s-d _ H. 

 d 1 - //. 



where //• = t^HjH. Compatibility of the cable displacement requires, in addition, that 



(B2) 



(1 - H.y = ^ (2//. - //.2) 

 24 



where 



mgl 

 H 



2 



/ 



- = 64 



d 



I 



2 



/ 





HL, 





HL, 







EA 









EA 



(B3) 



(B4) 



and 



Jo 



1 + 



3/2 



1 + 



(B5) 



dx = / 



The quantity EA is the product of the elastic modulus and the cross-sectional area of the cable while L^ 

 is the stretched cable length to the order of the linear theory approximation. According to Irvine and 

 Caughey the dimensionless variable X^ is the fundamental parameter of the extensible cable because it 

 accounts for both the elasticity and equilibrium geometry of the cable. In the subsequent notation H 

 will be taken to mean the horizontal component of tension in the extensible profile, i.e. the measured 

 tension. 



In the study of natural vibrations, the equations of motion can be linearized about the equilibrium 

 configuration and then the out-of-plane motions are decoupled to first order. The remaining in-plane 

 modes then fall into two classes. In the first class there are no first-order tension fluctuations induced 

 at the supports, whereas the second class induces first-order tension fluctuations. The two cases are 

 characterized respectively by mode shape symmetry and antisymmetry about the cable midpoint. The 

 antisymmetric motions of the sagging cable have the same frequency equation as the taut string, but 

 the symmetric modes obey a diff"erent eigenvalue equation. This means that the classical equation for a 

 taut cable is valid for < s// < 1:8 if n is even, whereas the symmetric mode frequencies are given by 



3 



tan 



^§i_ A_ 



(B6) 



124 



