Application of Bubnov-Galerkin method to determine fixed vibrational loads of launch vehicle compartments

The stage of qualification vibration tests of space rocketry products is one of the most important stages of their design. To carry out the tests it is necessary to know the levels of vibration loads as early as the system definition stage. It is necessary to use methods that were previously tried and found efficient when defining the modes of vibration and acoustic loading on the structural elements of advanced launch vehicles and the assembly and protective blocks. The results of calculations made according to efficient methods in most cases agree with the results of full-scale measurements. We propose a methodological complex that will help engineers to create necessary vibration dynamic impact on the structures of space-rocketry products. Equations of shell vibration dynamics and a way of solving them on the basis of Bubnov-Galerkin method is presented in the paper. A method of forming the right-hand sides of the equations is also presented. The equations under consideration are equivalent to the actual spectra of external acoustic loads determined at the stage of flight development tests. A way of forming frequency-dependent damping characteristics of the structure is described. Spectral characteristics of vibration dynamic impact on a launch vehicle of the “Soyuz” type obtained by the results of processing of telemetric information are given. The vibration dynamic impact on the structure of the launch vehicle compartments is calculated on the basis of the characteristics specified. The results of the probability analysis of the vibration loads obtained are presented.