On the flexural vibrations of arms with variable length. An exact solution

Energetics and Invariants of Axially Deploying Beam with Uniform Velocity

“…Kalaycioglu and Misra [9] presented approximate analytical solutions and numerical solutions for beamtype appendage deployment and tethered system deployment and verified the accuracy of the approximate method. Bergamaschi and Sinopoli [10] used the Wentzel-Kramers-Brillouin theory to obtain the analytical solutions of the deploying beam, while the gyroscopic term was neglected. Another approximate analytical procedure, the method of multiple scales, was used to study the transient dynamics of deploying and retreating beams by AlBedoor and Khulief [11].…”

Transverse Vibrations of a Flexible Beam Sliding Through a Prismatic Joint

“…They considered the beam in¯exure, derived the equations of motion using Newton's law and presented certain properties of the mode shapes. In the following studies reported in the literature, some researchers have searched for direct analytical solutions for this vibration problem, like Bergamaschi and Sinopoli [2], while most of them have used approximate methods [3±27].…”