Dynamic Behaviour under Moving Distributed Masses of Nonuniform Rayleigh Beam with General Boundary Conditions

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 moduli K and rotatory inertia correction factor R0 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 R0 and K for the illustrative end conditions considered.

Influence of a Moving Mass on the Dynamic Behaviour of Viscoelastically Connected Prismatic Double-Rayleigh Beam System Having Arbitrary End Supports

“…Furthermore, it is still difficult to obtain an exact analytical solution to (28) and (29). Hence, one resorts to using an approximate analytical technique [1] which is a modification of the asymptotic method due to Struble [1,3]. This analytic technique involves obtaining a modified frequency (I) of the system due to the presence of the effect of rotatory inertia so that each of the differential operators in (28) and 29is replaced by an equivalent operator defined by the modified frequency.…”

“…otherwise, it is zero. Note that the Dirac delta function is an even function; therefore, it is expressed as a Fourier cosine series and we have [1,3] (…”

“…The problem of determining the dynamic response of elastic structures traversed by moving loads is of significant technological importance and various researchers (Engineers, Physicists, and Applied Mathematicians) continue to pay considerable attention to studying the various corresponding mathematical models [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Most of these studies have been carried out for simpler structures such as beams, plates, frames, and shells since such elastic structures form the fundamental components of various modern complex structures and the mathematical analysis involved is relatively less complicated.…”

“…For instance, the trolleys of overhead travelling cranes which move on their girders, as well as bridges on which trains or vehicles move, may be modeled as moving loads on beam [5]. The theory of vibration of single-beam or single-plate system subjected to moving loads with different boundary conditions has been extensively developed with hundreds of articles on it [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Frýba [2], in particular, gave a comprehensive survey of some of the techniques for solving various versions of this problem.…”

Behavioral Study of Finite Beam Resting on Elastic Foundation and Subjected to Travelling Distributed Masses

“…More recently, [Andi (2013), Ogunyebi (2006), Andi and Oni (2014)] carried out dynamical analysis of structural members carrying uniform partially distributed masses with general boundary conditions under travelling distributed loads. In these studies, versatile analytical techniques were used to obtain solutions valid for all variants of classical boundary conditions.…”