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27 April 2007 A simple model for the prediction of the discrete stiffness states of a homogeneous electrostatically tunable multi-layer beam
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The adaptive modification of the mechanical properties of structures has been described as a key to a number of new or enhanced technologies, ranging from prosthetics to aerospace applications. Previous work reported the electrostatic tuning of the bending stiffness of simple sandwich structures by modifying the shear stress transfer parameters at the interface between faces and the compliant core of the sandwich. For this purpose, the choice of a sandwich structure presented considerable experimental advantages, such as the ability to obtain a large increase in stiffness by activating just two interfaces between the faces and the core of the beam. The hypothesis the development of structures with tunable bending stiffness is based on, is that by applying a normal stress at the interface between two layers of a multi-layer structure it is possible to transfer shear stresses from one layer to the other by means of adhesion or friction forces. The normal stresses needed to generate adhesion or friction can be generated by an electrostatic field across a dielectric layer interposed between the layers of a structure. The shear stress in the cross section of the structure (e.g. a beam) subjected to bending forces is transferred in full, if sufficiently large normal stresses and an adequate friction coefficient at the interface are given. Considering beams with a homogeneous cross-section, in which all layers are made of the same material and have the same width, eliminates the need to consider parameters such as the shear modulus of the material and the shear stiffness of the core, thus making the modelling work easier and the results more readily understood. The goal of the present work is to describe a numerical model of a homogeneous multi-layer beam. The model is validated against analytical solutions for the extreme cases of interaction at the interface (no friction and a high level of friction allowing for full shear stress transfer). The obtained model is used to better understand the processes taking place at the interfaces between layers, demonstrate the existence of discrete stiffness states and to find guidance for the selection of suitable dielectric layers for the generation of the electrostatic normal stresses needed for the shear stress transfer at the interface.
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A. Bergamini, R. Christen, and M. Motavalli "A simple model for the prediction of the discrete stiffness states of a homogeneous electrostatically tunable multi-layer beam", Proc. SPIE 6525, Active and Passive Smart Structures and Integrated Systems 2007, 652514 (27 April 2007);

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