粘滞和粘弹性阻尼器减震结构的随机响应特性

利用积分型本构关系,针对带支撑任意线性粘滞和粘弹性阻尼器单自由度耗能结构,建立了微分和积分混合地震响应方程;基于随机平均分析法,推导出耗能结构振幅与相位瞬态联合概率密度函数、位移与速度瞬态联合概率密度函数、位移与速度瞬态响应方差、振幅动力可靠性、振幅首超时间任意阶统计矩的一般解析解;给出了带支撑广义Maxwell阻尼器和广义微分模型阻尼器耗能结构上述各种随机响应特性,从而建立了带支撑任意线性粘滞和粘弹性阻尼器单自由度减震结构的各种随机响应特性分析的统一解析解法。     

多自由度Maxwell阻尼器减震结构(Ⅱ)——等效阻尼

对多自由度带支撑Maxwell阻尼器减震结构的等效阻尼比进行了系统研究。构建了耗能结构一般微分和积分混合地震响应方程组;基于与多自由度随机平均法分析完全相同的等效准则,建立了耗能结构各振型等效阻尼比的一般解析计算式。与一些典型问题的模态应变能法的计算精度进行对比分析,结果显示:本文方法的计算结果在特定条件下与精确解完全相同;在一个二自由度系统中相对位移响应方差的误差分别为0.99%和0.45%,优于应变能法的8%和5.4%,表明了本文方法的有效性。从而为建立此类耗能结构等效阻尼分析的完备解析解法、直接应用反应谱法进行实际工程设计提供了依据。     

设置粘弹性阻尼器耗能框架结构随机振动分析

在时域分析基础上,对设置粘弹性阻尼器耗能框架结构进行随机振动研究,由此对时域分析结论进行补充验证.首先,使用随机振动理论对设置粘弹性阻尼器框架结构的振动方程进行求解,得出楼层位移及层间位移均方差,在时域分析基础上,对各楼层经济设置粘弹性阻尼器框架结构的地震反应进行随机振动分析,然后,研究设置粘弹性阻尼器框架结构的等效阻尼比.最后,针对一榀设置粘弹性阻尼器的十层框架结构进行随机振动分析,研究了改进Kanai-Tajimi功率谱地震激励作用下结构的楼层位移、楼层层间位移和楼层层间位移角等响应,分析了各楼层经济布置阻尼器结构的随机响应,并对设置粘弹性阻尼器框架结构的等效阻尼比进行了分析,由此对时域所得结论的可靠性进行补充分析.结果表明:框架结构各楼层均匀设置粘弹性阻尼器能够显著降低随机地震激励作用的响应;时域分析得出的粘弹性阻尼器在各楼层经济布置时的阻尼系数计算公式能够满足减震与经济两方面要求;该结构等效阻尼比的计算方法可以实现阻尼等效的目标.     

多自由度Maxwell阻尼器减震结构(Ⅰ)——随机响应特性

对多自由度带支撑Maxwell粘滞阻尼器减震结构的随机响应特性进行了系统研究。建立了结构一般运动方程;将运动方程按原结构振型展开,将运动方程化为振型广义坐标的微分和积分混合地震响应方程组;基于多自由度随机平均法理论,获得了结构随机平均It方程组的解析式,推导出耗能结构各振型振子的振幅与相位瞬态联合概率密度函数、位移与速度瞬态联合概率密度函数、位移与速度瞬态响应方差的一般解析解;根据SRSS组合方法,给出了耗能结构随机地震响应方差的一般解析式,从而建立了此类耗能结构随机响应特性分析的完备解析解法。     

附加粘滞阻尼器结构的随机地震响应谱分析

粘滞阻尼器在结构振动控制中应用广泛.附加粘滞阻尼器结构的随机地震响应分析中,存在的主要问题是此类结构的阻尼和刚度都是非线性的,通用的响应谱分析方法不再适用.为简化分析过程,采用等价线性化法,利用与弹性响应谱相一致的功率谱密度函数的概念以及结构峰值响应求解的方法,从而获得Clough-Penzien地震谱激励下单自由度结构的位移响应谱.在此基础上,讨论结构周期、阻尼器参数以及场地条件对结构地震响应计算结果的影响,将分析结果与蒙特卡洛模拟得到的结果进行对比,验证了该分析方法的准确性和适用性.     

粘滞阻尼器减震结构非线性随机振动的时域显式降维迭代随机模拟法

粘滞阻尼器在大型复杂结构减震设计中应用广泛。由于粘滞阻尼器的非线性阻尼力特性,粘滞阻尼器减震结构非平稳随机地震反应分析是一个典型的局部非线性随机振动问题。利用减震结构动力响应时域显式表达式的降维列式优势,仅针对与粘滞阻尼器相关的局部自由度进行非线性迭代计算,提出了局部非线性随机振动问题的时域显式降维迭代随机模拟法,为设置粘滞阻尼器的大型复杂减震结构非线性地震反应分析提供一种高效的随机振动方法。以安装了四个纵桥向粘滞阻尼器的某主跨1200m悬索桥为工程实例,开展E2水准地震激励下的非线性随机振动分析。计算结果显示,设置阻尼器后,主梁的纵桥向位移得到明显控制,降幅达到80%,大桥的关键截面内力也有5%左右的降幅。     

设置粘弹性阻尼耗能框架结构减震性能分析

研究粘弹性阻尼器对框架结构的减震性能,分析该阻尼器的阻尼参数对框架结构地震反应的影响,给出设置阻尼器后结构地震作用的计算方法。对设置粘弹性阻尼器框架结构振动方程进行傅里叶变换,求解该振动方程的频域解,再通过傅里叶逆变换得出该方程的时域解,由此研究阻尼器的阻尼系数C_d和松弛时间系数η等对结构地震响应的影响。在此基础上,提出粘弹性阻尼器的阻尼系数在各楼层经济分布的实用计算公式,并对设置粘弹性阻尼器框架结构地震作用给出计算方法,分析结构各楼层的地震作用及结构各振型的底部剪力。研究表明,设置于框架结构的粘弹性阻尼器宜控制其松弛时间系数η≤0.5～0.7。     

三种电流变阻尼器阻尼特性的对比分析

首先简要地介绍了电流变体材料以及电流变阻尼器的基本概念,进而阐明了剪切模式电流变阻尼器、流动模式电流变阻尼器和复合模式电流变阻尼器的工作原理。最后,应用非牛顿流体力学理论给出了它们的阻尼力模型,并对其各自的阻尼特性进行了一些理论分析和探讨。     

Design method for fluid viscous dampers

A basic design method of doubly acting fluid viscous dampers with double guide bars is presented. The flow of the viscoelastic fluid between two parallel plates, one of which is started suddenly and the other of which is still, is analyzed. According to this solution, the velocity and the shear stress of the fluid at the fringe of the piston are solved approximately. A mathematical model of viscous dampers is derived, and the shock test is carried out. From experimental results, the parameters of the mathematical model are determined. Consequently, a semi-empirical design equation is obtained. Applying this equation to a certain practical damper, the damping material is chosen and the physical dimensions of the damper are determined. Shock tests using this damper are performed. Theoretical results are in good agreement with experimental results, which validates the reliability of the calculated physical dimensions of the specimen damper and the validity of the basic design equation. An erratum to this article can be found at     

The force transmissibility of MDOF structures with a non-linear viscous damping device

In the present study, the concept of the Output Frequency Response Function (OFRF), recently proposed by the authors, is applied to theoretically investigate the force transmissibility of MDOF structures with a cubic non-linear viscous damping device. The results analytically show that the introduction of cubic non-linear damping can significantly reduce the transmissibility over all resonance regions for a Multiple Degree of Freedom (MDOF) structure and at the same time leave the transmissibility over the isolation region virtually unaffected. The analysis also indicates that a strong linear damping may shift the system resonances and compromise the beneficial effects of cubic non-linear viscous damping on the force transmissibility of MDOF structures. This suggests that a less significant linear damping together with a strong cubic non-linear damping can be used in MDOF structures to achieve a desired vibration isolation performance. This research work has a significant implication for the design of viscously damped MDOF structures for a wide range of practical applications.     

Estimating equivalent viscous damping ratio for RC members under seismic and blast loadings

It can be learned that the equivalent viscous damping (EVD) ratio as a function of displacement ductility is a crucial parameter in the application of the displacement based method. A set of generalized expressions are proposed herein for estimating the EVD ratio for individual and multiple reinforced concrete (RC) members. For individual RC members under seismic loads, the EVD ratio was derived based on their hysteretic response and hysteretic energy dissipated under fully reversed cyclic loading. Because of the nature of blast loads only the energy dissipated up to maximum displacement was considered to estimate the EVD ratio for individual RC members under blast loads. For multiple degree of freedom systems consisting of RC members, the EVD ratio was derived based on equating the total energy dissipated in the system to the sum of the energy dissipated by its individual members. Analytical studies presented here and elsewhere indicate that the EVD ratio is highly dependent on the damaged displacement ductility, which can be directly correlated to damage. These analytical results along with the expressions to compute the EVD ratio for RC members under seismic and blast loads are presented and discussed in this paper.     

ANALYTICAL SOLUTION FOR MODE Ⅲ DYNAMIC RUPTURE OF STANDARD LINEAR VISCOELASTIC SOLID WITH NONLINEAR DAMPING

Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating the integral term, a PDE of third-order is obtained. Then, applying the small parameter expansion method, linearized asymptotic governing equation for each order of the small parameter is obtained. Dividing the third-order PDE into an elastic part with known solution, the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one. The WKBJ method is still adopted to solve it analytically.     

Stability and chaotic motion in columns of nonlinear viscoelastic material

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Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating

The combined effects of viscous dissipation and Newtonian heating on boundary layer flow over a moving flat plate are investigated for two types of water-based Newtonian nanofluids containing metallic or nonmetallic nanoparticles such as copper (Cu) and titania (TiO₂). The governing partial differential equations are transformed into ordinary differential equations through a similarity transformation and are solved numerically by a Runge-Kutta-Fehlberg method with a shooting technique. The conclusions are that the heat transfer rate at the moving plate surface increases with the increases in the nanoparticle volume fraction and the Newtonian heating, while it decreases with the increase in the Brinkmann number. Moreover, the heat transfer rate at the moving plate surface with Cu-water as the working nanofluid is higher than that with TiO₂-water.     

主动约束层阻尼梁的数值模型

为对主动约束层阻尼结构建立精确完善的数学模型，采用有限元建模，并考虑到压电材料的机电耦合效应和粘弹性材料的本构关系随温度、频率的变化而变化的特点，将有限元方法与粘弹性材料的GHA模型相结合，从而避免因粘弹性材料导致的非线性微分方程，能直接求解模态频率、模态阻尼及结构响应。为进一步设计控制器，先在物理空间进行动力缩聚，将系统降至适当的维数，然后在状态空间用鲁棒防阶的方法进一步降阶。这样既能大大降低系统维数，又能保证降阶后系统稳定、可控、可观。这对于重量轻、柔度大、低频密集的大型空间柔性结构尤其重要。