应用数学和力学

2016 Vol. 37, No. 2

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A Theoretical Algorithm for Jump Heights of Iced Transmission Lines After Ice Shedding

WU Chuan, YAN Bo, ZHANG Liang, ZHANG Bo, LI Qing

2016, 37(2): 117-126. doi: 10.3879/j.issn.1000-0887.2016.02.001

Abstract(1746) PDF(868)

Abstract:
An analytical model for multi-span transmission lines to estimate jump heights after ice shedding was set up, and an algorithm for the jump heights was developed by means of the energy equation, stress-sag relation, deformation and balance relation of the lines during the motion after ice shedding. The algorithm was verified through the comparison of the line jump heights determined respectively with the present algorithm, the finite element method and the Morgan theoretical algorithm. Furthermore, the present algorithm, the finite element method and the formula proposed in the Chinese design code for transmission lines were employed to evaluate the jump heights of typical transmission lines with different parameters after ice shedding, based on which the practicability of the present algorithm was discussed. It is indicated that the present algorithm could be used easily and quickly to determine the isolation clearance in the design of transmission lines located in icing zones.

Study of THz Wave Propagation in Tilted Carbon Nanotube Arrays Based on Symplectic Formulation

ZHANG Yu, DENG Zi-chen, ZHAO Peng

2016, 37(2): 127-137. doi: 10.3879/j.issn.1000-0887.2016.02.002

Abstract(1216) PDF(646)

Abstract:
With the equivalent medium model, the problem of planar waveguides filled with periodic parallel finite-length carbon nanotube arrays was introduced into the Hamilton system. Firstly, based on the equivalent medium theory, the dielectric property of the tilted carbon nanotubes was derived. Then, in view of the ideal conductive boundary conditions, the symplectic formulation was used to solve the eigenvalue problem of electromagnetic wave propagation and the dispersion relation was obtained. The numerical results show that, the dominant mode of the electromagnetic waves can hardly propagate in the carbon nanotube arrays in a narrow frequency band, while in the rest frequency bands it propagates well with very low loss, which means the carbon nanotube arrays have excellent transmission characteristics compared with the traditional materials. Through the optimization design, the best tilt angle was given to greatly enhance the transmission characteristics in the whole frequency range. The present research of THz wave propagation in carbon nanotube arrays makes a theoretical reference for the design of waveguide devices in the THz frequency bands.

Locally Confined Buckling Analysis of Self-Rotating Cantilever Beams

XIAO Shi-fu, CHEN Hong-yong, NIU Hong-pan

2016, 37(2): 138-148. doi: 10.3879/j.issn.1000-0887.2016.02.003

Abstract(1364) PDF(620)

Abstract:
The nonlinear model of a self-rotating cantilever beam confined by a restrictor located at an arbitrary position along the beam, was established. The stability of the system was investigated with the Ritz method. For the restrictor without friction, the critical values related to the restrictor’s position of the system losing its stability, the bifurcation modes, the post-buckling solutions and the optimal position of the stabilizing restrictor were obtained. Then the analytical critical values and the optimal position were numerically verified with the finite element method. The results obtained with the 2 methods were consistent with each other. Furthermore, the influences on the system stability by the frictions caused by the clamping force and the supporting force from the restrictor were studied. The investigation shows that a critical value of the rotational velocity exists for the self-rotating cantilever beam locally confined by a restrictor. After the rotational velocity exceeds the critical value, the trivial equilibrium loses its stability through the pitchfork bifurcation. While the rotational velocity recovers from the buckling state, significant hysteresis occurs due to the friction caused by the clamping force of restriction, and the buckling system comes back to the trivial equilibrium with a rotational velocity lower than the critical value. The optimal position of the stabilizing restrictor is located at about 78% of the beam length from the cantilever fixed end. These results are useful to guide the restrictor installation.

Damage Identification for Bridge Structures Based on the Wavelet Neural Network Method

XIAO Shu-min, YAN Yun-ju, JIANG Bo-lan

2016, 37(2): 149-159. doi: 10.3879/j.issn.1000-0887.2016.02.004

Abstract(1991) PDF(764)

Abstract:
Bridge structures will suffer complex loading environment during their service, and inevitable damages of structures may occur in long term service. If a damage can’t be found in time and treated properly, it may cause serious accidents. Therefore, the local small damage identification for bridge structures is of great significance for the timely maintenance. Generally, the measured global dynamic properties of a damaged structure are not sensitive enough to the local structural damages, especially to small damages, thus, it is necessary to extract more sensitive feature information to structural damages from the structural dynamic response signals. The finite element model of a bridge structure was established, and the dynamic characteristics were analyzed. The wavelet packet analysis was used to process the structural dynamic response signals and the structural damage index was presented. Then the damages of the bridge structure were positioned according to the damage index with the artificial wavelet neural network method. The results show that the wavelet packet energy change ratio makes an effective damage index; the properly trained neural network can fairly precisely position the bridge structural damages in the numerical test; the higher the damage degree is, the lower the positioning error comes.

Iterative Learning Instantaneous Optimal Control of Discrete Systems and Optimization

TONG Shao-wei, TANG Huai-ping

2016, 37(2): 160-172. doi: 10.3879/j.issn.1000-0887.2016.02.005

Abstract(1307) PDF(588)

Abstract:
Through combination of the instantaneous optimal control (IOC) and the iterative learning control (ILC), one new hybrid control strategy called the iterative learning instantaneous optimal control was proposed. The discrete linear system was chosen as the target model for the new control strategy, and the quadratic performance functional of the discrete system was taken as the objective function to be minimized. During the controlling process of the system, the core idea of the ILC was introduced in order to modify the control signals which were initialized by the IOC. With the method of matrix norms, the sufficient condition for convergence of the new control strategy was established. Compared with the IOC, the iterative learning instantaneous optimal control gives simulation results of improved effectiveness. Furthermore, based on the improved genetic algorithm (GA), the optimization of the actuator positions in a multistory building to be controlled was investigated. Results of the numerical simulation indicate that, while the actuators are partially positioned at some optimally seleted floors, the control effects may reach or even be better than those in the case of full installation of actuators at all floors.

Nonlinear Vibration Bifurcation Characteristics of Multi-Clearance 2-Stage Gear Systems

WANG Shu-guo, ZHANG Yan-bo, LIU Wen-liang, GUO Li-feng, LIAO Peng-tai, QI Li-mei

2016, 37(2): 173-183. doi: 10.3879/j.issn.1000-0887.2016.02.006

Abstract(1226) PDF(711)

Abstract:
A 5-DOF nonlinear vibration model for multi-clearance 2-stage gear systems was established with the lumped-mass method. In view of transmission errors, time-varying meshing stiffness and multiple gear clearances, the dimensionless dynamic equations for the system were derived. By means of the Poincaré maps and bifurcation diagrams, the bifurcation properties of the system were discussed under the effects of the rotation rate and the damping ratio. Given the various nonlinear factors, the 2-stage gear system exhibits rich and complex bifurcation characteristics. With the changes of the related parameters, the system will be in short-period motion, or long-period motion, or quasi-periodic motion or chaotic motion. For different damping ratios, with the decrease of the rotation rate, the system state changes from stable period-1 motion into stable period-2 motion through period-doubling bifurcation; then the system state changes into quasi-periodic motion through the Hopf bifurcation, in turn changes into stable period-1 motion after a catastrophe; finally the system enters into chaos through the Hopf bifurcation-phase locking. Moreover, with the increase of the rotation rate, the system damping ratio range corresponding to chaotic motions reduces, and the system will be in stable period-1 motion, or long-period motion or quasi-periodic motion, while the damping ratio range corresponding to long-period motion and quasi-periodic motion shortens and that corresponding to period-1 motion lengthens.

Lattice Boltzmann Simulation of Double Diffusive Natural Convection in a Square Enclosure Filled With Porous Medium

LI Bei-bei, YAN Zhen-rong, CHEN Jian, XU Hong-tao, YANG Mo

2016, 37(2): 184-194. doi: 10.3879/j.issn.1000-0887.2016.02.007

Abstract(1158) PDF(662)

Abstract:
The lattice Boltzmann method was adopted to investigate the double diffusive natural convection in a square enclosure filled with porous medium. The temperature and concentration on surrounding walls were low and those on the inner heat cylinder surface were high. The influences of Darcy number D_a(10^-4≤D_a≤10^-2) and buoyancyratio B(-5.0≤B≤5.0) on average Nusselt number Nu_av and Sherwood number Sh_av on the heat cylinder surface were studied. The results indicate that both Nu_av and Sh_av increase with D_a except for the case of B=-1.0,and both Nu_av and Sh_av are almost independent of B for D_a=10^-4.Both Nu_av and Sh_av first decrease and then increase with B increasing from -5.0 to 5.0 for D_a=10^-3 and 10^-2 and reach the minimal value for B=-1.0.

A Non-Splitting PML for Transient Analysis of Poroelastic Media and Its Finite Element Implementation

ZHOU Feng-xi, GAO Bei-bei

2016, 37(2): 195-209. doi: 10.3879/j.issn.1000-0887.2016.02.008

Abstract(1245) PDF(494)

Abstract:
The perfectly matched layer (PML) absorbing boundary condition had been proved to be a highly effective absorption technique for the numerical simulation of wave propagation and therefore widely used. In order to solve the problems of absorbing boundary conditions in the numerical modeling of 2nd-order elastic wave equations for the infinite domain poroelastic media, a non-splitting perfectly matched layer (NPML) was proposed. Firstly, based on the theory of Biot’s wave equations and in view of the compressibility of solid particles and pore fluid, the inertia and the pore fluid viscosity, the 2nd-order dynamic governing equations were established in the form of solid and fluid displacements. Secondly, according to the complex coordinate stretching technique, the frequency domain formulations of the NPML were obtained by means of the Laplace transform. Afterwards, with the aid of auxiliary functions in the absorption layer, an effective NPML was built through the transform of the frequency domain formulations back to the time domain. Finally, the time domain finite element scheme of the NPML on the basis of Galerkin approximate method was provided. The effectiveness of the NPML in the dynamic response analysis of saturated poroelastic media is demonstrated with several numerical examples.

Time-Delayed Feedback Control of Flutter for Supersonic Airfoils

QI Huan-huan, XU Jian, FANG Ming-xia

2016, 37(2): 210-218. doi: 10.3879/j.issn.1000-0887.2016.02.009

Abstract(1197) PDF(702)

Abstract:
An active delayed feedback control technique was proposed to control the flutter of supersonic airfoils. It’s intended to increase the critical flow velocity. Firstly, the delayed feedback control strategy was designed to suppress the flutter of the 2D airfoil, in turn the delayed differential equations (DDEs) were formulated for the controlled system under consideration. Then, the stability of the uncontrolled system, the nondelay feedback controlled system and the timedelayed feedback controlled system were analytically determined, respectively, and the flutter stability boundary of the delayed feedback controlled system as a function of the time delay was predicted. Finally, numerical simulation in time domain with the MATLAB/SIMULINK software was made to demonstrate the effectiveness of the present theoretical analysis results. The results show that, the critical flow velocity is significantly increased through regulation of the time delay magnitude, and the proposed delayed feedback control strategy for flutter control of supersonic airfoils is not only valid but also easily applicable to engineering structures.

Modeling of Hydrodynamics for Grid Fins With Cavitating Interference

CHEN Wei-qi, XIA Yan-yan, WANG Bao-shou, YAN Kai

2016, 37(2): 219-226. doi: 10.3879/j.issn.1000-0887.2016.02.010

Abstract(971) PDF(521)

Abstract:
The supercavitating flow hydrodynamics of grid fins of flat plates was addressed, and the effects on the grid fins’ hydrodynamic performances by different parameters including the grid fin plate number, the spacings between plates, the plate thickness, the attack angle and the cavitation number, were analyzed. A new hydrodynamic model for supercavitating grid fins was built and validated with experimental results. The hydrodynamic interference mechanism of the cavitating flow between the plates was explored and the experimental phenomena was explained. The results given by the proposed model with the numerical and experimental simulation show that, although the increase of the grid fin’s plate number promotes the lift force and drag force, the consequent decrease of the plate spacings, even down to the cavity thickness, will cause severe cavitating interference to weaken the hydrodynamic performances of the grid fin. Therefore, for a grid fin with certain sizes, the plate number has an optimal value.