Predicting the vibrations of a spinning inflated membrane
Abstract
The primary difficulty of computing the vibration of spinning inflated membranes arises from the low natural frequencies of such systems. When such systems are rotated near their own natural frequencies the dynamics equations must account for higher order kinematics than is necessary for more rigid structures. These complications results from the membrane loads that develop within the bodies in reaction to the accelerations of the overall body. When second order kinematics act against these membrane loads, the resulting energies become of the same order as the potential and kinetic energies of the vibrations that would be calculated by first order kinematics. These complications apply to the problem addressed here. We consider a spinstabilized, inflated membrane, spinning around its minor axis. This structure is very flexible and somewhat viscoelastic, so vibrations excited by the overall motion of the structure will dissipate energy of the system, thus, reducing the kinetic energy. A reduction in kinetic energy consistent with a conservation of angular momentum results in coning and, eventually, tumbling. Here we must address the excitation of vibration by the rigidbody motion and then we must address the retarding effect of the energy dissipation on the rigidbody motion.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1993
 Bibcode:
 1993STIN...9414456S
 Keywords:

 Angular Momentum;
 Conical Bodies;
 Energy Dissipation;
 Grid Generation (Mathematics);
 Membranes;
 Oscillations;
 Potential Energy;
 Prediction Analysis Techniques;
 Resonant Frequencies;
 Rigid Structures;
 Tumbling Motion;
 Vibration;
 Viscoelasticity;
 Conservation;
 Excitation;
 Kinematics;
 Kinetic Energy;
 Loads (Forces);
 Low Frequencies;
 Rotation;
 Structural Mechanics