%0 Journal Article
%T Dynamic Behaviour under Moving Distributed Masses of Nonuniform Rayleigh Beam with General Boundary Conditions
%A Emem Ayankop Andi
%A Sunday Tunbosun Oni
%J Chinese Journal of Mathematics
%D 2014
%R 10.1155/2014/565826
%X 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 moduli and rotatory inertia correction factor 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 both and for the illustrative end conditions considered. 1. Introduction This paper is sequel to an earlier one by Oni and Ayankop-Andi in [1] that considered the response of a simply supported nonuniform Rayleigh beam to travelling distributed loads. In particular, this paper is a generalization of the theory advanced in [1]. For more than a century, the analysis of continuous elastic system subjected to moving systems has been the subject of interest in many fields, from structural to mechanical to aerospace engineering. Various structures ranging from bridges and roads to space vehicles and submarines are constantly acted upon by moving masses and hence the problem of analyzing the dynamic response of these structures under the action of moving masses continues to motivate a variety of investigations. In most of the studies available in literature, such as the works of Sadiku and Leipholz in [2], Oni in [3], Gbadeyan and Oni in [4], Huang and Thambiratnam in [5], Lee and Ng in [6], Adams in [7], Chen and Li in [8], Savin in [9], Rao in [10], Shadnam et al. in [11], and Oni and Awodola in [12], the scope has been restricted to structural members having uniform cross-section whether the inertia of the moving load is considered or not and the load modelled as moving concentrated load. In practice, cross-sections of elastic structures such as plates and beams are not usually uniform and the moving loads are commonly in distributed forms. To this end, in [13] an attempt was made on the studies concerning
%U http://www.hindawi.com/journals/cjm/2014/565826/