2015 Vol. 36, No. 7

Display Method:
Nonlinear Numerical Simulation of Rotor Dynamics
XU Xiao-ming, ZHONG Wan-xie
2015, 36(7): 677-685. doi: 10.3879/j.issn.1000-0887.2015.07.001
Abstract(956) PDF(1229)
A symplectic numerical method using the finite element algorithm in time scheme was proposed for rotor dynamics involving nonlinear factors, in which the Euler angle representation was introduced into the dynamic rotor system for the description of the nonlinear motion of rotation. The swirling motion of the rotor system including the beam-disc combination was analyzed. The numerical results demonstrate the validity and correctness of the proposed method, which can be used for the analysis of swirling motion of rotor systems in various situations.
Transverse Vibration Control of Moving Printing Membranes With Bending Stiffness
WU Ji-mei, JING Tao, WANG Yan, LI Yan-feng, XUE Zhi-cheng, WU Qiu-min
2015, 36(7): 686-699. doi: 10.3879/j.issn.1000-0887.2015.07.002
Abstract(654) PDF(626)
The active control of transverse vibration of axially moving rectangular membranes with bending stiffness was investigated during the printing process. A computing model for the moving printing membrane with bending stiffness was established. The discretized dynamic equations for the moving membrane were obtained with the finite difference method, and the state equations of the transverse vibration control system for the moving membrane were derived. The suboptimal control method was applied to conduct the active control of transverse vibration of the moving membrane under various boundary conditions of actual printing processes. The calculated results show that the vibration of the moving rectangular membrane can be controlled effectively within a short time with the suboptimal vibration control method. The control effect will be better when the actuators act on some fixed nodes with 4 edges simply supported; when the actuators act on variable nodes, the control effect will be the best in the case of central point actuation under the 2 types of boundary conditions, where the dimensionless time of velocity attenuation to zero is shorter than those in the other cases of actuation at the rest nodes. It is indicated that the transverse vibration of axially moving rectangular membranes can be controlled effectively with the suboptimal control method, thus the printing precision can be promoted and the printing quality ensured.
Gauss Principle of Least Constraint for Cosserat Growing Elastic Rod Dynamics
XUE Yun, QU Jia-le, CHEN Li-qun
2015, 36(7): 700-709. doi: 10.3879/j.issn.1000-0887.2015.07.003
Abstract(800) PDF(767)
The dynamic modeling of growing elastic rods, with the background of a kind of growing, deforming and moving slender bodies in nature and engineering, was studied based on the Gauss principle of least constraint in the classical mechanics. This provides a new method for the dynamic modeling of growing elastic rods, and meanwhile expands the application scope of the Gauss principle of least constraint. With the Cosserat growing elastic rod as the object, the geometric rules for growth and deformation of the rod were analyzed, which show that the growing strain and elastic strain are in a nonlinear coupling relation. The constitutive equations were given as a linear relationship between the internal forces and elastic deformations of the rod’s cross section; through definition of the inverse of dyad, the Gauss principle of least constraint was used to model the growing elastic rod dynamics and get 2 equivalent forms of the Gauss variation, which reflect the symmetry between time and arc coordinates in the expression of rod dynamics. The closedform dynamic differential equations were derived. 2 forms of constraint functions were given, which indicate that the actual motion of an elastic rod made the function at a stationary value, and also the minimum value. Finally, some problems about the constraints and conditional extremums of the growing elastic rod dynamics were discussed.
Traveling Wave Mode Characteristics of Rotating Functional Gradient Material Cylindrical Shell Structures With Elastic Boundary Constraints
LI Wen-da, DU Jing-tao, YANG Tie-jun, LIU Zhi-gang
2015, 36(7): 710-724. doi: 10.3879/j.issn.1000-0887.2015.07.004
Abstract(849) PDF(837)
The traveling wave mode characteristics of rotating functional gradient material (FGM) cylindrical shells in free vibration and the effects of elastic boundary constraints were analyzed, in which the physical properties of FGM were expressed as exponential functions varying along the thickness direction. Based on Love’s shell theory, the vibration displacements in the 3 directions were constructed in the form of modified Fourier series to improve the derivative continuity of displacement functions on each boundary. Then the energy description and Rayleigh-Ritz method were combined to formulate the eigen-equations of rotating FGM cylindrical shells. Comparison between the current results and those from other approaches in previous literatures was made to verify the correctness and convergence of the present method. Subsequently, the effects of FGM properties, geometric parameters, boundary conditions and constraint stiffnesses on the traveling wave mode characteristics of rotating FGM cylindrical shells were studied in detail. From the computed results, it is clear that the boundary conditions have significant effects on the traveling wave mode characteristics, especially when the circumferential wave number or the length-to-radius ratio L/R of a shell is relatively small; while the influence of boundary conditions decreases gradually with the thickness-to-radius ratio H/R.Additionally, the effects of boundary constraint stiffnesses on the traveling wave mode characteristics are greatly dependent on the mode order of a rotating FGM cylindrical shell, the influence of FGM properties on the traveling wave mode characteristics increases with the mode order.
Collaborative Optimization of Structures With Periodic Composite Materials
CHENG Ke-peng, WANG Xian-jie, ZHANG Xun-an, LIAN Ye-da
2015, 36(7): 725-732. doi: 10.3879/j.issn.1000-0887.2015.07.005
Abstract(982) PDF(837)
In view of the coupling effects between the micro scale and macro scale, the structure-material collaborative optimization method was established based on the traditional bi-directional evolutionary topology optimization method. The equivalent elastic modulus and sensitivities were obtained with the homogenization theory, and these properties were integrated into the material unit cell design and macrostructure optimization. To eliminate the gray area, the 0-1 properties of the materials and uniformity of the macrostructure permutation were hypothesized for deduction, which made the results manufacturable. Several numerical examples were presented to validate that the proposed optimization algorithm is effective for the material unit cell design and macrostructure optimization. The method also can be used for the periodic composite material design under given macrostructures.
An Operator Semigroup Method for Rectangular Plates With 2 Opposite Sides Simply Supported
LIU Jie, HUANG Jun-jie, Alatancang
2015, 36(7): 733-743. doi: 10.3879/j.issn.1000-0887.2015.07.006
Abstract(848) PDF(547)
The problem of solving a rectangular thin plate with 2 opposite sides simply supported in elasticity theory by means of the operator semigroup method was addressed. First, the plate equations were transformed into the abstract Cauchy problem. Then, the Hilbert space was defined and it was proved that the corresponding operator matrix generates contraction semigroups. Finally, the uniformly continuous semigroup approximation was applied through the Fourier transform, and the analytical solutions to the equations were given. The method naturally implies the existence and uniqueness of the solution.
Numerical Analysis of Synergy Between Velocity Field and Temperature Field in Finned Tubes With Different Longitudinal Vortex Generators
ZENG Zhuo-xiong, WANG Zhang-jun, LIU Jian-quan
2015, 36(7): 744-755. doi: 10.3879/j.issn.1000-0887.2015.07.007
Abstract(769) PDF(625)
In order to explore the comprehensive properties of heat convection in H-type finned tubes installed with small rectangular wings or triangular wings as the longitudinal vortex generators, the field synergy principle was adopted in analysis. At the same attack angle, the surface average and volume average synergy angles of the small triangular wings are bigger than those of the small rectangular wings; at the same time, the volume average synergy angles are bigger than the surface average ones. With the increase of the attack angle, both the surface average and volume average synergy angles decrease first but increase later, which reach their minimum values at the 60° attack angle for the rectangular wings but at the 45° attack angle for the triangular wings. At the same inlet velocity, both the surface average and volume average synergy angles of the 45°-attack-angle triangular wings are bigger than those of the 60°-attack-angle rectangular wings. With the increase of the inlet velocity, both the surface average and volume average synergy angles increase for the 60°-attack-angle rectangular wings and the 45°-attack-angle triangular wings as well.
Global μ-Stability of Impulsive Complex-Valued Neural Networks With Mixed Time-Varying Delays
YAN Huan, ZHAO Zhen-jiang, SONG Qian-kun
2015, 36(7): 756-767. doi: 10.3879/j.issn.1000-0887.2015.07.008
Abstract(760) PDF(921)
The global μ-stability of impulsive complex-valued neural networks with mixed time-varying delays was investigated. For the considered complex-valued neural networks, the activation functions only need to satisfy the Lipschitz conditions. Based on the homeomorphism mapping principle in the complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural network was proposed in terms of linear matrix inequalities (LMIs). Through construction of appropriate Lyapunov-Krasovskii functionals, and with the free weighting matrix method and inequality technique, a delay-dependent criterion for checking the global μ-stability of the complex-valued neural networks was established in terms of LMIs. Finally, a simulation example was given to show the effectiveness of the obtained results.
A Modified Laplace-Homotopy Perturbation Algorithm
2015, 36(7): 768-778. doi: 10.3879/j.issn.1000-0887.2015.07.009
Abstract(721) PDF(832)
A modified NDLT-HPM (MNDLT-HPM for short) was proposed through introduction of a parameter into the NDLT-HPM (nonlinearities distribution Laplace transform-homotopy perturbation method). This parameter makes the solving process for the nonlinear differential equations more flexible and is able to adjust and control the convergence region of the series solution, meanwhile overcomes the limitations of the NDLT-HPM that the series solution may be non-convergent when embedded parameter p equals 1. The present algorithm gives series solutions which converge well to the corresponding exact ones, thus obtaining sufficiently accurate approximate analytical solutions. 2 numerical examples show the advantage and accuracy of this method.
Multiple Monotone Positive Solutions to 3rd-Order Boundary Value Problems Involving Riemann-Stieltjes Integral Conditions
2015, 36(7): 779-786. doi: 10.3879/j.issn.1000-0887.2015.07.010
Abstract(906) PDF(622)
A class of 3rd-order nonlocal boundary value problems (BVPs) with Riemann-Stieltjes integral conditions were studied. The existence of positive solutions to BVPs was explored via perturbed Hammerstein integral equations. Through the construction of the Green functions and discussion on their properties, the existence criterion for at least 3 or 2n-1 positive solutions was obtained by means of the generalization of the Leggett-Williams fixed point theorem. The results generalize and improve some known results of the latest literatures, and fully reflect the influence of nonlinear terms involving derivatives on the existence of positive solutions. An example was also included to illustrate the main results.