A modified pin force model for beams with active material bonded

• Neglect of the moment caused by pin force in actuator causes an overestimation of bending curvature.
• Neglect of the expansive or contract effect caused by pin force in substrate causes an overestimation of bending curvature.
• Pin-connect assumption can give a considerable prediction in most regions of active beam.
• Bending test of beams with macro fiber composite (MFC) bonded is well predicted by the proposed modified pin force model.

The Pin-Force Model (PFM) and the Enhanced Pin-Force Model (EPFM) for analyzing the mechanical behavior of a composite beam with active materials are widely used because of simplicity and adaptability. However, the PFM and the EPFM overestimated the deformation of composite beams under a small thickness ratio of substrate and actuator. In this paper, the reasons for the above phenomenon are analyzed first. Then a revised model named Modified Pin Force Model (MPFM) is proposed, which involves the factors neglected in previous models. The detailed derivation and description of the models for both unimorph and bimorph bonding forms are given. The bending curvature of a composite beam predicted by the MPFM is compared with that obtained by both the Euler-Bernoulli beam model and finite element analysis. The result shows a good consistency even in the small thickness ratio. Experiments based on MFC materials were performed to validate the MPFM. The results demonstrate that the proposed model can well predict the bending deformation of a composite beam with mounted actuators in the small thickness ratio, which extends the application range of pin-force models.

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