【摘要】 基于方程差的均方最小准则,探讨了硬弹簧杜芬系统高斯白噪声作用稳态位移响应的线性与立方恢复力等效模型的适用性。结果表明:等效化误差率取决于相对刚度硬化系数η;随着η的增加,线性化等效模型预测精度下降而立方恢复力等效模型预测精度提高;η具有一个临界值η=0;η=η0时,线性与立方恢复力等效模型具有相同的预测精度而在η>η0 情况下,立方恢复力等效模型优于线性化模型。更多还原

【Abstract】 Based on the criterion for minimizing the mean square of equation difference, the applicability of the equivalent models with linear or cubic restoring force for the steady-state displacement response of hardening spring Duffing systems, subjected to Gaussian white noise, was approached. The results show that the equivalent error rate depends on the relative hardening stiffness coefficient η; the prediction precision of the linear equivalent model declines but that of the cubic restoring force equivalent model improves with η increasing; η has one critical value η₀; the cubic restoring force equivalent models have the same prediction precision as the linear one when η=η₀; and for η>η₀, the cubic restoring force equivalent model is better than the linearization model.更多还原