Discrete Equivalent Loading Method for Continuous Structural Distributed Dynamic Loads

To address the challenge of accurately applying distributed dynamic loads in experiments, a method is proposed whereby concentrated dynamic loads are applied at Gauss points to achieve an equivalent effect. This approach utilizes modal truncation in the modal space, discretizes the distributed dynamic load through a modal force equivalence method, and calculates the coefficients of the concentrated dynamic loads using the Gauss-Legendre quadrature formula. In numerical simulations, dynamic responses of a cantilever beam and a simply supported plate under both distributed and equivalent concentrated dynamic loads are analyzed, with the modal superposition method used to evaluate the dynamics of the beam and plate. Results indicate that the acceleration response error under distributed and equivalent concentrated loads does not exceed 4. 5% , and the displacement response error does not exceed 4. 2% . Additionally, the variation of equivalent results under noise in the concentrated loads is examined. The simulation results validate the accuracy and applicability of this equivalent method for distributed dynamic loads.