AN APPROXIMATE ANALYTICAL SOLUTION OF BEAM VIBRATIONS DURING AXIAL MOTION

An approximate analytical solution for the transverse vibrations of a beam during axial deployment is derived. The approach relies on removi ng the time dependency from the boundary conditions, and transferring it to the differential equation. The resulting partial differential eq uation with time-dependent coefficients is solved by employing the cla ssical method of separation of variables and the method of multiple sc ales. The approximate analytical solution is obtained for axially movi ng beams with different end conditions, at constant deployment rates. Except for those assumptions associated with slow axial movement and E uler's beam theory, no further assumptions were necessary. To verify t he validity of the approximate analytical solution, comparisons with a vailable numerical solutions are presented. Some numerical results wer e presented for axially moving beams with moving end supports. (C) 199 6 Academic Press Limited