Model order reduction for dynamic simulation of beams with forcing and geometric nonlinearities

• We study the applicability of Trajectory Piecewise Linear Model Order Reduction (TPWLMOR) method for dynamic simulation of nonlinear beam problems.
• Nonlinearities which include both forcing and geometric nonlinearities are considered.
• To improve accuracy of TPWMLOR a new method is suggested based on minimization of residual at linearization point.
• Factors affecting the accuracy of the modified TPWLMOR are studied in detail.

The objective of the paper is to investigate the applicability of a model order reduction technique for dynamic simulation of beams with forcing and geometric nonlinearities. A cantilever and a doubly clamped beams actuated by an electrostatic force are considered in the paper. The governing partial differential equations for the two cases which account for the nonlinearities are presented. These equations are spatially discretized using the Galerkin finite element method (FEM). The resulting system of nonlinear ordinary differential equations is reduced using the trajectory piecewise linear model order reduction (TPWLMOR) method. Simulation indicates that the use of the original TPWLMOR method leads to the presence of a phase error in the long term dynamic simulation of the models. To improve the accuracy of the dynamic response, a modification to the original TPWLMOR based on minimization of residual at linearization point is proposed. Further, the parameters affecting the accuracy of the modified TPWLMOR are studied.