Moving Mass - Cantilever System The Disharmony Time Finite Element Algorithm

In this paper, a time-varying dynamic system of cantilever beam under moving mass with mathematical modeling, numerical algorithms and experimental research is presented, under the background of a "××××time-varying mechanical study".Time-varying properties of system are analyzed and a time-discontinuous Galerkin finite element method for analyzing the time-varying equations is studied, which is based on weighted residual method and inherits higher order accuracy and unconditionally stable behavior. Algorithm based on Lagrange is derived and specific solutions of differential equations with time-varying coefficients are given. Excellent characteristics such as feasibility, effectiveness and superiority in solving time-invariant problems as well as time-dependent issue are validated by algorithm analysis and numerical example.The structure features and motion law of constant cantilever beam system are analyzed by which moving force model and moving mass model are established. The cantilever beam is discretized in space by finite element method or assuming modal method,and time-varying dynamic equations are derived. The TDG finite element method is adopted to solve the differential equations. The validity of mathematical modeling and numerical algorithms is validated by two modeling methods of solution and comparison analysis. The inertia effect of moving mass on the dynamic response of cantilever beam is investigated subjected to the analysis of time-varying systems. Also the quality and speed of mass are studied which can affect characteristics of the time-varying system.The model of cantilever beam with varying section and contact gap subjected to moving force or moving mass is established. The TDG finite element method is adopted to solve the corresponding numerical examples by which the validity of mathematical model-ing and numerical algorithms is validated.The experimental about time-varying mechanical properties of cantilever beam under moving mass is studied and reasonable test scenario is developed on the basis of test content and experimental principle. The effectiveness and inadequate of mathematical modeling and numerical algorithms are validated by contrasting the test and numerical calculation results.