Dynamic Behaviour under Moving Distributed Masses of Nonuniform Rayleigh Beam with General Boundary Conditions. (23rd March 2014)

• Record Type: Journal Article
• Authors: Andi, Emem Ayankop; Oni, Sunday Tunbosun
• Other Names: Sun B. Academic Editor.; Sun J. Academic Editor.
• Is Part Of: Chinese journal of mathematics. Volume 2014(2014)
• Publication Date: 2014-03-23
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals
• DOI: 10.1155/2014/565826
• Languages: English
• ISSNs: 2314-8071

Abstract

Abstract : This paper investigates the flexural vibration of a finite nonuniform Rayleigh beam resting on an elastic foundation and under travelling distributed loads. For the solution of this problem, in the first instance, the generalized Galerkin method was used. The resulting Galerkin's equations were then simplified using the modified asymptotic method of Struble. The simplified second-order ordinary differential equation was then solved using the method of integral transformation. The closed form solution obtained was analyzed and results show that, an increase in the values of foundation moduliK and rotatory inertia correction factorR 0 reduces the response amplitudes of both the clamped-clamped nonuniform Rayleigh beam and the clamped-free nonuniform Rayleigh beam. Also for the same natural frequency, the critical speed for the moving distributed mass problem is smaller than that for the moving distributed force problem. Hence resonance is reached earlier in the former. Furthermore, resonance conditions for the dynamical system are attained significantly by bothR 0 andK for the illustrative end conditions considered.