Dynamic modeling of taut strings carrying a traveling mass

Abstract

In this paper, a new consistent dynamic model is proposed, aimed at studying linear vibrations induced in an elastic wire by a bilaterally constrained single mass moving with a constant velocity. Starting from a variational formulation, through the Hadamard’s condition, a corrective term to the local linear stiffness is determined in the continuum model as a function of the moving mass velocity; in this way, the boundary conditions are properly found. The representation of the solutions of the hyperbolic equations governing the motion of the wire presents some difficulties, which are solved by means of a suitable coordinate transformation in a time-invariant domain and a judicious choice of the set of shape functions, to be used in the discrete formulation of the problem. This new description allows an easy estimation of high-order deformations that are neglected by a purely linear approach. When the mass velocity is sufficiently high, displacements near the supports show high gradients: in these cases, it is necessary to use an unknown velocity or introduce an advanced mechanical model in order to correctly describe the motion of the mass. Numerical examples confirm the stability of the proposed solution in all conditions examined

Constitutive models for strongly curved beams in the frame of isogeometric analysis

“…Furthermore, the variational techniques presented in [56], being adapted to dissipative phenomena, may be used in this context. Finally, it seems attractive for the application of higher continuum models such as those described in [57][58][59][60]; damage detection referring to the procedure proposed by [61,62] which considers traveling loads as signals or in identification problems such as those described in [63][64][65][66]; the extension to plasticity for evaluating collapse load, see for example [67][68][69][70][71][72], or to piezoelectric materials, see [73,74], in the framework of structural control. The closed-form solution for load cases LC1 (bending couple, W) and LC2 (vertical force, P) are given in [33].…”

Sardinia radio telescope finite element model updating by means of photogrammetric measurements

“…• damage detection is an emerging and very important field which deserves attention; some examples consider travelling loads as signals [66,67] or identification problems [68][69][70][71]; • extension to plasticity, with the aim to evaluate the collapse load [72][73][74][75][76][77]; also the variational techniques presented by dell'Isola et al [78] are interesting for dissipative phenomena; • smart materials, such as piezoelectric materials, might advantageously be used to improve the structural control [79][80][81].…”

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

“…Although a huge literature has been developed in the field, many open problems seem to wait for a solution. We refer to [156] for an overview of some of them. Here, we limit ourselves to report some aspect of the involved phenomena which need to be more precisely modeled and more deeply understood: (i) the role of geometric nonlinearities in the string deformation, especially in the vicinity of the endpoint of the considered string, (ii) the effect of deformability of the constraints limiting the kinematics of the deformable string, (iii) the effect of the finite dimensions of the moving mass, and (iv) the role of material nonlinearities in the behavior of the deformable string.…”