Abstract
IN THIS PAPER, A THEORY OF SINGLE SAGGING PLANER WEIGHTLESS ELASTO-FLEXIBLE 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 CONTRAGRADIENT 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 ÂFREEÂ VIBRATION OF THE SYSTEM PERTURBED FROM ITS EQUILIBRIUM STATE IS IDENTIFIED. SIGNIFICANCE OF THE PROPOSED THEORY OF WEIGHTLESS SAGGING ELASTO-FLEXIBLE CABLES IS DISCUSSED.
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