Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

TRIGONOMETRIC CURVE MODIFICATION OF SCROLL PROFILE AND ITS EFFECT ON PERFORMANCES OF A SCROLL COMPRESSOR

A modification of central profile with trigonometric curve is proposed based on the theory of engagement of scroll compressor. General modification equations for central profile of a pair of scrolls are given and various modification patterns are discussed. The equidistant method is employed to calculate the volume of a sealed chamber and a set of general equations is represented. Modification parameters affecting geometric and dynamic property of a scroll compressor are analyzed systematically, and the relations between them are accurately determined. The condition for transforming a trigonometric curve modification into an arc-curve modification is explained. The conclusions can also be applied to other scroll fluid machines.

Recognition Methods of Geometrical Images of Automata Models of Systems in Control Problem

The laws of functioning of discrete deterministic dynamical systems are investigated,presented in the form of automata models defined by geometric images.Due to the use of the apparatus of geometric images of automata,developed by V.A.Tverdokhlebov,the analysis of automata models is carried out on the basis of the analysis of mathematical structures represented by geometric curves and numerical sequences.The purpose of present research is to further develop the mathematical apparatus of geometric images of automaton models of systems,including the development of new methods for recognizing automata by their geometric images,given both geometric curves and numerical sequences.

Influence of Curve Geometric Parameters on Curving Performance of Sub-frame Radial Bogie

Based on the theory of vehicle-track coupling dynamics,the coupling dynamic model of the freight car mounted with the sub-frame bogies and the numerical model of curved track were established,utilizing the fast numerical integration method,the curving performance of the vehicle was simulated to study the influence of the curve geometric parameters such as curve radius,transition curve length and superelevation of outer rail on the wheel-rail dynamic interaction.The simulation results indicate that:(1)Increasing the curve radius can decrease the wheel-rail wear,but the effect will weaken while the curve radius is greater than 800m.(2)If the transition curve length is less than 30m,vibrations will appear at the transition-circle connecting point,and the smaller the transition length,the bigger the vibrations,the worse the wheel-rail wear,but when the length is bigger than 50m,its further variation has very little effect on wheel-rail wear.(3)The superelevation of outer rail can affect the distribution and difference of the inner and outer wheel-rail forces,and too large deficient or excessive superelevation will worsen the wheel-rail wear either.However,an appropriate deficient superelevation of outer rail(e.g.<20mm)is helpful to reduce the wheel-rail wear,which is consistent with the engineering practice of settling a certain deficient superelevation value.