Free vibration analysis of straight thin-walled box beams including thickness warping effect

The equations of motion for a straight thin-walled rectangular box beam consisting of four plates are derived. The contour warping and the thickness warping of cross-section of the box beam are accounted for. An analytical method is presented to examine the free vibration of the box beam. Further, the shape functions of one stripe of the box beam are presented to implement the finite stripe computation. The orthogonality of any two distinct sets of mode shape functions is derived. The geometric effects of the box beam on the modal frequencies of the structure are investigated. The modal frequencies of the box beam obtained from the finite stripe computation are compared with those of analytical solutions.