Numerical Procedure for the Dynamic Analysis of Three-Dimensional Aeronautical Structures

A numerical procedure, which arises from the Rayleigh› Ritz method, previously applied for the dynamic analysis of plane aeronautical structures, has been used for the computation of frequencies and vibration modes of the same structures, but formed by bidimensional component elements in a threedimensional space. The structural components may be typical parts of wings or tail surfaces in different planes. The expressions of the strain and kinetic energy, corresponding to both in-plane and out-of-plane elastic behavior, have been written. From these, by utilizing polynomial power series expansions for the independent variables, it is possible to evaluate the stiffness and mass matrices by an analytical rather than numerical method. Then from the Hamilton’ s principle, imposing the stationary conditions of the total energy leads to the generalized eigenvalue problem, whose solution is found by an appropriate algorithm. A comparison of the obtained results with those of the e nite element method program MSC/ NASTRAN has been performed to better understand the convergence rate of the proposed method.