On dynamics of elastic rod based on exact Cosserat model

The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.

PROPAGATION OF SURFACE ACOUSTIC WAVES IN PRESTRESSED ANISOTROPIC LAYERED PIEZOELECTRIC STRUCTURES

The propagation of surface acoustic waves in layered piezoelectric structureswith initial stresses is investigated. The phase velocity equations are obtained for electricallyfree and shorted cases, respectively. Effects of the initial stresses on the phase velocity and theelectromechanical coupling coefficient for the fundamental mode of the layered piezoelectricstructures are discussed. Numerical results for the c-axis oriented film of LiNbO_3 on a sapphiresubstrate are given. It is found that the fractional change in phase velocity is a linear functionwith the initial stresses, and the electromechanical coupling factor increases with an increase ofthe absolute values of the compressive initial stresses. The results are useful for the design ofsurface acoustic wave devices.

Stability and vibration of a helical rod with circular cross section in a viscous medium

The stability and vibration of a thin elastic helical rod with circular cross section in a viscous medium are discussed. The dynamical equations of the rod in the viscous medium are established in the Frenet coordinates of the centreline with the Euler angles describing the attitudes of the cross section as variables. We have proved that the Lyapunov and Euler conditions of stability of a helical rod in the space domain are the necessary conditions for the asymptotic stability of the rod in the time domain. The free frequencies and damping coefficients of torsional and flexural vibrations of the helical rod in the viscous medium are calculated.

Numerical and experimental studies on impact dynamics of a planar flexible multibody system

In this paper a computational methodology on impact dynamics of the flexible multibody system is presented. First, the floating frame of reference approach and nodal coordinates on the basis of finite element formulation are used to describe the kinematics of planar deformable bodies. According to the kinematic description of contact conditions, the contact constraint equations of planar flexible bodies are derived. Based on the varying topology technique the impact dynamic equations for a planar multibody system are established. Then the initial conditions of the equations in each contact stage are determined according to the discontinuity theory in continuum mechanics. The experiments between the aluminum rods are performed to check the correctness of the proposed method. Through the comparison between the numerical and experimental results the proposed method is validated. Experimental results also show that the impulse momentum method cannot accurately predict the complex impact dynamic phenomena and the continuous model may lead to a serious error when used to simulate the impact problems with significant wave propagation effects.

THE ANALYSIS OF DYNAMIC STRESS INTENSITY FACTOR FOR SEMI-CIRCULAR SURFACE CRACK USING TIME-DOMAIN BEM FORMULATION

The time-domain BEM was developed to analyze the dynamic stress intensity factor ( DSIF) of 3-D elastodynamic crack problems. To simulate the stress singularity along the front of a crack, eight-node isoparametric singular elements were used, and the DSIF for a semi-circular surface crack was firstly calculated based on displacement equation using the time-domain BEM formulation. The new scheme to determine the time step was brought forward. By the dynamic analysis program of time-domain BEM compiled by its, several numerical examples are presented, which demonstrate the unconditional stability and high accuracy of time-domain BEM applied to 3-D elastodynamic crack problems.

ACTIVE CONTROL OF A FLEXIBLE CANTILEVER PLATE WITH MULTIPLE TIME DELAYS

Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.

Finite Eement Facture Aalysis of the Main Arm of Tower Cranes with the 3-D Cracks

In this paper the local solutions of displacement fields in front of three-dimensional cracks are introduced and a new singular element of three-dimensional crack problems is constructed, and a new method for calculating stress intensity factors of three-dimensional crack problems is presented. With the present method, the structural strength of with longitudinal closed cracks under axial tensions is analyzed. It is possible for the crack to propagate because there are ring tensile stresses near joints of the main arm in tower cranes under axial press stresses. The stress and the stress intensity factor are calculated at joints on the main arm of tower cranes. Influences of welding residual stress on stress intensity factors and stresses are discussed.

THE CRACK-INCLUSION INTERACTION AND THE ANALYSIS OF SINGULARITY FOR THE HORIZONTAL CONTACT

Using the basic solutions of a single crack and a single inclusion, and making use of the principle of linear superposition of elastic mechanics, the interaction problem between a planar crack and a flat inclusion in an elastic solid is studied. The problem is reduced to solve a set of standard Cauchy-type singular equations. And the stress intensity factors at points of crack and inclusion were obtained. Besides, the singularity for the horizontal contact of crack and inclusion was analyzed. The calculating model put forward can be regarded as a new technique for studying the crack and its expanding caused by inclusion lip. Then several numerical examples are given.

Non-Newtonian steady shear flow characteristics of waxy crude oil

The experimental research on the non-Newtonian flow characteristic of a waxy crude oil was conducted through a rotational parallel-plates rheometer system.The test temperature is about 6.5 ℃ higher than its gel point.The shear stress and viscosity of the waxy crude oil show sophisticate non-Newtonian characteristics in the shear rate of 10-4-102 s-1,in which the shear stress can be divided into three parts qualitatively,i.e.stress-up region,leveling-off region,and stress-up region.This indicates that there is a yielding process in shearing for the waxy crude oil at the experimental temperature,which is similar to the yield phenomenon in thixotropy-loop test discussed by CHANG and BOGER.Furthermore,the steady shear experiment after the pre-shear process shows that the stress leveling-off region at low shear rate disappears for the waxy crude oil and the stress curve becomes a monotonic climbing one,which demonstrates that the internal structure property presenting through yielding stress at low shear rate can be changed by shearing.The experimental results also show that the internal structure of waxy crude oil presenting at low shear rate has no influence on the shear viscosity obtained at the shear rate higher than 0.1 s-1.The generalized Newtonian model is adopted to describe the shear-thinning viscosity property of the waxy crude oil at high shear rate.

Discretization of Preisach hysteresis model

In order to reduce the partial derivative errors in Preisach hysteresis model caused by inaccurate experimental data,the concept and correlative method of discretization of Preisach hysteresis model are proposed,the essential of which is to centralize the distribution density of Preisach hysteresis model in local region as an integral,which is defined as the weight of a certain point in that region.For the input composed of an ascending segment and a descending segment,a method to determine the initial weights together with an additional method to determine present weights is given according to the number of input ascending segments.If the number of input ascending segments increases,the weights of the corresponding points in updating rectangle are updated by adding the initial weights of corresponding points.A prominent advantage of discrete Preisach hysteresis model is its memory efficiency.Another advantage of discrete Preisach hysteresis model is that there is no function in the model,and thus,it can be expediently operated using a computer.By generalizing the above updating rectangle method to the continuous Preisach hysteresis model,identification method of distribution density can be given as well.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT-VENANT BENDING

Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.

ON THE PARTIALLY CAVITATING FLOW AROUND TWO-DIMENSIONAL HYDROFOILS

The steady partially cavitating flow around two-dimensional hydrofoils war simulated numerically by the low-order potential-based boundary integration method. The cavity shape and length are determined for given cavitating numbers in the course of iteration by satisfying the kinematic and dynamic boundary conditions. The re-entrant jet model and the pressure-recovery close model are adopted to replace the high turbulent and two-phase wake forming behind the cavity. The results are compared with the other published numerical ones.

CHAOTIC ATTITUDE MOTION OF A MAGNETIC RIGID SPACECRAFT

Chaotic attitude motion of a magnetic rigid spacecraft in a circular orbit of the earth is treated. The dynamical model of the problem was derived from the law of moment of momentum. The Melnikov analysis was carried out to prove the existence of a complicated nonwandering Cantor set. The dynamical behaviors were numerically investigated by means of time history, Poincar map, power spectrum and Liapunov exponents. Numerical simulations indicate that the onset of chaos is characterized by break of torus as the increase of the torque of the magnetic forces.

NON-INTEGRABILITY AND CHAOS OF A CONSERVATIVE COMPOUND PENDULUM

By using a series of canonical transformations (Birkhoff's series), an approximate integral of a conservative compound pendulum is evaluated. Level lines of this approximate integral are compared with the numerical simulation results. It is seen clearly that with a raised energy level, the nearly integrable system becomes non-integrable, i.e. the regular motion pattern changes to the chaotic one. Experiments with such a pendulum device display the behavior mentioned above.

QUALITATIVE ANALYSIS OF A ROLLING HOOP WITH MASS UNBALANCE

The dynamical behavior of a rolling hoop with an unbalanced point mass under the influence of gravity is discussed.The whole process from rolling to hopping of the hoop is analyzed qualitatively.The conditions of slipping,hopping and touching down of the hoop are obtained.It is shown that the hoop cannot maintain a pure rolling before hopping up,and the slippage is unavoid- able.The hoop has neither vertical velocity nor vertical acceleration at the moment when the normal constraint force vanishes.The hopping motion of the hoop can occur only when the derivative of the vertical acceleration with respect to time is positive.It requires that the angular velocity of the hoop should be larger than a critical value,and the mass point should be located in the fourth quadrant of the hoop circle at the moment of hopping.The whole process of the pure rolling,rolling with slipping, hopping and falling motions of the hoop is shown in the phase plane,and the physical explanation of the hopping motion is given.

Design method of multiple time-delay controller for active structural vibration control

An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. A time-delay controller is then designed based on this standard equation using the discrete optimal control method. Effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in the instability of the control system if it is not compensated in the control design. Time delay may be compensated effectively by the proposed controller, in the mean time, an effective control may be obtained. The proposed controller is valid for both small and large time delays.

ELEMENT FUNCTIONS OF DISCRETE OPERATOR DIFFERENCE METHOD

The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.

A new semi-empirical spectrum model for complex steady shear viscosity of complex fluids

A semi-empirical spectrum model is proposed to describe the experimental data of the steady shear properties of a Shengli waxy crude oil near its gel point, where sophisticated structural effects become apparent due to the existence of waxy crystals in the crude oil. The model, consisting of a time spectrum, can well fit the steady shear viscosities of the waxy crude oil over the whole experimental shear rate region from 10-4 to 102 s- 1. Two other experiments on complex fluids reported recently in the literature are also well described by this model demonstrating the applicability and accuracy of the model.

Nonlinear formulation for flexible multibody system with large deformation

In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.

An exact nonlinear hybrid-coordinate formulation for flexible multibody systems

The previous low-order approximate nonlinear formulations succeeded in capturing the stiffening terms, but failed in simulation of mechanical systems with large deformation due to the neglect of the high-order deformation terms. In this paper, a new hybrid-coordinate formulation is proposed, which is suitable for flexible multibody systems with large deformation. On the basis of exact strain- displacement relation, equations of motion for flexible multi-body system are derived by using virtual work principle. A matrix separation method is put forward to improve the efficiency of the calculation. Agreement of the present results with those obtained by absolute nodal coordinate formulation （ANCF） verifies the correctness of the proposed formulation. Furthermore, the present results are compared with those obtained by use of the linear model and the low-order approximate nonlinear model to show the suitability of the proposed models.