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A new computational scheme using Chebyshev polynomials is proposed for the numerical solution of parametrically excited nonlinear systems. The state vector and the periodic coefficients are expanded in Chebyshev polynomials and an integral equation suitable for a Picard-type iteration is formulated. A Chebyshev collocation is applied to the integral with(More)
The paper deals with an approximate analysis of non-linear, non-stationary vibrational systems with multiple degrees of freedom subjected to a pulse excitation. The non-stationary system parameters, which may include masses, restoring forces or damping, are considered to be slowly varying functions of time. A general procedure for obtaining the first order(More)
Chebyshev polynomials are utilized to obtain solutions of a set of pth order linear differential equations with periodic coefficients. For this purpose, the operational matrix of differentiation associated with the shifted Chebyshev polynomials of the first kind is derived. Utilizing the properties of this matrix, the solution of a system of differential(More)
The study involves an approximate analysis of non-linear, non-stationary vibrational systems subjected to an arbitrary pulse excitation. The non-stationary system parameters, which may include masses, restoring forces, material properties or damping, are considered to be slowly varying functions of time. A general procedure for obtaining the first and the(More)
The paper deals with an approximate method of stability analysis for second order linear systems with p<;riodiQcoefficients. The periodic functions are approximated during the first period of motion by a constant, a linear or a quadratic function of time such that the resulting approximate equations have known closed form solutions. The approximate(More)
Some new techniques for reduced order (macro) modeling of nonlinear systems with time periodic coefficients are discussed in this paper. The dynamical evolution equations are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the new set of equations become time-invariant. The techniques presented here reduce the order(More)
A symbolic computational technique is used to study the secondary bifurcations of a para-metrically excited simple pendulum as an explicit function of the periodic parameter. This is made possible by the recent development of an algorithm which approximates the fundamental solution matrix of linear time-periodic systems in terms of system parameters in(More)