Non-Gaussian equivalent linearization for nonstationary random vibration of hysteretic mechanical system

Abstract

An approximate analytical technique is developed for obtaining the nonstationary response of a single-degree-of-freedom mechanical system with bilinear hysteresis subjected to amplitude modulated non-white random excitations. The hysteretic behavior is described by introducing an additional state variable and non-linear functions. The equivalent linear coefficients and also the moment equations of the equivalent linear system are derived using a non-Gaussian probability density function which is composed of a truncated Gaussian probability density function and a couple of delta functions. The mean square responses and the mean dissipated hysteretic energy are calculated by solving the moment equations and are compared with the corresponding digital simulation results.

近似解析法を開発し、AM波により不規則励起した双1次ヒステリシスを持つ自由度1の機械系の非定常応答を得た。付加状態変量と非線形関数を導入してヒステリシス挙動を記述した。等価線形系の等価線形係数とモーメント方程式を非ガウス確率密度関数を用いて求めた。この非ガウス確率密度関数は、分布の両端を切り捨てたガウス確率密度関数と1対のデルタ関数より構成したものである。モーメント方程式を解いて、平均平方応答と平均散逸ヒステリシスエネルギーを求め、これを相当する数値シミュレーション結果と比較した。