Equilibrium Forms of an Initially Curved Bernoulli–Euler Beam in Electric and Thermal Fields

Abstract

On the basis of a geometrically nonlinear model of a Bernoulli-Euler beam, the influence of the amplitude and shape of the initial curvature on the nature and stability of the static equilibrium positions of the system under conditions of electrostatic and thermal effects has been studied. With the help of numerical methods of the theory of bifurcations, a complete parametric analysis of the diagrams of evolution of the equilibrium positions for beams with initial curvature in terms of symmetric and asymmetric lower modes of free vibrations is conducted. The regions in the parameter space of the values of the axial force of a mechanical or temperature nature and the strength of the electrostatic field, in which the elastic system has the property of bistability, are determined. The prospect of using the considered class of structures with projected geometry perturbations as sensitive elements of high-precision microelectromechanical sensors of various physical quantities is noted.