Nonlinear light-induced vibration behavior of liquid crystal elastomer beam

Abstract

Recent studies have shown the coupling of optical and mechanical energy in a class of liquid crystal elastomers that contain light-sensitive molecules. As shown experimentally in the literature, these materials can undergo large, reversible elastic deformation under light illumination, and therefore geometric nonlinearity effects can be significant. In this paper, we present a large deflection model for the light-induced bending vibration of a liquid crystal elastomer beam. In this regard, the von Karman's nonlinear strain–displacement relationship is used to account for the large deflection of the beam. The effect of light on the liquid crystal elastomer beam is modeled as an inhomogeneous and time-dependent light-induced contraction strain and the dynamic equations of the beam are derived using the Hamilton's principle. Finite element formulation is developed to analyze the nonlinear dynamic response of the beam under uniform light illuminations. In addition, numerical results are presented and effects of different physical and geometrical parameters, including light intensity, light source position, contraction coefficient, and the thickness of the beam on the vibration characteristics of the beam are investigated. The model developed in this paper can be used to design liquid crystal elastomer based structures such as optically sensors, photo-mechanical energy harvesters, or other reversible opto-mechanically active structures.