设置连接阻尼器的相邻结构随机地震动响应的简明封闭解

针对两相邻结构间设置连接阻尼器对结构的减震影响问题,研究了基于Kanai-Tajimi谱地震动激励下的Kelvin型粘弹性阻尼器与相邻结构形成的组合体系的随机地震动系列响应(绝对位移及层间位移)的简明封闭解。首先,利用Kelvin型粘弹性阻尼器本构关系及Kanai-Tajimi谱的滤波方程,将组合体系基于复杂地震动激励精确转化为基于简明白噪声激励的运动方程;其次,利用复模态法获得了组合结构相对于地面的绝对位移、层间位移等系列响应方差及0阶~2阶谱矩的统一简明封闭解。最后,通过算例及与虚拟激励法进行对比,证明本文方法的正确性和简明性;通过与未设置阻尼装置结构体系的动力响应对比,说明了阻尼装置对相邻结构具有良好的减震效果,但局部楼层的层间位移及层间剪力会有所增加。     

阻尼耗能减振框架结构地震作用振动方程求解及地震反应分析Calculation of vibration equation and analysis of seismic response for damping energy dissipation frame structure

研究了设置耗能阻尼器框架的地震作用振动方程求解及该结构的地震反应。框架结构设置耗能阻尼器后,振动方程的阻尼矩阵不再对振型具有正交性,本文对该振动方程给出了状态方程直接积分法,并与传统强制解耦法进行了比较分析,结果表明强制解耦法对结构第一阶振动反应求解偏差较小,而对于高阶振动反应差别较大,并且强制解耦法高估了阻尼器的减震效果。继而采用状态方程直接积分法对设置有粘滞阻尼器的框架结构进行了地震反应分析,探讨了阻尼器位置对框架结构地震反应的影响,结果表明设置有阻尼器的楼层减振效果明显,未设置阻尼器的楼层减振效果差别较大,甚至有可能出现楼层层间侧移增大的现象,由此提出耗能阻尼器应在结构中合理设置。     

基于最小范数点的响应面方法

针对传统的响应面法难以实现大范围精度近似,可靠度计算效率和精度偏低的问题,本文从可靠度指标的几何意义入手,提出一种基于最小范数点的改进响应面方法。该方法在响应面上的最小范数点附近选取新的试验点,再对这些样本点进行二次多项式插值校正,从而构建出更加逼近极限状态方程的响应面形式,一定程度上提高了计算的精度。另一方面,本文引入了一种双重收敛准则进行判断性评估,能够有效地节省迭代的过程,提高计算效率。最后,算例分析验证了本文方法的合理性和适用性。     

Responses of SDOF Structures With SPIS-Ⅱ Dampers Under Random Seismic Excitation北大核心CSCD

A closed-form solution of responses of SDOF structures with SPIS-Ⅱ dampers under seismic excitation modeled with the Clough-Pezien spectrum was proposed, and the shock absorption performance and influential factors of this system were studied based on the proposed method. Firstly, the motion equation for the SPIS-Ⅱ damper was established, and the unified expressions of frequency domain solutions of structural responses, such as the structural displacement and the inerter force, were obtained. Secondly, based on the rational expression decomposition and the residue theorem, the quadratic orthogonal equations of the frequency response eigenvalue function and the Clough-Pezien spectrum were obtained respectively, and in turn the quadratic orthogonal equation of the structural response power spectrum was deduced. Thirdly, the concise closed-form solutions of the 0~2nd-order spectral moments of the structural responses were acquired. The proposed method and the virtual excitation method were used to analyze a case respectively, which verifies the correctness of the proposed method. Finally, the proposed method was used to analyze the effects of the inerter parameters on the seismic performances of the structure. The research shows that, the proposed method gives closed-form solutions better than those given by the virtual excitation method in terms of computation efficiency and accuracy. The damping performance will improve with the increase of µm and µξ for a constant µω and the damping performance will reach the optimum for µω=1. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

结构设计竞赛中纸质杆件相关参数确定及极限承载力研究1）

为确定纸质杆件的材料参数,并研究白卡纸杆件极限承载力的影响因素及杆件极限承载力计算方法,制作多组白卡纸杆试件并进行加载试验.测得白卡纸的泊松比为0.137 3,弹性模量为5.5GPa.杆件的抗压极限承载力受杆件的厚度、内径、长度、截面形状、白卡纸纹理方向以及涂胶宽度的影响;结合压杆稳定相关理论,由数据拟合得到白卡纸杆件极限承载力的近似计算方法;通过公式计算结果与试验结果比较,证明其准确有效.     

基于扩展有限元法的钢筋混凝土梁裂纹扩展的数值模拟

基于最大主应力准则,利用扩展有限元法对钢筋混凝土三点弯曲梁的裂纹扩展进行数值模拟。通过与已有模型试验结果的比对,验证了该方法的准确性与有效性。研究发现,带裂纹钢筋混凝土构件的裂纹扩展与力学性能不但受到单裂纹的尺寸、位置、倾角的影响,而且还受多裂纹间位置关系的影响;其中,裂纹横向分布位置和裂纹纵向分布位置是影响带裂纹钢筋混凝土梁裂缝扩展的主要因素。