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A method is presented to reduce the lateral vibration amplitude of an unbalanced rotor accelerating or decelerating through its critical speed, by means of modulating the response phase with varying acceleration rate. Theoretical and numerical analysis on the amplitude and the phase characteristics of lateral vibration of a rotor model are made. Numerical results show that when the rotor passes through its critical speed with a modulated phase, the response amplitude can be reduced by 20% or so, compared with the nonmodulated (constant) acceleration case. [DOI: 10.1115/1.1581893]

Abstract: Finite-difference methods of second order at the boundary points are presented for problems with one-dimensional second-order hyperbolic and parabolic equations with mixed boundary conditions. These methods do not require information at points outside the region of consideration. The linear stability of the algorithms developed is investigated. Numerical experiments are given for illustrating the accuracy and stability of the methods. Though the focus is on homogeneous boundary conditions, finite-difference methods with non-homogeneous mixed boundary conditions are also developed. To show the potential of the methods developed, in terms of CPU time, a comparison is made with the Crank–Nicolson method. [Copyright &y& Elsevier]

This paper deals with the approximation properties of the derivatives of rational cubic interpolation with a linear denominator. Error expressions of the derivatives of interpolating functions are derived, convergence is established and the optimal error coefficient c i is proved to be symmetric about the parameters of the rational interpolation. The unified integral form of the error of the second derivative in all subintervals is obtained. A simple expression of the jump of the second derivative at the knots and the conditions for the interpolating function to be C 2 in the interpolating interval are given. [ABSTRACT FROM AUTHOR]

Two finite-difference methods, which differ only in the way that they approximate the derivative boundary conditions, are developed for solving a particular form of the complex Ginzburg-Landau equation of superconductivity. The non-linear term in this equation is linearized in a way familiar to readers of Professor Mickens' work, and the numerical solution is obtained at each time step by solving a linear algebraic system. Consistency and stability are discussed and some numerical results are reported. [ABSTRACT FROM AUTHOR]

Finite-difference methods of orders six and eight are presented for second-order, non-linear, boundary-value problems. Both methods are economical in the sense that they use few function evaluations at interior grid points. The implementation of the methods is straightforward. The convergence of the methods is discussed. Numerical examples are considered to demonstrate computationally their order of convergence. [Copyright &y& Elsevier]