Research On The Dynamic Modeling Theory For The Rigid-flexible Coupling Functionally Graded Materials Trapezium Beams

At present,many components of vehicle and aerospace fields,such as satellite antennas and solar panels for astronomical telescopes,helicopter rotors,flexible manipulators,engine blades in ships,aviation,wind power and automobile turbines,can be regarded as the main part as a rigid body and attachment as a flexible body,the rigid-flexible coupling dynamics model,which can be simplified into a central rigid-isometric beam or a central rigid-variable beam system for dynamic modeling simulation and analysis.As homogeneous materials can not meet complex working conditions or actual needs,the new functionally gradient materials gradually replace traditional homogeneous materials and become a popular choice for the relevant staff.According to the dynamics of multi-rigid-body systems and the dynamics of flexible multi-body systems,with power law distribution of material properties along the thickness direction,as the large scale motion is known or unknown,the relevant dynamic modeling theory and simulation analysis of the central rigid-functionally gradient materials trapezium beams with additional mess systems are studied and the natural frequencies and dynamic responses of the systems are discussed.The main contents of this paper are:1.According to the high-order rigid-flexible coupling dynamics model,considering the longitudinal shortening term caused by transversal bending deformation,that is,the high-order term of nonlinear coupling deformation,the modeling theory of the central rigid-functionally gradient materials with additional mass system is researched with the large-scale plane motion and the deformation fields are discretized by the hypothetical modal methods and the second type of Lagrange equation is used to derive the rigid-flexible coupling dynamics equation of the functionally gradient trapezium beam and the additional mass considering the moment of inertia effect with respect,the two sides of which are added separately to obtain the high-order rigid-flexible coupling dynamics model of the whole system.2.The natural frequencies of the central body-functionally gradient materials trapezium beam systems for large-scale motion are studied and the dimensionless characteristic equation is obtained,with the different functionally gradient materials index,beam width ratio,beam height ratio and beam length ratio,under considering of the longitudinal deformation or not considering of the longitudinal deformation,the dimensionless transverse bending natural frequencies are discussed.Considering the contribution of the additional mass in the dimensionless characteristic equation,the effects of the moment of inertia ratio,position ratio and mass ratio of the additional mass for the transverse bending natural frequency of the whole system are studied.The influence of the moment of inertia is small,but it cannot be ignored.3.The dynamics simulation of the rigid body-functionally gradient materials trapezium beams with additional mass system is carried out,and the dynamic software is compiled to obtain the response of the functionally gradient materials trapezium beam with or without additional mass under the condition of large-scale motion known or large-scale motion unknown.The research shows that the functionally gradient materials index,beam width ratio,beam height ratio,beam length ratio,etc.all have a great influence on the dynamic response of the system,and should be considered comprehensively in actual working conditions.