Unified Finite Difference Formulation for Free Vibration of Cables

Control of dynamic stability of stays using passive viscous dampers

“…Natural frequencies of cables Natural frequencies of cables have been evaluated with Mehrabi and Tabatabai formula [3] as reported in a companion paper [4]. Table I summarizes these results, together with cable inclination (), cable chord length (L), cable sag at midpoint (f), cable diameter (D) and cable tension at the dead load configuration (T).…”

Dynamic testing of cable structures

“…For these cases, specific formulae based on simplified analytical solutions have been used [8][9][10][11], as well as numerical formulations allowing the identification of various cable parameters from the measurement of sets of natural frequencies and from particular assumptions respecting the boundary conditions [12][13][14]. Considering applications in low sagged cables, typical from long span cable-stayed bridges, it is relevant to cite the simplified formulae derived by Mehrabi and Tabatabai [10]. Accordingly, the i th order natural frequency of a cable n f is given by…”

“…The formulae derived in [10] include simultaneously sag and bending stiffness effects and are most accurate for cables with a ζ value no less than 50 and with an Irvine parameter 2 λ of less than 3.1. Mehrabi and Tabatabai refer that these restrictions are covered by 95% of the stay cables from cable-stayed bridges around the world.…”

Application of Radar Technology to Deflection Measurement and Dynamic Testing of Bridges

“…For the tension members that deviate from a taut string, still the cable forces can be predicted by using the identified natural frequencies with reference to more advanced formulations (accounting for the effects of both the sag and the bending stiffness on the dynamic behaviour of cables, see e.g. Casas 1994, Mehrabi & Tabatabai 1998. Subsequently, the knowledge of cable forces is used to check the correct distribution of the internal forces in the bridge at the end of construction, while monitoring the possible changes in stay cable forces over time may provide an efficient method for Structural Health Monitoring.…”