Research On Aeroelasticity Of Rotor Flexible Multibody System

The rotor flexible multibody system dynamic model is a research focus in rotor aeroelasticdynamics field. To introduce the flexible multibody system dynamics method into the rotor dynamicsmodeling, corresponding improvement should be implemented for multibody system dynamics androtor dynamics modeling. The rotor flexible multibody system dynamical model and its solutionmetheod of dynamic response have been investigated. To verify the developed model and method, thetransient analysis of a model blade and the aeroelastic analysis of rotors are also presented in thisdissertation.A high accuracy component dynamic model of rotor blade is developed, which is suitable foraeroelasticity analysis of rotor and integrated into flexible multibody system dynamic model easily.The nonorthogonal of base vectors in a helix coordinates, caused by the pretwist of the blade, and itsinfluence on the finite deflection strain tensor of the blade dynamic model is correlated. The exactnonlinear deflection geometry is also adopted. The implicit expressions of strain energy and kineticenergy could be discreted by displacement finite element. For the convenience of integrating intoflexible multibody system dynamic model, mass matrix is extracted using recurrence method. As theexpression form of the work of airload and constraint loads are the same, the Lagrange multipliers inthe component dynamic equations are represented by the constraint force directly. Based on the highaccuracy component dynamic equations, a second order accuracy blade component model is alsoobtained, which is suitable for modeling the small deflection and with much lower computationalcomplexity than the accuracy component model. To verify the correctness of the analysis result, aspecial-shaped blade mode test is conducted. Correlations between the analysis results and theexperimental data from Princeton beam test and Minguet’s composite beam experiments are alsoimpelementd.The rotor multibody system dynamic control equations are composed of the component dynamicequations, holonomic constraint equations and nonholonomic constraint equations. Connectionsbetween the structural components of rotor system produce the holonomic constraint equations, andnonholonomic constraint equations are produced in force elements used for airloads modeling. Tosimplify the form of holonomic constraint equations, the joint dynamic equations are introduced, andthe dynamic equations of component containing a joint are deduced. To avoid singularities for largerotations of the rotor, the angular constraint equations, expressed by Rodriguez parameters, are modified by introduced a nominal motion. The rotor airloads are calculated from the unsteady airfoilaerodynamics with dynamic stall and free wake model. Force elements of rotor airloads are alsodeduced, and integrated into the rotor multibody system as the nonholonomic constraints, in order toseparate the solution procedure of the aerodynamic model from the solution of multibody systemdynamic control equations.Using the generalized coordinate partitioning algorithm, dynamic control equations of rotormultibody system, with differential algebraic form, are reduced to ordinary differencal equations, anda locoal discontinuous Galerkin (LDG) integration method is developed to solve the equations. Thespectral radius, algorithmic damping and period elongation of LDG method are investigated.According to the nonlinear implicit expression and high stiffness ratio of the system equations, theLDG method, which is an implicit integration algorithm, are modified by combining with theNewton-Broyden method. The LDG integration method exhibits excellent numerical stability, andwithout calculating the Jacobi matrices and their inverse matrices, the method also exhibits goodcomputational efficiency.To verify the correctness of the developed rotor flexible multibody system dynamic model andtransient intergration method, the transient analysis of model blade and the aeroelastic analysis ofmodel rotor are implemented. The influence study of stability analysis method, blade structure modeland inflow model is also implemented. It demonstrates that the developed method is useful forimproving computation precision of aeroelastic stability.