Control of Cantilever Vibration via Structural Tailoring and Adaptive Materials

Abstract

A dual approach integrating structural tailoring and adaptive materials technology and designed to control the dynamic response of cantilever beams subjected to external excitations is presented. Whereas structural tailor- ing uses the anisotropy properties of advanced composite materials, adaptive materials technology exploits the actuating capabilities of piezoelectric materials bonded or embedded into the host structure. A control law relat- ing the piezoelectrically induced boundary bending moment with the velocity at given points of the structure is implemented and its effect on the closed-loop frequencies and dynamic response to harmonic excitations is inves- tigated. The combination of structural tailoring and control by means of adaptive materials proves very effective in damping out vibration. I. Introduction A Sthe requirements for higherexibility on high-speed aircraft increase, so do the challenges of developing innovative de- sign solutions. Whereas the increasedexibility is likely to provide enhanced aerodynamic performance, the aircraft also must be able to ful® ll a multitude of missions in complex environmental condi- tions and to feature an expanded operational envelope and longer operational life. To achieve such ambitious goals- advanced con- cepts resulting in the enhancement of static and dynamic response of the multimission- highlyexible aircraft must be developed and implemented. One way of achieving such goals consists of the in- tegration of advanced composite materials in the aircraft structure. 1 In this regard, the directionality property featured by anisotropic composite materials is capable of providing the desired elastic cou- plings through the proper selection of the ply angle. However, such a technique is passive in nature in the sense that, once the design is in place, the structure cannot respond to the variety of conditions in which it must operate. The situation can be mitigated by incorporating into the host structure adaptive materials able to respond actively to changing conditions. In a structure with adaptive capabilities, the natural fre- quencies, damping, and mode shapes can be tuned to reduce the vibration so as to avoid structural resonance andutter instability, and in general toenhance the dynamic response characteristics.The adaptivecapabilityisachievedthroughtheconversepiezoelectricef- fect,whichconsistsofthegenerationoflocalized strainsinresponse to an applied voltage. This induced strain ® eld produces, in turn, a change in the dynamic response characteristics of the structure. It is proposedheretoenhancethefreevibrationanddynamicresponseto externalexcitationsofwing structures by incorporating theadaptive capabilityreferredtoasinduced strain actuationinconjunctionwith structural tailoring. Under consideration is a cantilevered aircraft wing, modeled as a thin/thick-walled closed cross-section beam of anisotropic material. Implementation of a control law relating the applied electric ® eld to one of the mechanical quantities charac- terizing the response of the wing according to a prescribed func- tional relationship results in eigenvalue/boundary-value problems. The solution consists of closed-loop eigenvalues/dynamic response characteristics, which are functions of the applied voltage, i.e., of the feedback control gain. Investigation of static and dynamic control of aircraft wing structures via the simultaneous implementation of induced strain