Analysis of influence of the geometric parameters of mast systems on the natural frequency and vibration mode spectrum

Abstract

Natural frequencies and eigenmodes of oscillations are the determining values in the study of dynamic processes in many constructions, including mast systems when they are affected by time-varying loads: wind, seismic, etc. [7]. The article suggests a method of forming, by means of a purposeful variation of the geometrical parameters of the mast, the spectrum of natural frequencies of bending vibrations. The basis is the necessary optimality conditions for one-dimensional models in the form of the maximum principle [1, 3, 8]. The analysis of the sensitivity of the spectrum [9] to small changes in geometric parameters that inevitably arise during the operation of the masts is carried out. An algorithm for using functional derivatives for finding optimal solutions is constructed.