EXACT SOLUTION FOR FINITE DEFORMATION PROBLEMS OF CANTILEVER BEAM WITH VARIABLE SECTION UNDER THE ACTION OF ARBITRARY TRANSVERSE LOADS

This paper deals with finite deformation problems of cantilever beam with variable sec- tion under the action of arbitrary transverse loads.By the use of a method of variable replacement, the nonlinear differential equation with varied coefficient for the problem can be transformed into an equation with variable separable.The exact solution can be obtained by the integration method. Some examples are given in the paper,and the results of these examples show that this exact solution includes the existing solutions in references as special cases.

Oscillatory Dynamics of a Spherical Solid in a Liquid in an Axisymmetric Variable Cross Section Channel

The dynamics of a solid spherical body in an oscillating liquid flow in a vertical axisymmetric channel of variable cross section is experimentally studied.It is shown that the oscillating liquid leads to the generation of intense averaged flows in each of the channel segments.The intensity and direction of these flows depend on the dimensionless oscillating frequency.In the region of studied frequencies,the dynamics of the considered body is examined when the primary vortices emerging in the flow occupy the whole region in each segment.For a fixed frequency,an increase in the oscillation amplitude leads to a phase-inclusion holding effect,i.e.,the body occupies a quasi-stationary position in one of the cells of the vertical channel,while oscillating around its average position.It is also shown that the oscillating motion of a liquid column generates an averaged force acting on the body,the magnitude of which depends on the properties of the body and its position in the channel.The quasi-stationary position is determined by the relative density and size of the body,as well as the dimensionless frequency.The behavior of the body as a function of the amplitude and frequency of fluid oscillation and relative size is discussed in detail.Such findings may be used in the future to control the position of a phase inclusion and/or to strengthen mass transfer effects in a channel of variable cross section by means of fluid oscillations.

Finite element analysis of rolling process for variable cross-section blade

Due to the variation of the blade cross-section, the deformation stress and strain of the workpiece keep changing during the rolling process and the conventional rolling theory is no longer valid. The complexity and diversity of the blade cross-section determine it impossible to establish an universal theoretical model for the rolling process. Finite element analysis(FEA) provides a perspective solution to the prediction. The FEA software DEFORM was applied to discovering the deformation, stress, strain and velocity field of the variable cross-section workpiece, and the effects of friction coefficient and rolling speed during the rolling process. which indicates that the average rolling force at friction coefficient of 0.4 is 6.5% higher than that at 0.12, and the rolling velocity has less effect on the equivalent stress and strain distribution, which would confer instructive significance on the theoretical study as well as the engineering practice.

THE GENERAL SOLUTION FOR DYNAMIC RESPONSE OF NONHOMOGENEOUS BEAM WITH VARIABLECROSSSECTION

In this paper by means of the exact analytic method [1], the general solution fordynamic response of nonhomogeneous beam with variable cross section is obtained un-der arbitrary resonant load and boundary conditions. The problem is reduced to solvea non-positive differential equation. Generally, it is not solved by variational method.By the present method, the general solution for this problem may be written as an ana-lytic form. Hence, it is convenient for structure optimizing problem. In this paper, itsconvergence is proved. Numerical examples are given at the end of the paper. which in-dicates satisfactory results can be obtained.

Dynamic analysis of double racks gear 3D roll forming machine

3 D roll-forming for high strength steel sheets is a new technology at present.Double racks gear 3D roll forming machine developed by our research group can be used to perform variable cross section roll forming for high strength steel.In the paper,a dynamic model of 8-DOF double rack gear 3D roll-forming machine is established by the method of Lagrange equation.The expression of the angle acceleration of the system response is obtained by solving the dynamic equations.Through an actual engineering example,the dynamical characters of the 3D roll forming machine are revealed.The results can support the design of 3D roll forming machine.Meanwhile,the research will play an active role in the development of control system.

Guest Editorial:Special Section on Integrating Ultra-High Levels of Variable Renewable Energy

Wind and solar energy have seen significant decreases in the cost of these technologies over that last decade which has lead to increasing levels integrated into the grid.They also offer unique benefits such as no fuel costs,quick installation,and no pollution.But as more variable renewable energy(VRE)such as wind and solar is integrated into electrical power systems.