Limitations of Using Membrane Theory for Modeling PVDF Patches on Inflatable Structures

Abstract

An underlying goal in structural modeling is to use the simplest mathematics possible that captures the physics of a problem accurately. Inflatable structures are normally fabricated from thin films, so they are often modeled as membranes, i.e., structural elements that cannot resist bending moments. Researchers have recently been looking at active control of inflated structures, so this raises the question of whether membrane theory can account for the effects of surface-mounted piezopolymer patches used as either sensors or actuators. This work discusses these effects on the dynamic behavior of a flat, rectangular coupon section and assesses the patch’s ability to sense and actuate transverse deflections of the thin film substrate using traditional membrane theory. The Rayleigh-Ritz method was employed to approximate the natural frequencies and mode shapes of this layered system. While including the additional mass of the patch, traditional membrane theory was unable to account for the added stiffness of the patch layer. When the piezoelectric behavior of the patch was considered, membrane theory failed to model the PVDF as a useful sensor. Also, excitation of transverse vibrations was not possible using membrane theory, which does not allow application of bending moments. However, PVDF actuation was modeled as an applied in-plane force, which allowed the patch the ability to suppress out-of-plane disturbances by altering the tension in the base layer as a function of applied voltage. This article discusses the limitations associated with using traditional membrane theory to analyze the dynamic behavior of thin-layered systems as well as model the interaction between an active PVDF patch and the torus substrate.

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