Static and dynamic analyses of free-hinged-hinged-hinged-free beam in non-homogeneous gravitational field: application to gravity gradiometry

Vibration control of a nonlinear cantilever beam operating in the 3D space

This paper addresses a control problem of a nonlinear cantilever beam with translating base in the three-dimensional space, wherein the coupled nonlinear dynamics of the transverse, lateral, and longitudinal vibrations of the beam and the base’s motions are considered. The control scheme employs two control inputs applied to the beam’s base to control the base’s position while simultaneously suppressing the beam’s transverse, lateral, and longitudinal vibrations. According to the Hamilton principle, a hybrid model describing the nonlinear coupling dynamics of the beam and the base is established: This model consists of three partial differential equations representing the beam’s dynamics and two ordinary differential equations representing the base’s dynamics. Subsequently, the control laws are designed to move the base to the desired position and attenuate the beam’s vibrations in all three directions. The asymptotic stability of the closed-loop system is proven via the Lyapunov method. Finally, the effectiveness of the designed control scheme is illustrated via the simulation results.

Acoustic and vibration isolation for a gravity gradiometer

Vibration in the audio frequency band affects the performance of rotating gravity gradiometers used for airborne mineral exploration. This is probably due to translation to rotation coupling inside the gradiometer platform. It was found that the DC gravity gradient signal was proportional to the square of the third time derivative of position, or jerk squared. The demanding airborne environment for such instrumentation demands a light weight broadband acoustic shield and vibration isolator. This paper presents the design principles for such an isolator, based on vibration isolated spherical shell structures. Performance data are presented as well as flight test data that demonstrated a 14% gravity gradient noise reduction compared with an unshielded instrument.