Study on Linearization Criterion and Vibration Mechanism based on Duffing Systems
基于杜芬系统的线性化准则与振动机理研究

Based on the two assessment indexes of the equivalent error rate and entropy error rate,the predict precision of the analytic linearization solutions of the steady-state response distribution of Duffing systems to Gaussian white noises is contrastively analyzed,abided by the two equivalent criterions of response moment limited and minimizing the mean square of equation difference,respectively; the relativity between the systemic parameters and excitation intensity,and their synthetical influence on systemic vibrations are discussed.The results show that the predict precision of the linearization solutions is controlled by the principle of maximum entropy;the basic attribute of linearization solutions is located by the criterion of minimizing the mean square of equation difference,and its forecast precision may be improved by use of known moment information;the assessment conclusions corresponding to the two indexes above-mentioned have consistency;the influences of the systemic parameters and excitation intensity on response distributions can be synthetically expressed by the relative hardening stiffness coefficient.