Dynamic characteristics of statically determinate space-truss platforms

The geometry of a class of statically determinate platforms is developed and vibration frequencies determined. Such configurations allow shape control by changing the member lengths to be accomplished with small forces. An additional advantage of a statically determinate structure is that it is free of thermal stress under any temperature distribution. Frequency comparisons between statically determinate and more conventional redundant platforms are presented. Vibration of curved platforms that can be used as antenna concepts is also investigated. Alternative concepts incorporating the statically determinate design, but having improved dynamic characteristics, are suggested. Nomenclature D — width of platform E = Young's modulus of material / = frequency of vibration F = focal length of parabolic surface platform H = depth of platform J = number of joints in platform M = number of members in platform w = mass per unit length of member W = concentrated mass at a joint p =mass density of material