Dynamics of 3D Timoshenko gyroelastic beams with large attitude changes for the gyros

• A 3D Timoshenko beam with a continuous distribution of gyros (gyricity) is considered.
• Large attitude changes for the gyros are taken into account.
• Both bending and torsional deformations of the beam are taken into account.
• Numerical examples illustrate the modal and dynamic behavior of the gyroelastic.
• It is shown how the gyricity can be used to recover the gyroelastic beam from a resonance situation.

This work is concerned with the theoretical development of dynamic equations for undamped gyroelastic beams which are dynamic systems with continuous inertia, elasticity, and gyricity. Assuming unrestricted or large attitude changes for the axes of the gyros and utilizing generalized Hooke׳s law, Duleau torsion theory, and Timoshenko bending theory, the energy expressions and equations of motion for the gyroelastic beams in three-dimensional space are derived. The so-obtained comprehensive gyroelastic beam model is compared against earlier gyroelastic beam models developed using Euler–Bernoulli beam models and is used to study the dynamics of gyroelastic beams through numerical examples. It is shown that there are significant differences between the developed unrestricted Timoshenko gyroelastic beam model and the previously derived zero-order restricted Euler–Bernoulli gyroelastic beam models. These differences are more pronounced in the short beam and transverse gyricity cases.