Rayleigh–Ritz method and method of initial parameters in the problem of calculation of dynamic characteristics of multibeam elastic structures

The solution of the problem of dynamic synthesis based on the application of the Rayleigh–Ritz method is considered. A method is proposed for determining the dynamic characteristics of a composite beam structure, taking into account the calculation of the shapes of oscillations of partial substructures using the method of initial parameters. Two variants of the formation of coordinate functions, using static and dynamic condensation, are considered. When carrying out static condensation, in order to increase the accuracy of the result, the internal physical degrees of freedom of the element were added to the boundary degrees of freedom to the reduced model degrees of freedom. When conducting dynamic condensation, modal degrees of freedom were added to the physical degrees of freedom of the boundary nodes of the reduced model, which are, in fact, coefficients in the accepted decomposition of the field of partial forms calculated with fixed boundary degrees of freedom. In the framework of the proposed approach, test calculations were carried out for a beam with variable mass-stiffness characteristics along the length, which showed good convergence of the target parameters to exact values. The proposed approach can be used to carry out calculations of composite elastic structures based on the method of initial parameters in cases where the application of the finite element method is irrational or difficult. In addition, if necessary, on the basis of the approach considered in this paper, the combined use of these two methods can be organized.