Statics of Shallow Inclined Elastic Cables under General Vertical Loads: A Perturbation Approach

Abstract

Abstract:The static problem for elastic shallow cables suspended at points at different levels under general vertical loads is addressed. The cases of both suspended and taut cables are considered. The funicular equation and the compatibility condition, well known in literature, are here shortly re-derived, and the commonly accepted simplified hypotheses are recalled. Furthermore, with the aim of obtaining simple asymptotic expressions with a desired degree of accuracy, a perturbation method is designed, using the taut string solution as the generator system. The method is able to solve the static problem for any distributions of vertical loads and shows that the usual, simplified analysis is just the first step of the perturbation procedure proposed here.

A Multi-Parameter Perturbation Solution for Functionally Graded Piezoelectric Cantilever Beams under Combined Loads

“…Finally, it should be noted here that in our multi-parameter perturbation method, the parameters are not dependent on each other, thus leading to a large number of independent perturbation equations. However, in the literature, there exists an alternative and much more efficient method [ 38 , 39 , 40 , 41 , 42 ], in which all the parameters (irrespective of their number) are perturbed together along straight lines in the parameter space, thus formally re-conducting the multi-parameter case to that of a single parameter. At the end of the procedure, however, the parameters can be varied independently, since the exploring straight line can be freely chosen.…”

Identification of Cable Tension Through Physical Models and Non-Contact Measurements

“…Perturbation methods are powerful asymptotic techniques that are widely used in a large variety of scientific research fields, ranging from direct problems concerning linear and nonlinear dynamics, stability and bifurcation [42][43][44][45] to inverse problems dealing with modal identification, optimal spectral design, damping and damage detection [46][47][48][49][50][51]. Perturbation methods are also classical and well-established strategies to study different problems in cable mechanics, including static behaviors [52,53], linear and nonlinear dynamic phenomena [2,3,[54][55][56][57], aerodynamic instabilities [58][59][60], active vibration control [61,62].…”

A Continuum Approach to the Nonlinear In-Plane Galloping of Shallow Flexible Cables

“…Under self-weight, the cable hangs on points and in the vertical plane, spanned by the unit vectors (a , a ), and occupies the equilibrium configuration shown in thin line in Figure 1. Possible evaluation of the equilibrium configuration via perturbation methods is discussed in [15,16]. An orthogonal uniform wind U = a is assumed to flow, which causes the cable to reach an unknown current configuration, shown in thick line in Figure 1.…”