基于代数算法的单元模态应变能灵敏度分析

Element modal strain energy sensitivity analysis based on an efficient algebraic method

模态应变能在基于振动的结构损伤识别中得到了广泛的应用,其灵敏度分析成为了当前的一个重要问题。采用代数方法解析推导出了无阻尼线性系统单元模态应变能一阶和二阶灵敏度的解析表达式,该表达式简洁紧凑,便于编程,而且只需一阶模态信息,不存在模态截断引起的误差问题。通过数值模拟算例,对得到的单元模态应变能一阶灵敏度进行了参数分析,并着重考查了损伤及其噪声的影响。结果表明,低阶单元模态应变能比高阶模态能更好地反映出结构损伤,而且抗噪能力更好。

Modal strain energy has been widely used in vibration-based structural damage detection.Thus,how to calculate its sensitivity becomes a crucial problem.Here,the first-order and the second-order sensitivity formulae of an element modal strain energy for a real symmetric undamped structure with distinct eigenvalues were derived based on an efficient algebraic method.The formulae were simple and compact,and they were easy to be programmed.Moreover,they only required one eigenvector known and had no errors caused by mode truncation.Via numerical parametric studies,the general properties of the first-order sensitivity of the element modal strain energy were analyzed and the effects of damage and noise on it were checked.It was demonstrated that the element modal strain energy of the lower modes is better than that of the higher modes to reflect the structural damage and has better ability against noise.