Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams. (27th June 2018)

• Record Type: Journal Article
• Authors: Martin, Blake; Salehian, Armaghan
• Other Names: Vanali Marcello Academic Editor.
• Is Part Of: Shock and vibration. Volume 2018(2018)
• Publication Date: 2018-06-27
• Subjects: Shock (Mechanics) -- Periodicals; Vibration -- Periodicals; 534.5
• DOI: 10.1155/2018/4627865
• Languages: English
• ISSNs: 1070-9622

Abstract

Abstract : The Lindstedt-Poincaré method is applied to a nonuniform Euler-Bernoulli beam model for the free transverse vibrations of the system. The nonuniformities in the system include spatially varying and piecewise continuous bending stiffness and mass per unit length. The expression for the natural frequencies is obtained up to second-order and the expression for the mode shapes is obtained up to first-order. The explicit dependence of the natural frequencies and mode shapes on reference values for the bending stiffness and the mass per unit length of the system is determined. Multiple methods for choosing these reference values are presented and are compared using numerical examples.