Equivalent modeling of IPMCs based on beam theories

1 Equivalent modeling of IPMCs based on beam theories 

One way to present a gray box model of IPMC is to use an equivalent beam and an equivalent bimorph beam model and combine them with important physical properties of IPMCs Young s modulus and electromechanical coupling coefficient, determined from the rule of mixture bi- 

With this relationship, a cantilever-beam model (see Fig. 2.37 (a)) with the free-body diagram (see Fig. 2.37 (b)) can be developed. The reaction 

To improve the modeling accuracy, the equivalent bimorph beam model of IPMC, as shown in Fig. 2.38, was developed. It assumes that IPMC has two virtual layers that have the same thickness, and under an imposed electric field, the upper and the lower layers expand or contract, opposing each other. Generally, blocking force and displacement calculations of a bimorph cantilevered beam assume outer layers and an elastic layer between [Wang et al. (1999)]. Here, however, no elastic layer is assumed. Then the relationship between input voltage, V, and induced tip displacement, s, can be written as [Wang et al. (1999)]  

This provides us the electro-mechanical coupling coefficient d for the measured tip displacement (F = 0 in Fig. 2.36)  

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