基于杜芬系统的线性化准则与振动机理研究

基于等效化误差率和熵值误差率两种评估指标并分别利用响应矩受限和方程差均方最小等效化准则,对比分析了高斯白噪声作用的杜芬系统稳态响应分布线性化解析解的预测精度;探讨了系统参数和激励强度的相关性及其对系统振动的综合影响.结果表明,线性化解的预测精度受最大熵原理支配;方程差均方最小准则规定了线性化解的基本属性,而采用已知矩信息可以改善线性化解的预测精度;上述两种评估指标的结论具有一致性;系统参数和激励强度对系统响应的影响可按相对刚度硬化系数综合表述.

Study on Linearization Criterion and Vibration Mechanism based on Duffing Systems

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.