Hermite Finite Element Method for Variable Coefficient Damping Beam Vibration Problem

Beam is the most common component in mechanical equipment and construction. The heterogeneous beam and the variable cross-section beam both have good structural performance. In this study, a Hermite finite element method is proposed for variable coefficient damping beam vibration. The first-order time derivative is approximated by the Richardson format, the second-order time derivative is approximated by the central difference method, and the fully discrete scheme is obtained. The variable coefficients are processed, the error estimate is analyzed in detail. Finally, we verify the validity of the scheme by Matlab and observe influence of damping coefficient variation on beam vibration.