Vibrations of continuous systems with a general operator notation suitable for perturbative calculations
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2001
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Abstract
The operator notation previously developed to analyze vibrations of continuous systems has been further generalized to model a system with an arbitrary number of coupled differential equations. Linear parts of the equations are expressed with an arbitrary linear differential and/or integral operators, and non-linear parts are expressed with arbitrary quadratic and cubic operators. Equations of motion are solved in their general form using the method of multiple scales, a perturbation technique. The case of primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations is considered. The algorithm developed is applied to a non-linear cable vibration problem having small sag-to-span ratios. © 2001 Academic Press.