K. Sandeep

The effect of speed of balanced rotor on nonlinear vibrations associated with ball bearings

The paper deals with the structural dynamic response of rotor supported by ball bearings. The mathematical model takes into account the sources of nonlinearity such as Hertzian contact force, surface waviness, varying compliance and internal radial clearance resulting transition from no contact to contact state between rolling elements and races. In terms of the feature that the nonlinear bearing forces act on the system, a new reduction method and corresponding integration technique is used to increase the numerical stability and decrease computer time for system analysis. The effects of speed of balanced rotor in which ball bearings show periodic, quasi-periodic and chaotic behavior are analyzed. The results are presented in the form of time displacement responses, frequency spectra and Poincare maps. It is implied from the frequency spectra that peak amplitude of vibrations appear at the varying compliance frequency.

HEAT TRANSFER ANALYSIS OF TWO-DIMENSIONAL FINS USING MESHLESS ELEMENT FREE GALERKIN METHOD

This article deals with the transient and steady-state solution of two-dimensional heat transfer through the fins using a meshless element free Galerkin method. Moving least-square approximants are used to approximate the unknown function of temperature T h (x) with Th (x) . These approximants are constructed by using a linear basis, a weight function, and a set of nonconstant coefficients. The variational method has been used for the development of discrete equations. Essential boundary conditions are enforced by using Lagrange multipliers. A hyperbolic weight function has been proposed. The results are obtained for a two-dimensional model and compared with the results of the finite-element method.

THE ELEMENT FREE GALERKIN METHOD IN THREE DIMENSIONAL STEADY STATE HEAT CONDUCTION

This paper deals with the solution of three dimensional steady state heat conduction problems using a meshless Element Free Galerkin Method. The unknown function T(x, y, z) is approximated by using moving least square approximants. These approximants are constructed using a weight function, a monomial basis and a set of non-constant coefficients. The governing equations are developed using a variational technique and essential boundary conditions are imposed by using Lagrange multiplier method. A hyperbolic weight function has been proposed. The results are obtained for a three dimensional model by taking different types of weight functions. the Element Free Galerkin Method has been validated by comparing the results with those obtained by finite element and analytical methods.

A Fast Progressive Image Sampling Using Lifting Scheme And Non-Uniform B-Splines

This paper proposes lifting scheme based a new fast algorithm for progressive image acquisition that enables an approximation of whole image at each step. The detail coefficients of second generation wavelets have been used to find the most significant samples. An image, which is considered here as the functions of non-uniform B-splines over the Delaunay triangulation, is developed by using recursively obtained scattered data set of significant pixels. The efficiency of the present method is shown and the visual qualities of the multiresolution images are compared with those obtained by other methods.

Effects of Preload and Number of Balls on Nonlinear Dynamic Behavior of Ball Bearing System

In this paper, the radial and axial vibrations of rigid shaft supported by ball bearings are analyzed. In analytical formulation, the contacts between the balls and races are considered as nonlinear springs, whose stiffness is obtained by using Hertzian elastic contact deformation theory. The governing differential equations of motion are obtained using Lagranges equations. The implicit type numerical integration technique Newmark-ß with Newton-Raphson method is used to solve the nonlinear differential equations iteratively. The effects of two important parameters viz., preload and the number of balls are investigated in perfect bearings.

Postbuckling of symmetrically laminated, moderately thick, axisymmetric shallow spherical shells

The paper deals with the buckling and postbuckling behaviour of cylindrically orthotropic, axisymmetric laminated, moderately thick shallow spherical shells under uniformly distributed normal loading. Considering the effects of transverse shear, the governing equations of equilibrium for the shells are derived and expressed in terms of normal deflection W, slope \qf and stress function \gy. An iterative Chebyshev series solution technique is employed for the buckling and postbuckling analyses. Critical loads are estimated and the effects of boundary conditions, material properties, shell parameter, base radius to thickness ratio and number of layers on the postbuckling behaviour are shown.

Second generation wavelets based GIS terrain data compression using Delaunay triangulation

Purpose – In GIS applications for a realistic representation of a terrain a great number of triangles are needed that ultimately increases the data size. For online GIS interactive programs it has become highly essential to reduce the number of triangles in order to save more storing space. Therefore, there is need to visualize terrains at different levels of detail, for example, a region of high interest should be in higher resolution than a region of low or no interest. Wavelet technology provides an efficient approach to achieve this. Using this technology, one can decompose a terrain data into hierarchy. On the other hand, the reduction of the number of triangles in subsequent levels should not be too small; otherwise leading to poor representation of terrain.Design/methodology/approach – This paper proposes a new computational code (please see Appendix for the flow chart and pseudo code) for triangulated irregular network (TIN) using Delaunay triangulation methods. The algorithms have proved to be ef...

Quasi-periodic, Subharmonic and Chaotic Motions of a Rotor Bearing System

The paper deals with structural vibrations of rolling elements as well as inner and outer races. The mathematical formulation takes into account the sources of nonlinearity such as Hertzian contact force, surface waviness and internal redial clearance resulting transition from no contact to contact state between rolling elements and the races. The contacts between the rollers and races are treated as nonlinear springs and the springs act only in compression to simulate the contact deformation and resulting force. The nonlinear stiffness is obtained using Hertzian elastic contact deformation theory. In terms of the feature that the nonlinear bearing forces act on the system, the implicit type numerical integration technique Newmark-ß with Newton Raphson method is used to solve the nonlinear differential equations iteratively. Poincare maps, rotor trajectories, time responses with contact force and displacement are used to elucidate and to illustrate the diversity of the system behavior. It is shown that due to defects such as surface waviness and internal radial clearance the system exhibits undesirable jump phenomenon with quasi-periodic, subharmonic and chaotic motions.

Analysis of Laminates using Multiquadric Radial Basis Function

Multiquadric radial basis function (MQRBF) is developed for static and dynamic analysis and to estimate natural frequency of laminated plate at various boundary conditions. MQRBF is applied for spatial discretization and Newmark implicit scheme is used for temporal discretization. The spatial discretization of the differential equations generates a greater number of algebraic equations than the unknown coefficients. The multiple linear regression analysis, which is based on the least square error norm, is employed to obtain the coefficients. Numerical results are compared with those obtained by other analytical methods.

Wavelet based schemes for linear advection–dispersion equation ☆

Abstract In this paper, two wavelet based adaptive solvers are developed for linear advection–dispersion equation. The localization properties and multilevel structure of the wavelets in the physical space are used for adaptive computational methods for solution of equation which exhibit both smooth and shock-like behaviour. The first framework is based on wavelet-Galerkin and the second is based on multiscale decomposition of finite element method. Coiflet wavelet filter is incorporated in both the methods. The main advantage of both the adaptive methods is the elimination of spurious oscillations at very high Peclet number.