We propose the modeling of contactless switching of a bistable slender beam using Laplace force actuation. The model beam is based on the elastica approach which allows large amplitudes of the cross-section rotation and large elastic transformations. Furthermore, the extensibility of the elastic beam is accounted for and it plays a crucial role in the switching process. The study is devoted particularly to the actuation mechanism of the bistable beam uniformly loaded by a density of lineic force which is permanently perpendicular to the beam deformation. Such actuation can be produced by the Laplace force due to an electric current travelling along the beam placed in a magnetic induction. The mechanism of the bistable switching is analyzed in detail using a variational formulation and stable and unstable equilibria are described. We investigate numerically the post-buckling behavior to capture the exact buckling modes that follow the path in the unstable region. The numerical simulations are also used to obtain the bistable response in terms of actuating force (or electric current amplitude), beam end-shortening and mid-point displacement of the beam. We also perform a finite element computation and provide a validation of the results obtained by solving the set of equations of the boundary value problem. The second part of the work is focussed on the experimental validation of the switching mechanism of the bistable beam presented in the analytical part. We design an experimental setup for the fine measurement of the mid-point displacement of the bistable beam as a function of the electric current travelling the beam. The region of bistable instability is revealed by experimental adjustment of the bifurcation point associated with the actuating force. All the results extracted from experimental tests are compared to those coming from the modeling investigations, which ascertains with good accuracy the approach of the proposed model for bistable beam.

We report a study of an elastic buckled beam undergoing a contactless magnetic actuation of Laplace type. The beam model is based on the elastica beam theory including the beam extensibility. The Laplace force is produced by an electric current travelling along the beam placed in a magnetic induction. The magnitude of the electric current is the control parameter and by increasing the electric current the beam switches from one stable state to the other one for a given beam end-shortening. The main purpose of the study is to investigate the bistable response, more precisely, the diagram of the electric current as function of the midpoint vertical displacement of the beam according to the magnet location along the elastic beam. The model equations are established and they are numerically solved using an algorithm developed for nonlinear boundary value problem.A second part of the study is devoted to experimental validation of the model and comparisons with the results extracted from the numerical solutions to the model equations. Especially, the comparisons ascertain with good accuracy the approach of the proposed bistable beam model. In addition, the influence of the model parameters on the bistable response is clearly identified.

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