基于SMA的结构随机振动控制研究-结构工程专业论文.docxVIP

摘 要 超弹性形状记忆合金（shape memory alloy，简称 SMA）因其独特的功能特性 而成为结构振动被动控制的理想材料。目前，关于 SMA 阻尼器对结构振动控制研 究多是在确定性荷载下进行，鲜有涉及随机振动激励环境。本文围绕 SMA 阻尼器 控制结构随机振动展开理论研究，具有重要现实和理论意义。 本文介绍了与随机振动相关的数学基础知识，分析了单自由度结构和多自由度 结构随机振动反应。利用 SMA 的超弹性特性提出了一种新型 SMA 自复位阻尼器， 建立了阻尼器基于 Graesser 本构模型的力-位移关系曲线，进而提出了简化的力学模 型。利用等价线性化方法推导出了 SMA 阻尼器控制单自由度结构分别在白噪声和 地震作用下的随机振动响应公式，并通过算例，将蒙特卡罗模拟法和等价线性化法 计算结果相比较，证明等价线性化法的正确性。利用等价线性化方法推导出了 SMA 阻尼器控制多自由度结构在地震作用下的随机振动反应，验证了阻尼器的减震功效。 关键词：SMA 阻尼器 结构随机振动 等价线性化法 蒙特卡罗模拟法 I ABSTRACT Superelastic shape memory alloy（SMA）is an ideal material of passive vibration control of structure due to its unique features. At present, the researches on SMA damper in structural vibration control are carried out under the deterministic load, rarely involving in random vibration environment. This article carries on theoretical researches on SMA damper controlling structure random vibration theory. The achievements have important practical and theoretical significance. This paper introduces the basic mathematical knowledge related to the random vibration, analyzes the random vibration responses of the single-degree-of-freedom structure and multi-degree-of-freedom structure. Using the superelastic property of SMA, a new SMA self-recentering damper is proposed. Based on the Graesser’s constitutive model of SMA, the force-displacement relation of the damper is built, and furthermore, a simplified mechanical model of the damper is advanced. Using the equivalent linearization method, the random vibration responses of the single-degree-of-freedom structure with the SMA damper subjected to white noise excitation and earthquake excitation are deduced. Numerical simulations are carried out to compare the results between the Monte Carlo simulation method and the equivalent linearization method. The results prove the validity of the equivalent linearization method. Using the equivalent linearization method, the random vibration responses of the multi-degree-of-freedom structure with the