单自由度带支撑Maxwell阻尼减震系统随机响应标准振子分解法

Standard oscillator decomposition method for single-degree-freedom system with Maxwell damper under earthquake

为建立耗能结构保护系统的抗震设计方法,针对单自由度带支撑Maxwell阻尼器减震系统随机地震响应问题进行系统研究.首先,考虑阻尼器设置支撑的影响,建立了时域非扩阶微分积分混合动力方程;然后,采用传递函数法,获得了减震系统在任意激励条件下位移、速度和阻尼器受力的时域非扩阶瞬态响应精确解;运用标准振子分解,将结构响应的方差解析式精确分解为一阶和二阶标准振子响应方差的线性组合;最后,用限带白噪声激励的线性组合逼近任意指定形状的谱和更接近于实际激励,且物理含义明确,并用数值积分法与本文方法作对比,验证了本文的正确性,从而获得了结构基于限带白噪声平稳随机激励响应特性分析的一整套解析分析法.

Stochastic responses for a single-degree-freedom（SDF） system with Maxwell damper are systematically investigated to establish the design method for protecting energy consumption system against earthquake. Firstly,structural dynamic integral-differential equations are built on account of influence of supporting stiffness.Secondly, by using transfer function method, exact time-domain solutions of the system are obtained under arbitrary excitation and non-zero initial conditions, of which are displacement and speed of the system and force of the damper. Thirdly, the variances of structural response are accurately disintegrated into linear combinations of oneorder standard variance and second-order standard variance oscillators based on the methods of standard oscillator decomposition. Finally, linear combinations of band-limited white noise excitations are applied to approximate arbitrary shape spectrum, which are more close to the actual excitations and easy to understand in physics. A example shows that the presented method is verified by comparison with numerical integration method. So, a whole set of analytical solutions for dynamic characteristics of a structure with Maxwell damper under limited-band white noise excitation is obtained.