Monoharmonic method for calculating the frequency characteristics of the dynamic stiffness of nonlinear dynamic objects

Abstract

The paper comprises results of algorithm design for monoharmonic method for calculating the frequency characteristics of the dynamic stiffness of nonlinear dynamic objects with a specified computational error and for a minimum time. The proposed alternative method relates to auto-integration methods and is based on numerical integration of the nonlinear differential equation system for a mathematical model of a dynamic object with monoharmonic input actions at fixed frequencies, and analysis of responses to these actions by Fourier method. The integration process at each fixed frequency continues until the average values of Fourier coefficients of the investigated harmonic of dynamic stiffness of a nonlinear dynamic object on the input monoharmonic force or moment action for a passed number of periods of the input signal become sensibly constant. The efficiency of the developed method and algorithm is studied using the example of calculation of frequency characteristics of the dynamic stiffness of a hydraulic power cylinder with closed hydraulic lines. The obtained frequency characteristics of the dynamic stiffness can be used to evaluate the damping properties of nonlinear dynamic objects. Key words: frequency characteristics of dynamic stiffness; calculation method; nonlinear dynamic objects.