Dynamic Behavior of a Moving Belt Supported on Elastic Foundation

Abstract

The dynamic behavior of a belt moving on an elastic foundation and supported on two pulleys at the ends is investigated. The problem is formulated to include the nonlinear terms arising from large amplitude oscillations as well as material damping and the variation in tension along the belt. The differential equation of motion is solved employing numerical techniques, and the spatial response variations with time are presented graphically for different belt velocities. These results indicate that in the absence of damping, the system is unstable for any belt velocity larger than the wave velocity in the belt material. The results are useful in investigating the stability of large continuous conveyor systems supported on elastic foundations.

The vibration and stability of a friction-guided, translating string

“…where the constitutive relation R = EA W,, and equations (4) and (5) have been used and R2 is the prescribed downstream tension. With U(X, T) = U, for 0 < X < D and VCX, T) = U, for D < X < L, the equation of transverse motion (2) becomes:…”

“…The stability of a translating string is limited by a critical translation speed; above this speed a buckling instability occurs [2]. The critical speed remains unaltered when the translating string is coupled to subsystems that do not affect the system tension such as elastic guides [3,4] and elastic foundations [5,6]. Any distributed elastic foundation, however, renders the translating string model dispersive, and significant attenuation of vibration amplitudes is possible by the proper selection of the foundation stiffness and the translation speed [6].…”

Lateral Vibration of Two Axially Translating Beams Interconnected by a Winkler Foundation

“…Vibration of a translating string supported by an elastic foundation was studied by Bhat et al. [10], Perkins [11], Wickert [12] and Parker [13]. Bhat et al formulated the problem to include the non-linear deformation of the string arising from large amplitude oscillations, as well as the gyroscopic terms.…”

Vibrations of a continuous web on elastic supports

“…Arbitrary excitations and initial conditions were analyzed with the help of modal analysis and a Green's function method in (44). Travelling strings and beams on an elastic foundation have been investigated by, e.g., (9), (30), (43), and (29). Travelling viscoelastic beams with timedependent speed were recently considered by (11).…”