Nonlinear free and forced vibrations of a fiber-reinforced dielectric elastomer-based microbeam

This paper investigates the nonlinear free and forced vibrations of a fiber-reinforced dielectric elastomer-based microbeam using the Euler–Bernoulli beam theory. The nonlinear material properties have been taken into account based on the original Gent hyperelastic approach. Also, the generalized von Kármán theory is utilized for obtaining nonlinear strains. We assumed that the elastomeric microbeam is incompressible. The system's free energy fibrous component has been formulated using the Holzapfel-Gasser-Ogden model, which is appropriate to the two families of collagen fibers with the same mechanical properties. An electric part is connected to the system to aim to excite the microbeam considering two types of voltage: a DC (static) and a DC+AC (dynamic) voltage. Governing equations of motion have been derived using Hamilton's principle. Subsequently, the reduced-order vibration model of the fiber-reinforced microbeam has been obtained by using the Galerkin method. We have calculated the nonlinear natural frequencies (free vibration) via the Hamiltonian scheme. Also, for the forced vibration, the shooting method combined with the arc-length continuation method has been applied to explore the resonant response of the system. The results show that fiber reinforcement affects the performance of the dielectric elastomers. Eventually, the present study can be considered to develop biological structures such as arterial walls and soft tissues because of their fibrous structures.