Study on a Nonlinear Dynamic Model and Its Parameters Determination Method for Half-Sine Programmer

Abstract

A nonlinear dynamic model for describing shock response of half-sine programmer in shock test is constructed, in which many important factors in half-sine programmer such as size, hard nonlinearity, damping and initial impact velocity are considered, based on the damped Duffing equation, and the empirical static stiffness and shock stiffness calculation formulas of cylindrical rubber isolator. The shock pulse of half-sine programmer is measured and calculated by using shock test machine and Runge-Kutta method. Taking the minimum determination coefficient between the calculated and the measured shock pulse as the optimization objective, the parameters in the present model are determined by using quantum genetic algorithm (QGA), and meanwhile the extreme capacity in the present model for describing the dynamic behavior of half-sine programmer under shock excitations can also be verified. Experiments were implemented with drop shock test machine. The experimental results show that the present model is precise and efficient, and the prediction errors of pulse peaks and pulse widths were all below 5%, the waveform fitting errors between the calculated and the measured pulses are all less than 15%. The present results are helpful for designing the half-sine programmer.

College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations

“…Table 1 Types and stability of balance points determined by the feature equation On the contrary, when αβ < k1, it is unstable (Figures 3 and 4), that is to say, when αβ < k1, after a long enough time, the consumption amount of both sides will tend to infinity, which will lead to adverse consequences for both sides of comparing consumption [12]. 1.…”