M. Mukhopadhyay et Ah. Sheikh, LARGE-AMPLITUDE VIBRATION OF HORIZONTALLY CURVED BEAMS - A FINITE-ELEMENT APPROACH, Journal of sound and vibration, 180(2), 1995, pp. 239-251
Large amplitude free flexural vibrations of horizontally circular curv
ed beams have been investigated for the first time. Numerical solution
s have been obtained by the finite element method. A three-noded horiz
ontally curved isoparametric beam element has been chosen for this pur
pose. A non-linear stiffness matrix has resulted due to bending-membra
ne coupling. The non-linear eigenvalue problem has been solved by the
direct iteration technique. As no existing results are available for t
he problem at hand, large amplitude frequencies obtained for curved be
ams having large radius and small included angle are first compared wi
th straight beams for varying parameters having different support cond
itions. A large number of results for the non-linear frequencies of ho
rizontally curved beams having varying included angles, radii, amplitu
de ratios and support conditions have been evaluated.