应用数学和力学

Study on Combined Resonance of Low Pressure Cylinder-Generator Rotor System With Bending-Torsion Coupling

LI Jun, CHEN Yu-shu

2011, 32(8): 895-911. doi: 10.3879/j.issn.1000-0887.2011.08.001

Abstract(1688) PDF(947)

Abstract:
The nonlinear model of the low pressure cylinder-generator rotor system was presented for the study of sub-synchronous resonance and combined resonance.Analytical results were obtained by the averaging method.The transition sets and bifurcation diagrams were obtained by the singularity theory for two-state variable system.The bifurcation characteristics were analyzed,which can provide a basis for the optimal design and fault diagnosis of the rotor system.Finally,the theoretical results are verified by the numerical results.

Green’s Function for T-Stress of a Semi-Infinite Plane Crack

CUI Yuan-qing, YANG Wei, ZHONG Zheng

2011, 32(8): 912-919. doi: 10.3879/j.issn.1000-0887.2011.08.002

Abstract(1877) PDF(886)

Abstract:
Green's function for the T-stress near a crack tip was addressed by an analytic function method for a semi-infinite crack lying in an elastical,isotropic,and infinite plate.The cracked plate was loaded by single inclined concentrated force at interior point.The complex potentials were obtained by a superpo sition principle,which provide the solutions to the plane problems of elasticity.The regular parts of the potentials were extracted by an asymptotic analysis.Based on the regular parts,Green's function for the T-stress was obtained in a straight-forward manner.Furthermore,Green's functions were derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimpo sing method.Then Green's function was used to predict the do ain-switch-induced T-stress in a ferroelectric double cantilever beam(DCB)test.The T-stress induced by the electro mechanical loading was used to judge the stable and unstable crack growth behaviors observed in the test.The prediction results roughly agree with the experimental data.

Diagonal Form Fast Multipole Boundary Element Method for 2D Acoustic Problems Based on Burton-Miller BIE Formulation and Its Applications

WU Hai-jun, JIANG Wei-kang, LIU Yi-jun

2011, 32(8): 920-933. doi: 10.3879/j.issn.1000-0887.2011.08.003

Abstract(1618) PDF(909)

Abstract:
The formulations and implementation of the fast multipole BEM (FMBEM) for 2D acoustic problems were described indetail.The kernel function expansion theory was summarized,and the four building blo ks of the FMBEM-moment calculation,moment to moment translation,moment to local translation,and local to local translation,were described in detail.A data structure for the quad-tree construction was proposed which can facilitate the implementation.An analytical moment expression was derived which was more accurate,stable and efficient than direct numerical computation.Numerical examples were presented to demonstrate the accuracy and efficiency of the FMBEM,and the radiation of a 2D vibration rail mode was simulated using FMBEM.

Application and Analysis of a Functionally Graded Piezoelectrical Rotating Cylinder as a Mechanical Sensor Subjected to Pressure and Thermal Loads

G. H. Rahimi, M. Arefi, M. J. Khoshgoftar

2011, 32(8): 934-945. doi: 10.3879/j.issn.1000-0887.2011.08.004

Abstract(1620) PDF(773)

Abstract:
The exact thermoelastic analysis of a functionally graded piezoelectrical (FGP) rotating cylinder was investigated analytically.The cylinder was subjected to a combination of electrical,thermal and mechanical loads simultaneously.This structure was a simplified model of a rotational sensor or actuator.Basic governing differential equation of the system had been obtained using the energy method.A novel term which was named as additional energy was introduced in order to exact evaluation of energy functional.The solution of the governing differential equation was presented for two types of boundary conditions including free rotating cylinder and rotating cylinder exposed to inner pressure.The effect of angular velocity was investigated on the radial distribution of various components.The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to pressure and temperature.The obtained results indicate that the electrical potential is proportional to angular velocity.

Model Reduction and Active Control of a Flexible Beam Using Internal Balance Technique

XIE Yong, ZHAO Tong, CAI Guo-ping

2011, 32(8): 946-955. doi: 10.3879/j.issn.1000-0887.2011.08.005

Abstract(1459) PDF(820)

Abstract:
The internal balance technique was effective for model reduction in flexible structures,especially ones with dense frequencies.However,due to the difficulty in extracting internal balance modal coordinates from physical sensor readings,research so far on this topic has been mostly theo retic and little on experiment or engineering applications.The internal balance method theo retically as well as experimentally was studied,and further an active controller based on the reduction model was designed.The research works on a DSP TMS320F2812-based experiment system with a flexible beam and brings forward an approximating approach to access internal balance modal coordinates.Simulation and test results have proven the proposed approximating approach feasible and effective,and the designed controller successful in restraining the beam vibration.

Collision Efficiency of Two Nanoparticles With Different Diameters in the Brownian Coagulation

WANG Yu-ming, LIN Jian-zhong

2011, 32(8): 956-963. doi: 10.3879/j.issn.1000-0887.2011.08.006

Abstract(1416) PDF(751)

Abstract:
Collision efficiency of two nanoparticles with different diameters in the Brownian coagulation was investigated.The collision equations were solved to obtain the collision efficiency for the dioctyl phthalate nanoparticle with diameter changing from 100nm to 750nm in the presence of van der Waals force and elastic deformation force.It is found that the collision efficiency decreases as a whole with the increase of both the particle diameter and radius ratio of two particles.There exists an abrupt increase in the collision efficiency when the particle diameter is equal to 550 nm.Finally a new expression for the collisio n efficiency of two nanoparticles with different diameters was presented.

Effect of Turbulence Intensity on Airfoil Flow: Numerical Simulations and Experimental Measurements

LI Shao-wu, WANG Shu, WANG Jian-ping, MI Jian-chun

2011, 32(8): 964-972. doi: 10.3879/j.issn.1000-0887.2011.08.007

Abstract(1668) PDF(714)

Abstract:
Effect of the turbulence intensity of the oncoming stream on the aerodynamic characteristics of NACA-0012 airfoil was investigated by a direct numerical simulation.The numerical results were found to be consistent with the experimental measurements.Based on the finite spectral QUICK scheme,the simulation gets the high accuracy results.Both the simulation and experiment reveal that the airfoil stall does not exist for low turbulence intensity,however,occurs when the turbulence intensity increases sufficiently.Besides,the turbulence intensity has a significant effect on both the airfoil boundary layer and the separated shear layer.

Thin Liquid Film Morphology Driven by Electro-Static Field

Emily M. Tian, Thomas P. Svobodny, Jason D. Phillips

2011, 32(8): 973-980. doi: 10.3879/j.issn.1000-0887.2011.08.008

Abstract(1742) PDF(809)

Abstract:
The development of stationary patterns on a thin polymer surface subject to an electric field was studied by means of a hexagonal-planform weakly nonlinear stability analysis and numerical simulations.The time evolution of the interface between air and polymer film on the unbounded spatial domain was described by the thin film equation,incorporating the electric driving force and the surface diffusion.The nonlinear interfacial growth includes the amplitude equations and superpo sition of one-dimensional structures at regular orientations.The pattern selection is driven by the subcritical instability mechanism in which the relative thickness of the polymer film plays a critical role.

Effects of Magnetic Field,Porosity and Wall Properties for Anisotropically Elastic Multi-Stenosis Arteries on the Characteristics of Blood Flow

Kh. S. Mekheimer, Mohamed H. Haroun, M. A. El Kot

2011, 32(8): 981-997. doi: 10.3879/j.issn.1000-0887.2011.08.009

Abstract(1557) PDF(717)

Abstract:
A mathematical model for blood flow through an elastic artery with multi-stenosis under effect of a magnetic field in a porous medium was presented.The arterial segment under consideration was simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood.The analysis was carried out for an artery with mild local narro wing in its lumen forming a stenosis.The effects of arterial wall parameters that represent the viscoelastic stresses components acting along the longitudinal and circumferential directions T_t and T_θ respectively,the degree of anisotropy of the vessel wall γ, the total mass of the vessel and the surrounding tissues M and the contributions of the viscous and elastic constraints to the total tethering C and K respectively on the resistance impedance, the wall shear stress distribution,the radial and axial velocities had been well illustrated.Also the effects of the stenosis shape m,the constant of permeability κ,the Hartmann number Ha and the maximum height of the stenosis size δ on the fluid flow characteristics were investigated.The obtained results show that the flow was appreciably influenced by the surrounding connective tissues of the motion of the arterial wall and the degree of aniso tropy of the vessel wall play an important role to determine the material of the artery.Further the wall shear stress distribution increases with increasing Tt and γ while it decreases with increasing T_θ,M,C and K.The transmission of the wall shear stress distribution and the resistance impedance at the wall surface through a tethered tube were substantially lower than those through the free tube while the shearing stress distribution at the stenosis throathad inverse character through to tally tethered and free tubes.The trapping bolus increases in size to ward the line center of the tube as the constant of permeability κ increases and it decreases by increasing Hartmann number Ha.Finally the trapping bolus appears gradually in the case of non-symmetric stenosis while it seems to disappear in the case of symmetric stenosis and the size of trapped bo lus for the stream lines in the free isotro pictube(means the tube which initially unstressed) was smaller than those in the tethered tube.

Chemical Reaction Effects on an Unsteady MHD Flow Past a Semi-Infinite Vertical Porous Plate With Viscous Dissipation

J. A. Rao, S. Shivaiah

2011, 32(8): 998-1010. doi: 10.3879/j.issn.1000-0887.2011.08.010

Abstract(1790) PDF(730)

Abstract:
A chemical reaction effect on an unsteady magnetohydrodynamic flow past a semi-infinite vertical porous plate with viscous dissipation was analyzed.The governing equations of motion,energy and species were transformed into ordinary differential equations using time dependent similarity parameter.The resultant ordinary differential equations were then solved numerically by a finite element method.The effects of the various parameters on the velocity,temperature and concentration profiles were presented graphically and values of skin-friction, Nusselt number and Sherwood number for various values of physical parameters were presented.

Generalized Riemann Problem for Gas Dynamic Combustion

LIU Yu-jin, SHENG Wan-cheng

2011, 32(8): 1011-1020. doi: 10.3879/j.issn.1000-0887.2011.08.011

Abstract(1730) PDF(721)

Abstract:
The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin(t＞0)in the(x,t)plane was considered.Under the modified entropy conditions, the solutions were constructed uniquely,which were the limits of the selfsimilar ZND combustion model.It was found that,for some cases,there were intrinsical differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions.Especially,a strong detonation in the correspo nding Riemann solution may betransformed into a weak deflagration coalescing with pre-compression shock wave after perturbation.And in some cases,although there is no combustion wave of the corresponding Riemann solution,it may occur after perturbation,which shows the instability of unburnt gases.

2011 Vol. 32, No. 8