Flight Vibration Optimization via Conformal Mapping

Abstract

An analytical spproach based on the principle of conformal transformations is presented for evaluating the effects of structural dynamic changes on flight vibrations. Structural dynamic changes are characterized by discrete and multidimensional impedance adjustments. Discrete impedance changes such as point mass, colinear stiffness, and dynamic absorbers are emphasized to illustrate the ~rarlical as~erts of the a~~r o a c h for flight. .vibrstion optimization. Conformal mapping, through inspections of complex-plane response circles, offers the capability for rapid evaluation of discrete impedance change effects on flight vibrations. The operational equations require only baseline vibration data and Impedance change dynamics. Specific criteria for reducing vibrations are established using the response circle equations. In addition, the required impedance change to achieve minimum or zero vibration is uniquely defined. Flight vibration optimization is illustrated using a remote absarbcr in conjunction with AH-IG helicopter ground and flight vibration measurements. Vibration reduction and absorber performance are assessed at several flight conditions and airframe stations.