Dynamic analysis of an axially moving plate subjected to thermal loading

Dynamic analysis of axially moving thermally loaded two-dimensional system is presented in this paper. Using the Hamilton's principle, the differential equation of the transverse motion of the moving plate is derived. Using the extended Galerkin method the approximate solution is determined in this work. To verify the present approach, the calculation results of buckling thermal load for stationary plate are compared with the results published in literature. Dynamic analysis of axially moving aluminum plate subjected to thermal loading is presented. Besides the thermal critical loading the effects of transport speed and axial tension on dynamic behavior of axially moving aluminum plate are presented.     

Non-linear global dynamics of an axially moving plate

In the present study, the geometrically non-linear dynamics of an axially moving plate is examined by constructing the bifurcation diagrams of Poincaré maps for the system in the sub and supercritical regimes. The von Kármán plate theory is employed to model the system by retaining in-plane displacements and inertia. The governing equations of motion of this gyroscopic system are obtained based on an energy method by means of the Lagrange equations which yields a set of second-order non-linear ordinary differential equations with coupled terms. A change of variables is employed to transform this set into a set of first-order non-linear ordinary differential equations. The resulting equations are solved using direct time integration, yielding time-varying generalized coordinates for the in-plane and out-of-plane motions. From these time histories, the bifurcation diagrams of Poincaré maps, phase-plane portraits, and Poincaré sections are constructed at points of interest in the parameter space for both the axial speed regimes.     

Interaction of an axially moving band and surrounding fluid by boundary layer theory

The vibration characteristics of a submerged axially moving band are investigated. Where earlier studies used the ideal fluid assumption for modelling the effect of the surrounding air, the viscous flow of the air particles is included here by using an analytical model of a boundary layer on moving continuous flat surfaces. In order to use this theory to calculate boundary layer thicknesses, the shape of the boundary layer was assumed, so that the additional mass terms coming from the boundary layer flow could then be evaluated. Since the coefficients of the equation of motion for the submerged axially moving band changes as a function of the longitudinal coordinate, due to the change in the boundary layer, the equation is solved by the finite element method. The results show the difference between the present results and earlier ones to be significant, close to the critical velocity.     

Visco-elastic fluid flow past an infinite vertical porous plate in the presence of first-order chemical reaction

An analysis has been developed to study the unsteady free convection flow of an incompressible visco-elastic fluid on a continuously moving vertical porous plate in the presence of a first-order chemical reaction. The governing equations are solved numerically using an implicit finite difference technique. The obtained numerical solutions are compared with the analytical solutions. The velocity profiles are presented. A parametric analysis is performed to illustrate the influences of the visco-elastic parameter, the dimensionless chemical reaction parameter, and the plate moving velocity on the steady state velocity profiles, the time dependent friction coefficient, the Nusselt number, and the Sherwood number.     

Dynamic interaction of an oscillating sphere and an elastic cylindrical shell filled with a fluid and immersed in an elastic medium

The paper studies the interaction of a harmonically oscillating spherical body and a thin elastic cylindrical shell filled with a perfect compressible fluid and immersed in an infinite elastic medium. The geometrical center of the sphere is located on the cylinder axis. The acoustic approximation, the theory of thin elastic shells based on the Kirchhoff—Love hypotheses, and the Lamé equations are used to model the motion of the fluid, shell, and medium, respectively. The solution method is based on the possibility of representing partial solutions of the Helmholtz equations written in cylindrical coordinates in terms of partial solutions written in spherical coordinates, and vice versa. Satisfying the boundary conditions at the shell—medium and shell—fluid interfaces and at the spherical surface produces an infinite system of algebraic equations with coefficients in the form of improper integrals of cylindrical functions. This system is solved by the reduction method. The behavior of the hydroelastic system is analyzed against the frequency of forced oscillations.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 75–86, September 2004.