Introduction

The piezoelectric smart materials and structural systems with highly integrated sensors and actuators have led to a revolution in control of complex flexible structures such as aerospace, automobile, civil structures etc. The smart materials technology can be applied most efficiently in highly flexible systems. Such structures, when subjected to compressive loads, are susceptible to form failure.

Form failure may be triggered due to imperfections caused by either geometry of the structure or loads on the structure. Euler determined the critical load for form failure on a perfect strut by applying a perturbation to it. The method does not predict the lateral deformation of the strut when the load is applied axially. In practice, however, the struts are not perfect and they must have a finite deformation for varying axial loads. This problem can be alleviated in the imperfection approach. In this approach, an initially imperfect strut is used in determining its load deflection diagram. In this paper, the solutions for actuation and active control of thin steel sheet struts with initial geometric imperfections under the externally applied axial compressive load are discussed. In this method, the load deflection curve asymptotically approaches the secondary path of elastic buckling (Euler critical load). In a feedback control system it is essential to know its deformed shape for various levels of loads. By applying appropriate remedial voltage it is possible to prevent the form failure of the imperfect strut beyond the Euler buckling load.

Most investigations, however, attempted to find out the critical buckling load for piezolaminated struts. Previous researchers observed that the buckling of a flexible beam can be postponed beyond the first critical load by means of a feedback control using piezoelectric actuators and strain sensors. Optimal stabilization of column buckling and plate buckling were also attempted using micro-electro-mechanical systems (MEMS) and smart materials as sensors and actuators. Most of these investigations follow Eulerian method of finding the buckling loads and they do not predict prebuckling deformations in the struts. Although some investigators have discussed that the efficacy of the imperfection approach the method has remained unattempted in smart struts.

In this paper, the exact solutions for the stability control of piezolaminated struts are discussed. The imperfection approach, that is hitherto not applied by the previous investigators is discussed here. A simply supported perfect steel strut made of PVDF bimorph is subjected to actuation along with axial compressive loads. The lateral deflection of the strut is calculated. The remedial actuation is applied based on a feedback control system. The control formulation for a thin steel plate like strut with fully surface bonded PVDF layers under axial static and dynamic loading is presented. The results have been compared with that of the nonlinear finite element analysis.

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