应用数学和力学

2017 Vol. 38, No. 6

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An Investigation on Nonlinear-Damping and Nonlinear-Stiffness Vibration Isolation Systems Under Random Excitations

LI Jue-min, LU Ze-qi, CHEN Li-qun

2017, 38(6): 613-621. doi: 10.21656/1000-0887.370277

Abstract(1902) PDF(1313)

Abstract:
Both nonlinear damping and nonlinear stiffness were introduced in vibration isolation systems under random excitations to improve the isolation performance. The nonlinear damping and nonlinear stiffness were realized through the geometric arrangement of the horizontal springs and horizontal dampers. The performance of the nonlinear vibration isolator under random excitation was evaluated with the equivalent FokkerPlanckKolmogorov (FPK) equation transformed by the nonlinear stochastic vibration equation. The effects of the nonlinearity introduced in stiffness and damping on the transmissibility and its probability were studied. It is found that, for high levels of random excitations, the damping nonlinearity brings larger reduction of the random vibration response, and the gap between the linear and the nonlinear dampings is enlarged; however, for low levels of random excitations, the nonlinear damping has less efficacy than the linear damping.

Influence of Potential Well Depth on Power Generation Performance of Bistable Electromagnetic Energy Harvesting Systems

ZHANG Xiao-jing, LIU Li-lan, REN Bo-lin, LI Shu-chao

2017, 38(6): 622-632. doi: 10.21656/1000-0887.370246

Abstract(1079) PDF(1689)

Abstract:
With the development of the electromagnetic vibration energy harvesting technology from single-to multi-stable-state systems, the response frequency bandwidth was broadened and the output voltage was increased, hence better power generation performance was obtained. The bistable electromagnetic vibration energy harvester with a linear vibrator was investigated, the effects of potential well depth on the power generation performance was studied, and the influences of the system structure parameters of the mass ratio and the tuning ratio were analyzed based on the potential well depth under the optimal power performance. Numerical simulation results show that, when the external excitation is at low frequencies, the potential well depth will be larger, and the vibrator of the bistable system can only work in small vibration; when the potential well depth is small to a certain extent, the vibrator will enter large chaotic or periodic motion across the barrier between 2 potential wells, with the average output power higher than that during the small motion. Through numerical simulation, the optimal mass ratio, tuning ratio and damping ratio of the system were obtained.

Application of the Volterra Kernel Function Method in Feature Extraction of Bearing Ball Wear

WANG Hai-tao, ZHANG Xiao, SHI Li-chen, WANG Kun

2017, 38(6): 633-642. doi: 10.21656/1000-0887.370243

Abstract(1116) PDF(778)

Abstract:
The fault features are difficult to be extracted from the worn rolling ball bearings. To tackle this problem, an algorithm of the Volterra series kernel based on the multiple-pulse excitation method was proposed. This method belongs to the cross diagnosis for nonlinear system models, which utilizes the sampled signal input and output of the bearing system to establish the Volterra nonlinear identification system model and applies the Volterra low-order kernel algorithm based on the multiple-pulse excitation method to obtain the low-order kernel, then the low-order kernel will be compared in aspects of the GIRF and the GFRF to estimate the present running state of the bearing system. The major bearing of a centerless lathe was taken for example to verify this method through experiment. In contrast to the traditional wavelet analysis method, the multiple-pulse excitation method helps extract the fault features of the ball bearing conveniently and exactly. Thus, the proposed method has much significance to the diagnosis of such faults.

Analysis and Optimization on Inverse Kinematics for Multi-Robot Parallel Lifting Systems

ZHAO Zhi-gang, WANG Yan-lin, SU Cheng, LI Jin-song, JI Gang

2017, 38(6): 643-651. doi: 10.21656/1000-0887.370147

Abstract(1061) PDF(1015)

Abstract:
The inverse kinematics problem of close-coupling multi-robot parallel lifting systems was discussed. Firstly, the kinematic and dynamic models for the system were established by means of geometrical relations and wrench balance equations. Secondly, the inverse kinematics for the system, which was divided into two cases of fixed lengths and variable lengths of cables, was analyzed. Subsequently, the ways to solve the problems were given when the inverse kinematics had infinite solutions, multiple solutions or no solution at one moment, respectively. Then the optimization goal for finding the optimum solution was given in the case of multiple solutions. Finally, the numerical experiment platform for the parallel lifting system was established based on software UG/ADAMS/MATLAB, and the parameters of a real system were given for simulation. The simulation results show that, the proposed method effectively solves the multi-solution problem, and provides a foundation for further research on dynamical stability, cable tension optimization and control algorithm design for the system.

A Stochastic Tensile Damage Model for Loading/Unloading of Concrete and Experimental Validation

HU Shao-wei, HUANG Yi-qun

2017, 38(6): 652-662. doi: 10.21656/1000-0887.370254

Abstract(1153) PDF(745)

Abstract:
To analyze the mechanical properties of concrete in the case of tensile loading and unloading, a stochastic elastoplastic tensile damage model of mesoscopic springs was proposed for the axial loading and unloading of concrete, with the loading and unloading stress-strain relationships of concrete deduced. To validate the rationality and accuracy of the model, an experimental research on axial tensile loading and unloading of concrete was carried out, where the concrete parameters and the stress-strain relationships were measured. Comparison between the experimental results and the calculation model results shows that, the model can well predict the ultimate tensile strength, meanwhile nicely depict the strength softening, the residual strain after unloading and the elastic modulus degradation of concrete.

Investigation on Structural Dynamic Responses of Vertical-Axis Tidal Current Turbines

ZHANG Peng-kun, LI Ye

2017, 38(6): 663-675. doi: 10.21656/1000-0887.370267

Abstract(1052) PDF(892)

Abstract:
The 3D numerical analysis on the blade dynamic responses of the vertical-axis tidal turbines was presented based on the discrete vortex method of University of British Columbia (DVM-UBC) and the geometrically exact beam theory (GEBT). For the first time the GEBT was used to perform the dynamic analysis for tidal current turbines. Compared with the traditional 3D finite element method, the proposed method has advantages of saving computing cost, easily building the model, high calculation accuracy and so on. In the modal analysis, the obtained natural frequencies of the single blade and the entire turbine with various height-to-radius (H/R) ratios show that, the arm size has larger influence on the frequency than the blade size. In the transient dynamic analysis, the deflections at blade tips in one rotation cycle with various H/R ratios were calculated. According to the design optimization of the turbine geometry, it is found that when the H/R ratio is greater than 3.0, the maximum blade deflection will go beyond the critical blade deflection, which means strength failure of the turbine blades.

A Robust Adaptive Backstepping Control Method for ElectroHydraulic Position Servo Systems

YANG Si-yang, HAN Jiang, ZHANG Kui-bang, XIA Lian

2017, 38(6): 676-684. doi: 10.21656/1000-0887.370272

Abstract(1219) PDF(1475)

Abstract:
Aimed at the tracking control problem of electro-hydraulic servo systems due to the parameter uncertainties and nonlinear characteristics et al., a robust adaptive backstepping method with parameter adaptive performances was presented based on the Lyapunov stability theory. The adaptive law was designed to suppress the influences of parameter uncertainties on the tracking control performances of the system and the robust control law rendered the system globally uniformly asymptotically stable. In addition, the discontinuity caused by the direction change of the servo valve was approximated. With the servo valve-controlled symmetric cylinder as the control object, the simulation results show that, compared with the traditional PD control method, the proposed backstepping control method renders the tracking error fluctuation of the electro-hydraulic position servo system slighter and the convergence rate faster, and requires a much lower input signal voltage for the servo valve smoother, so the uncertain parameters can converge to and keep at the their stable values after a short period of time. An example proves the effectiveness of the proposed algorithm.

Numerical Analysis of Downhole Drill Strings With a Longitudinal and Lateral Coupled Vibration Model

TIAN Jia-lin, WU Chun-ming, YANG Yong-wen, YAO Yu, YANG Zhi, YUAN Chang-fu, WU Bo

2017, 38(6): 685-695. doi: 10.21656/1000-0887.370214

Abstract(1060) PDF(860)

Abstract:
Aimed at the complicated motion of the downhole drill string and based on the existing dynamics theory, the longitudinal and lateral coupled vibration model for the drill strings was established, and the numerical solution was obtained. According to the actual working condition of the downhole drill string, the entire drill string was regarded as the object of study. The concrete expressions of the dynamic stiffness, dynamic damping and the 1st 2 orders of natural frequencies were deduced with the analytical method and the dimensionless method in view of the coupled vibration characteristics of the downhole drill string. The research findings reveal that when the vibration frequency of the downhole drill string increases, the dynamic stiffness will periodically change with amplitude attenuation and the dynamic damping will periodically change with amplitude enhancement. The greater the length and the cross-sectional area of the downhole drill string are, the smaller the vibration amplitudes of the dynamic stiffness and the dynamic damping will be. Moreover, the Poisson’s ratio of the downhole drill string has no effect on the dynamic stiffness, the dynamic damping and the 1st 2 orders of natural frequencies. Meanwhile, the 2nd-order natural frequency of the drill string is always greater than the 1st. The proposed methods and model provide theoretical references and practical significances for further analysis and design optimization of the bottom-hole assembly (BHA).

Study on Hamel’s Embedding Method via the Udwadia-Kalaba Theory

ZHAO Han, ZHAO Xiao-min, JIANG Jian-man

2017, 38(6): 696-707. doi: 10.21656/1000-0887.370327

Abstract(1457) PDF(887)

Abstract:
Hamel embedded the constraint directly into the kinetic energy of unconstrained motion to avoid the use of Lagrange multiplier, which made a simple, straightforward, but incompletely correct method. Hamel stated that this method may lead to wrong results, but did not point out the applicable conditions for its correctness. Based on the Udwadia-Kalaba theory, the necessary and sufficient condition for Hamel’s embedding method was found. Besides, examples show that Rosenberg’s work on the validity of Hamel’s embedding method is insufficient. Hamel’s embedding method may be correct under nonholonomic constraint and may be incorrect under holonomic constraint. According to the theoretical and exemplary analysis, the correctness of Hamel’s embedding method is not only determined by the constraints, but also determined by the mechanical system model.

A Geometric Explanation of Hamilton-Jacobi Methods Based on the Frobenius Theorem

XIAO Jing, LIU Chang, WANG Yong

2017, 38(6): 708-714. doi: 10.21656/1000-0887.370268

Abstract(1735) PDF(669)

Abstract:
With the differential geometry method, a geometric explanation based on the Frobenius theorem for characteristic equations of 1st-order partial differential equations was presented. According to the Frobenius theorem, the characteristic equations can be deduced directly from the 1st-order partial differential equations. Based on this, how to use the geometric method to find the corresponding Hamilton-Jacobi equations from Hamiltonian canonical equations was discussed. This method could be utilized to address the nonconservative or nonholonomic Hamiltonian mechanical problems. The classical Hamilton-Jacobi method is only a special case of this method.

Scalarization of Mixed Vector Variational Inequalities and Error Bounds of Gap Functions

LIU Dan-yang, JIANG Ya

2017, 38(6): 715-726. doi: 10.21656/1000-0887.370292

Abstract(1315) PDF(639)

Abstract:
The Konnov scalarization method for variational inequality problems was used to further generalize the classical strongly variational inequalities (SVIs) and the classical weakly variational inequalities (WVIs). The strongly generalized mixed vector variational inequalities (SGMVVIs) and the weakly generalized mixed vector variational inequalities (WGMVVIs) were studied based on setvalued mappings in view of their gap functions. Under proper conditions, the relationship between the gap function of the strongly generalized mixed setvalued variational inequality (SGMVI) and that of the SGMVVI, and the relationship between the gap functions of the WGMVVI and the SGMVI, were discussed. At last, the global error bounds of the gap functions were obtained.