Abstract
Proposed space missions involve large structures which must maintain precise dimensional tolerances during dynamic maneuvers. In order to attenuate disturbances in the many modes of vibration of such structures, active and passive vibration control has been proposed. Passive control is to be achieved by placing viscous or viscoelastic members in a structure to absorb energy, while active control similarly could involve structural members (struts) capable of sensing axial displacement and exerting axial control force.
With conventional modal analysis, the effect of a control element on a system is computed by summing its influence on many immutable modes. Since changes in mode shape must be described by this summation, truncation of higher modes results in inaccuracies.
The compliant model of vibration to be presented accurately accounts for the effects of locally-acting control elements without inclusion of high-frequency modes. The motion of each spring-mass system representing a structural mode is modified by a control element in series with another stiffness inherent to the structure for that mode and control position. In order to predict the influence of several control elements or dampers on closely-spaced modes, the compliant models for those modes are integrated into a spherical model in which one lumped mass is acted upon by orthogonal modal stiffnesses. In the spherical model, control elements influent the lumped mass from orientations determined by mode participation factors. The resulting equations of motion are stated in standard state-space form.
To test accuracy, the compliant model is used to predict eigenvalue shifts due to springs and dampers acting upon an axially-vibrating rod, and the spherical model is used to predict damping accurately in a lumped-mass system with closely-spaced modes.
Passive control of flow structure interaction between a sphere and free-surface
