The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is...The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beam solutions of the loads with di?erent distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation o?ers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length o?ers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The e?ects of dielectric layer thickness and electrostatic voltage on the cantilever beam stiction are studied. The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.展开更多
文摘The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beam solutions of the loads with di?erent distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation o?ers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length o?ers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The e?ects of dielectric layer thickness and electrostatic voltage on the cantilever beam stiction are studied. The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.
