多自由度参激系统稳定性分析的数值解法

现有参激系统的动力稳定性问题研究主要集中在主不稳定区域上。为获得组合不稳定区域,基于Floquet方法,采用Bolotin方法在不同周期数下设解形式,结合特征值分析法得到确定多自由度参激系统动力不稳定区域的数值解法。对一个两自由度受周期轴向力的旋转轴系算例的稳定性分析,发现通过增加设解近似项数可获得高阶不稳定区域,且各阶不稳定区域边界随近似次数的增加逐渐趋于稳定,此外,增大阻尼可使各不稳定区域边界变得更加平滑。本文方法可用于一般多自由度周期参激阻尼系统,是一种简明易操作的直接数值解法。     

阻尼与纵向共振对结构动力稳定的影响

推导了有阻尼与发生纵向共振时柱状结构的动力稳定计算公式 ,计算了水中平台动力失稳区间 ,探讨了阻尼与纵向共振的影响 ,得出了一些有应用价值的结果     

非均质土层下基桩的动力稳定性研究

本文根据桩在轴向谐振力作用下，探讨了非均质层下基桩的动力稳定性问题，分析了各种地基土横向抗力系数K以及桩的几何特征，激振频率，桩土阻尼对桩动力稳定性的影响，结果表明，随地基土层的不同，基桩的动力不稳定区域将发生不同的变化，随桩径，桩长的增大，基桩的动力不稳定区域将逐渐减小，表明地基土的横向抗力对桩的动力稳定性起加强作用，桩土阻尼对基桩的动力稳定性影响较大，得出了一些有价值的结论，可为工程设计提供参考依据。     

计算结构动力方程三次精度的直接积分法

以往计算结构动力方程的无条件稳定积分格式的证明,是在阻尼矩阵满足振型正交条件下得到的,文本给出的三次精度无条件稳定积分格式的证明,可不要求阻尼矩阵满足振型正交条件。此外本文提出的高精度方法和以往的高精度方法相比具有存贮空间小,计算量少的优点,本文方法还具有没超越现象的优点。     

一种利用复阻尼理论计算结构自由振动响应的数值方法

复阻尼理论的运动方程通解中包含有发散项,导致结构自由振动响应不能稳定收敛。在复阻尼理论的频域微分方程基础上,修正阻尼项,进而得到滞变阻尼理论表达式,可保证结构自由振动时程计算结果的稳定性。针对滞变阻尼理论的特点,本文依据正弦函数的希尔伯特变换,提出了相应的时程计算方法,可有效计算滞变阻尼理论下结构的自由振动响应。算例分析表明:基于滞变阻尼理论的结构自由振动响应是稳定收敛的,且与黏性阻尼理论计算结果近似相等;相比基于滞变阻尼理论的直接积分法,本文方法具有计算过程简单和计算量小的优点。     

计算及推算结构失稳临界荷载的方法与实测验证

分析了结构失稳时Ｐ＿δ试验曲线的图形性质；提出了以最大曲率计算及推算结构失稳临界荷载，并导出了相应的计算公式。运用压杆和刚架弹性稳定试验的实测数据，说明本文所述方法既精确又简便。特别是结构或模型不允许作破坏试验时，可直接推算失稳临界荷载。     

粘弹性结构动力稳定性分析的谐波平衡法

本文分析了线粘弹性结构的长期动力稳定特性。设材料具积分型本构关系，且其松弛模量能用Prony级数描述，将微分-积分型控制方程化成微分型方程，应用谐波平衡法确定动力稳定区域，着重讨论了材料参数及系统振动频率对动力稳定区域的影响发现该类粘弹性结构具有与一般阻尼系统不同的动力稳定特性。文中也将系统平衡法直接应用于微分-积分型控制方程，忽略卷积积分运算后产生的随时间衰减的非谐波项来得到决定动力稳定边界的特征方程，并对两种应用所得结果进行了比较。     

大型非经典阻尼系统的动态解耦方法

提出了大型非经典阻尼系统动力分析的动态解耦方法，同时在特征值问题的求解和动力响应的计算中完全避免复数运算．方法适用于无阻尼陀螺系统、非经典阻尼系统（包括阻尼陀螺系统），且不论系统亏损与否．得到了揭示阻尼作用的有趣的理论结果和实用的数值方法     

非线性动力有限元重叠区域分裂的隐式并行算法

针对大规模结构非线性瞬态动力分析非常耗时,提出了相应的并行算法。该算法采用无条件稳定的Ne-wmark-β方法(平均加速技术)进行时间积分,并结合区域分裂技术进行分析。它不同于已有的采用非重叠区域的并行算法,而是采用重叠区域的并行算法。对给定结构有限元分析的质量、阻尼、刚度矩阵进行分裂可推出重叠区域分裂算法的计算公式。为改善每一步的求解,采用预估和校正子方案。编写了该算法的程序,在工作站机群上实现了数值算例,验证了算法的性能。计算结果表明该算法优于非重叠区域分裂算法。     

粘弹性板的非线性动力稳定特性分析

采用Boltzman积分型本构关系,分析了线粘弹性薄板在考虑几何线性与非线性时的长期动力稳定特性,设材料为标准线性固体,将系统的微分一积分型控制方程转化成微分型控制方程,由增量谐波平衡法确定主要动力不稳定区域的边界,发现粘弹性结构具有与一般阻尼系统不同的动力稳定特性,由于材料的粘性阻尼与松弛效应的综合影响,动力不稳定区域有不同程度的缩小与偏移,且在考虑几何线性与非线性情形下,其影响程度又不一样。     

BAR SIMULATION METHOD FOR BENDING NORMAL STRESS OF I-BEAM IN CONSIDERATION OF SHEAR EFFECT 1)

随着工字形短深梁和宽翼缘梁结构的发展,截面非线性剪切变形对弯曲应力的影响愈加突出,导致传统设计中所采用的初等梁理论计算结果误差较大,不再适用。本文基于比拟杆法综合考虑剪切效应,推导出工字形梁横力弯曲应力解析计算公式,并与有限元及现有解析计算方法进行对比分析。结果表明：当跨高比较小,翼缘腹板面积比较大时剪切效应对弯曲变形有显著影响。同时相比于现有解析方法,本文计算结果精度较高且适用范围更广,可用于梁结构设计。     

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针对连续Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵，分析了在使用连续梁单元 进行结构动态特性分析中的数值问题. 基于连续梁单元的运动方程，导出了连续 Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵. 分析了影响动态刚度矩阵中双曲函 数自变量的各个独立变量及其产生的影响，并给出了初估连续梁单元合理长度的方法. 使用 单一连续Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵分别进行了悬臂梁频响曲线 的数值求解. 研究表明，在合理选择连续梁单元的长度时，大多数工程结构的动态特性分析 中都不会产生数值问题.     

The use of pseudo-dynamic method in the evaluation of damping characteristics in reinforced concrete beams having variable bending stiffness

The objective of this work is to determine experimentally the damping properties of concrete reinforced beams under mechanical vibrations. This is a very important property in earthquake engineering once damping provides structure energy dissipation during moderate or strong earthquake motions. The experimental campaign used the pseudo-dynamic (PsD) method to analyse the beam dynamic behaviour. Essentially the PsD test method is a hybrid computer-driven testing procedure where a numerical algorithm and experimental step are used and combined on-line in order to solve a dynamic problem. The implementation of the method is not expensive and has the leading advantage of offering the operator a total control of any intermediate structure state during the test still keeping the realism of a real dynamic testing. In this analysis the dynamic model was assumed as single degree-of-freedom system (SDOF). For the calculation of the structural damping factor, the structure stiffness was determined prior the set-up of the time integration algorithm; thereafter a pseudo-dynamic process dealing with a free and a forced vibration scheme, where this last was achieved with an external harmonic load, led to the definition of the structure response where the dissipative effect of the damping properties of reinforced concrete beams was evidenced.     

地下结构多尺度动力分析方法

近年地下结构震害频发,针对目前地下结构抗震研究中实际存在的多尺度动力问题,提出了地下结构多尺度动力分析方法,该方法不需要任何附加的过滤和阻尼就能有效地消除高频波的虚假反射. 以桥域耦合理论为基础,引入拉格朗日乘子将不同尺度区域之间的约束关系,通过能量势函数隐含到动力方程中,推导出不同尺度域的动力控制方程;基于中心差分法,提出了用于地下结构多尺度分析的动力显式算法,以求解所建立的多尺度动力耦合体系. 以实际工程为应用实例,通过与传统的位移耦合方法的对比分析,说明了该多尺度方法用于地下结构动力分析的可行性以及对消除高频波虚假反射的有效性.     

Nonlinear dynamic stability analysis of Euler–Bernoulli beam–columns with damping effects under thermal environment

In this study, a unified nonlinear dynamic buckling analysis for Euler–Bernoulli beam–columns subjected to constant loading rates is proposed with the incorporation of mercurial damping effects under thermal environment. Two generalized methods are developed which are competent to incorporate various beam geometries, material properties, boundary conditions, compression rates, and especially, the damping and thermal effects. The Galerkin–Force method is developed by implementing Galerkin method into force equilibrium equations. Then for solving differential equations, different buckled shape functions were introduced into force equilibrium equations in nonlinear dynamic buckling analysis. On the other hand, regarding the developed energy method, the governing partial differential equation for dynamic buckling of beams is also derived by meticulously implementing Hamilton’s principles into Lagrange’s equations. Consequently, the dynamic buckling analysis with damping effects under thermal environment can be adequately formulated as ordinary differential equations. The validity and accuracy of the results obtained by the two proposed methods are rigorously verified by the finite element method. Furthermore, comprehensive investigations on the structural dynamic buckling behavior in the presence of damping effects under thermal environment are conducted.     

钢-混凝土组合梁负弯矩区畸变屈曲弯矩计算公式

侧向弯曲屈曲及侧向弯扭屈曲均为钢-混凝土组合梁负弯矩区钢梁的重要屈曲模式,而现有计算方法通常只考虑到侧向弯曲屈曲,未考虑到侧向弯扭屈曲,因此有一定局限性。本文在钢梁腹板对钢梁下翼缘的转动约束刚度及侧向约束刚度的计算公式上,结合弹性介质中薄壁杆件的屈曲理论推导了工形钢-混凝土组合梁负弯矩区的侧向弯曲屈曲弯矩及侧向弯扭屈曲弯矩计算公式。实例分析表明,现有计算方法均存在一定理论缺陷,本文计算方法更为合理;同时,本文计算式比现有文献中同类型计算式更为简洁,便于手算,实用性强并适于工程应用。     

多种非线性力作用下不平衡弹性转子的分岔特性

研究了4自由度不平衡弹性转子在非线性油膜力、非线性内阻力和非线性弹性力联合作用下的动力学特性。结果表明，当只有非线性油膜力作用时，转子只存在由于油膜失稳而导致的倍周期分岔。而当非线性油膜力与非线性内阻力共同作用时，在油膜失稳后，转子产生低频振动。转速继续增加，还会诱发内阻失稳，产生概周期运动。在倍周期分岔中，存在分岔激变现象。本文发现的由于油膜涡动而导致的内阻失稳(概周期运动)是一种未见报道的转子失稳模式(组合失稳)，它与油膜失稳(倍周期运动)一起可作为转子故障诊断的典型失稳模式。     

Explicit computational method of dynamic response for non-viscously damped structure systems

Non-viscous damping models in which the damping forces depend on the past history of velocities via convolution integrals over some kernel functions have been raised in many engineering fields. This paper describes an explicit computational method of dynamic response for the non-viscously damped structure systems. The explicit formula is derived using the differential property of convolution and the central difference formula of acceleration. The explicit computational procedure of dynamic response is given in detail. Finally, the dynamic responses of MDOF structure system with double exponential model dampers and SDOF structure system with Gaussian model damper are computed using the proposed explicit method. The accuracy and efficiency are discussed by comparison with other two developed methods.     

阻尼对空爆荷载等效静载动力系数的影响

为考查阻尼参数对空爆荷载等效静载动力系数的影响,理论推导了空爆荷载下结构等效单自由体系弹塑性位移解及延性比解,设计并计算了阻尼比0.000 1～0.1、延性比1～4的20种典型工况的动力系数,并与现行抗爆设计规范动力系数公式结果进行了对比。结果表明:阻尼比小于0.000 1时可基本代表无阻尼状态,阻尼比0.01的动力系数比无阻尼的最大降低幅度为2.08%,数值差异很小,因此阻尼比为0.01以内时,可忽略阻尼对动力系数的影响;阻尼比0.05的动力系数比无阻尼的降低幅度约9.92%,数值差异较大,认为阻尼比0.05以上时将具有明显的经济效益;现行设计规范动力系数更适用于柔性结构体系,运用于刚性结构抗爆设计时,计算误差较大,对阻尼比较小的结构设计更不利。     

Design and dynamic performance research of MR hydro-pneumatic spring based on multi-physics coupling model

Aiming at the problem that the damping coefficient of the traditional hydro-pneumatic spring cannot be adjusted in real-time, the magnetorheological (MR) damping technology was introduced into the traditional hydro-pneumatic spring with single gas chamber. A new shear-valve mode MR hydro-pneumatic spring was proposed. And its dynamic performance was analyzed based on multi-physical coupling simulation and mechanical property test. Firstly, a structural scheme of MR hydro-pneumatic suspension was proposed to ensure the original height adjustment function based on the working principle of traditional hydro-pneumatic suspension with single gas chamber. Secondly, based on the design requirements, the parameter of MR hydro-pneumatic spring damping structure was designed by using MR damper design method. Thirdly, the multi-physical coupling dynamic performance of the MR hydro-pneumatic spring damping structure was analyzed based on the electromagnetic field analysis theory, flow field analysis theory and thermal field analysis theory. The analysis results showed that the designed MR hydro-pneumatic spring has reasonable magnetic circuit structure and excellent working performance. Then, the mechanical properties of MR hydro-pneumatic spring were tested. The results showed that the maximum damping force can reach 20 kN, and the dynamic adjustable multiple can reach 6.4 times. It has good controllability and meets the design requirements. Finally, a nonlinear model of MR hydro-pneumatic spring was established based on the elastic force calculation model of the gas and the Bouc–Wen model. The simulation results of the established model agree well with the experimental results, which can accurately describe the dynamic properties of the hydro-pneumatic spring. The proposed design and modeling method of the MR hydro-pneumatic spring can provide a theoretical basis for the related vibration damping devices.