numerical Shock Instability and a Hybrid Curing Method
HU Li-jun, YUAN Li
2015, 36(5): 482-493. doi: 10.3879/j.issn.1000-0887.2015.05.004
Abstract(1112) PDF(737)
HLLC is a high resolution scheme, which can capture shock, contact discontinuity and rarefaction wave accurately. But when it is used to calculate multidimensional problems, the phenomenon of numerical shock instability may appear near the strong shock. Compared with the HLLC scheme, the FORCE scheme is stable near the strong shock, and the related numerical dissipation is lower than that of the HLL scheme. The stability of HLLC and FORCE under special conditions was analyzed, a hybrid scheme combining the HLLC and FORCE schemes in a special way was constructed, and a switching function to invoke the hybrid scheme in the transverse direction of the shock wave was defined. Numerical experiments demonstrate that the hybrid scheme not only presents good stability near the strong shock, but also retains the high resolution of HLLC.
Two Decoupling Methods for the Heat Transfer Model of a Plate Channel Filled With a Porous Medium
WANG Ke-yong, WANG Da-zhong, LI Pei-chao
2015, 36(5): 494-504. doi: 10.3879/j.issn.1000-0887.2015.05.005
Abstract(860) PDF(868)
A general heat transfer model of a parallel plate channel filled with a porous medium was constructed based on the Brinkman-Darcy extended model and the local thermal non-equilibrium model in view of the internal heat sources in fluid and solid phases. The temperature field of the porous medium under the fully developed heat transfer condition was respectively formulated with the direct and indirect decoupling methods of solving the fluid-phase and solid-phase energy equations. Compared to the direct decoupling method, the indirect one is more convenient to be employed to solve the 2nd-order differential equations under the original boundary conditions. The equivalence of the 2 decoupling methods was verified through comparison of the coefficients in the dimensionless temperature expressions and the temperature distributions between them. A good agreement was found between the temperature distributions obtained with the indirect decoupling method and those reported in the previous literatures in 2 limit cases, meanwhile the better generality of the proposed model was also proved to some extent. The parametric study shows that the temperature difference between the fluid and solid phases decreases with the Biot number or the effective thermal conductivity ratio, and the Nusselt number decreases with the internal heat source ratio.
Effects of Non-Smooth Surface Dimple Configuration on Vehicle Body Aerodynamic Characteristics
XIE Fei, DING Yu-mei, QIN Liu, YU Hua-chun, YANG Wei-min
2015, 36(5): 505-514. doi: 10.3879/j.issn.1000-0887.2015.05.006
Abstract(962) PDF(864)
According to the idea of bionic non-smooth revolution bodies, the SAE (Society of Automobile Engineers) standard model was selected as the object of study, and the computational fluid dynamics (CFD) method was used to investigate the effects of different non-smooth surface dimple array forms and densities on the aerodynamic performance of vehicle bodies. Through comparison of such flow field performance indicators as wake flow, airflow velocity, pressure field and turbulence kinetic energy between various models, the drag reduction mechanism of the dimpled non-smooth surface and the reasons for the difference of flow field properties between those models were analyzed. The results show that the minimum aerodynamic drag occurs when the dimple units are arranged in a rectangular configuration, and the aerodynamic drag decreases along with the longitudinal dimple distribution density, attaining the highest drag reduction ratio up to 4.1%.
A Modified Graph-Partitioning Algorithm for Vehicle Body Assembly Structure Optimization
HOU Wen-bin, HOU Da-jun, XU Jin-ting, ZHANG Wei
2015, 36(5): 515-522. doi: 10.3879/j.issn.1000-0887.2015.05.007
Abstract(838) PDF(790)
The optimization method for the vehicle body assembly structure was studied in view of the overall performance of manufacture and assembly. A modified graph-partitioning algorithm was proposed to optimally divide the vehicle body assembly structure into a set of components. A side frame model for the typical vehicle body in white was built as an example, in which the structure geometry was transformed to a topological graph at first, then the topological graph was partitioned into a set of simply connected and independent sub-graphs with constraints of engineering meanings. The genetic operators in algorithm NSGA-Ⅱ were combined with the FEM analysis to calculate the optimal partition of the product structure geometry. The results show that the proposed method realizes the objective of optimal comprehensive performance for the vehicle body assembly structure.
Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application
FU Bao-lian
2015, 36(5): 523-538. doi: 10.3879/j.issn.1000-0887.2015.05.008
Abstract(971) PDF(766)
It was discovered that the 2 main premises in the proposition of Betti’s reciprocal theorem for 3D linear elasticity, i.e. “1 elastic body” and “action of 2 sets of forces”, were contradictory to each other because either of the 2 sets of forces may change the given elastic body to another one. This contradiction leads to the result that Betti’s reciprocal theorem is one with error in logic. On the basis of the analysis of contradiction, the corrected reciprocal theorem was proposed, in which the correct proposition of the reciprocal theorem was given. In addition, the corrected reciprocal theorem provides a theoretical basis for the reciprocal method of works, which makes a novel and powerful way to the analysis of elastic bodies and structures.
Finite Element Application of the Time-Temperature Superposition Principle (TTSP) to Polymer
XU Jin-sheng, YANG Xiao-hong, ZHAO Lei, WANG Hong-li, HAN Long
2015, 36(5): 539-547. doi: 10.3879/j.issn.1000-0887.2015.05.009
Abstract(1262) PDF(1649)
To better describe the temperature-dependent mechanical properties of polymer materials, an improved WLF model was proposed, with a ‘zero time’ factor introduced to promote the precision of the relaxation modulus acquisition at different temperature levels for linearly viscoelastic materials. Thereafter, the improved WLF model was applied in the finite element calculation via user material subroutine UTRS in ABAQUS. The model parameters were obtained out of a series of relaxation tests at different temperature levels, and the feasibility and validity of the improved WLF model and the numerical method were verified through the constant-rate tensile tests of composite propellant specimens. The results show that, compared with the traditional findings, the relaxation moduli acquired in view of the ‘zero time’ factor at different temperature levels are more accurate, and the improved WLF model is more applicable and precise for the temperature-dependent description of composite propellants.
Sub-Equations and Exact Traveling Wave Solutions to a Class of High-Order Nonlinear Wave Equations
ZHANG Li-jun, CHEN Li-qun
2015, 36(5): 548-554. doi: 10.3879/j.issn.1000-0887.2015.05.010
Abstract(955) PDF(807)
The exact traveling wave solutions to a class of 5th-order nonlinear wave equations were studied with the sub-equation method and the dynamic system analysis approach. The lower-order sub-equations of this class of high-order nonlinear equations were first derived, then the traveling wave solutions were investigated via the various exact solutions to the sub-equations under different parameter conditions. As an example, 2 families of exact valley-form solitary wave solutions and 2 families of smooth periodic traveling wave solutions to the Sawada-Kotera equation were presented. This method can be applied to study the traveling wave solutions to high-order nonlinear wave equations of which the corresponding traveling wave system can be reduced to the nonlinear ODEs involving only even-order derivatives, sum of squares of 1st-order derivatives and polynomial of dependent variables.
Leader-Following Consensus of Fractional-Order Multi-Agent Systems With Nonlinear Models
2015, 36(5): 555-562. doi: 10.3879/j.issn.1000-0887.2015.05.011
Abstract(1180) PDF(1194)
The leader-following consensus of multi-agent systems with fractional-order nonlinear models was investigated. Under the assumption that the system communication topology contains a leader-rooted spanning tree, the control gain matrix was designed and the controllers were presented based on the theory of algebraic Riccati equations. Then, a sufficient condition for the leader-following consensus of multi-agent systems was given by means of the Laplace transform and inverse transform, the Mittag-Leffler function, the generalized Gronwall inequality and the stability theory of fractional differential equations. Finally, the numerical simulation results show the effectiveness of the proposed theoretical condition.