Theory of Weightless Sagging Elasto-Flexible Cables

Abstract

In this Paper, a theory of single sagging planer weightless elastoflexible cables is proposed. In reference to the instantaneous natural state, hypoelastic rate-type constitutive equations and third-order nonlinear differential equations of planer motion for massless cables with nodal masses are derived. New concepts like configurational complementary potential and contra-gradient principles are proposed. Typical dynamic response of these elastic cables with different sustained loads, axial rigidity and sag/span ratios is determined. Modal, subharmonic and internal resonances, jump and beat phenomena, etc., are predicted. A new mode of damping of 'free' vibration of the system perturbed from its equilibrium state is identified. Significance of the proposed theory of weightless sagging elasto-flexible cables is discussed.

Mechanics of Cable-Suspended Beams

“…The proposed theory involves rate-type constitutive equations and third order equations of motion. Pure and mixed configurational and elastic modes of vibration are predicted (Kumar et al, 2016a). These configurational and elastic vibration modes are shown to be predominantly associated with horizontal and vertical seismic excitations respectively (Kumar et al, 2015).…”

“…Based upon authors' theory of weightless sagging planar cables, a new Beam with Elasto-Flexible Support (BEFS) model is proposed for simulating the cable-deck interaction. Its main point of departure is the distinction between the elastic and configurational components of the suspension cable response (Kumar et al, 2016a). As discussed in Authors' earlier paper, the weightless elastic cables lack unique passive state but their equilibrium state under specified loads is unique.…”

“…Also, this natural state is identical with the equilibrium state of the corresponding inextensible cable. The nodal elastic displacements are measured relative to this natural state (Kumar et al, 2016a). In contrast to single sagging cables, the cable-suspended structures possess a unique natural passive state.…”

“…This description is based upon Authors' theory of weightless sagging planar cables (Kumar et al, 2016a). In its passive state, the cable configuration is defined by the coordinates of cable nodes Q , and R , assuming cable as inextensible.…”

Seismic Analysis of Sagging Elasto-flexible Cable using Placement Model

“…The dynamic response of such structures to harmonic nodal force is determined for different sustained nodal forces, axial elastic stiffness and sag/span ratios. Sub harmonic resonances, jump and beat phenomenon are predicted for elastic and inextensible cables [8]. In another approach the incremental equation of motion involving tangent stiffness matrix employed is equivalent to the third order equation of motion proposed [5].…”