Calculation of eigen frequencies of systems with damping

Abstract

This paper considers a problem of detecting all resonance frequencies during the design phase for complex technical objects made of sub-systems of various physical natures with the unknown point of application of a harmonic input. Consequently, it is required to choose a proper calculation method for eigen frequencies and eigen vectors for those systems. Results. Is to analyze mathematical methods for calculating eigen frequencies and eigen vectors of complex technical systems with sub-systems of different nature and give recommendations on selecting a proper method and its justification. Results. It is demonstrated that in order to calculate eigen frequencies of mechanical systems, a use of a system of Cauchy differential equations is appropriate because it allows avoiding limitations caused by a traditional mathematical model. It is shown that the eigen frequency and eigen vector analysis helps one to determine eigen frequencies in presence of dampening as well as the ratio of amplitude of oscillation on those frequencies. Practical significance. The proposed method for selecting calculation technique for eigen frequencies and eigen vectors helps one to determine eigen frequencies in presence of dampening as well as the ratio of amplitude of oscillation on those frequencies. This method is applicable to the nonlinear system analysis in arbitrary points of nonlinearity.