The modern state of the problem of analyzing the natural frequencies and modes of vibration of a composite structure

Abstract

Various methods for calculating the shapes and frequencies of natural vibrations of rod structures and blades are described in the literature. At present, there is still no one unified universal technique for ensuring the vibratory strength of blades, based on the exact solution of the problem of calculating the vibrational characteristics of modern impellers of complex design. Thus, the problem of the flexural-torsional flutter of working blades of turbo-machines is extremely relevant, in spite of the insufficient attention given to it in various literary sources. The above drawbacks can be avoided by applying various design analysis methods. Calculation methods for analyzing the strength of structures, as a rule, are divided into analytical and numerical. Analytical methods for studying the stress-strain and vibration state are based in most cases on simplified relations between the theories of rods, shells, and also the theory of oscillations. The advantage of analytical methods is the relative ease of use and convenience in performing valuation calculations at the initial stages of design. The paper reviews and analyzes works on the finding of frequencies and modes of vibrations of rod structures and compressor blades for their subsequent use for multi-layer anisotropic rod structures from composite materials (CM) during the design phase.