单轴扫频诱发帆板同步钢索旋转振动分析

为明确某帆板面内单轴扫频力学环境试验中同步钢索振动幅度过大和限位结构被破坏的原因,考虑集中质量和限位结构影响,采用有限段方法建立帆板同步钢索系统的动力学模型,对其在面内单轴扫频激励条件的响应进行数值模拟,结果再现了标志点的响应从面内振动发展到面外振动,再到绕两支撑点轴旋转振动的复杂振动模式,同时给出限位接触力和钢索标志点振幅,仿真结果与试验状态吻合。分析表明,持续旋转振动钢索施加在限位孔壁上的交变接触力是导致限位结构破坏的主要原因。     

热弹耦合偏微分方程的解

利用已有的Galerkin方法,对具有非线性项热弹耦合梁初边值问题进行了研究,证明了其在非线性边值条件下解得存在性,为其在力学方面的发展提供了理论基础。     

高压输电导线非线性振动分析

为研究高压输电线路导线由几何非线性引起的非线性振动特点,采用扩展的Hamilton原理建立水平悬垂输电导线的三维运动方程,并将其约化为二维振动方程,应用Galerkin方法对其进行模态截断,得到有限自由度的离散运动方程,然后使用四阶的Runge-Kutta方法对离散方程进行数值求解,得到了导线在简谐激励作用时的面内响应和面外响应.数值分析结果表明:当考虑由垂度引起的几何非线性因素时,输电导线不仅会发生主共振,还会发生次谐波共振和超谐波共振,且面外振动与面内振动之间由于发生密频内共振致使输电导线在实际振动中发生能量传递,引起非直接受激的面内产生大幅振动,同时非线性振动也会对线路振动产生调频作用.     

Mapping analysis of vibrating fundamental frequency for simple-supported elastic rectangle-plates with concentrated mass

By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of fundamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.     

Mapping analysis of vibrating fundamenta frequency for simple-supported elastic rectangle-plates with coneentrated mass

By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of ftmdamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.     

Calculation of natural circulation under heaving motion

Wide validation of self-developed program of natural circulation under oceanic conditions has been conducted compared with experimental data of inclination,zero-power condition and hot-state condition.Experiments were performed on a full-scale,whole parameterization natural circulation loop designed with reference to 5 MW experimental low temperature nuclear heating reactor(NHR)of Tsinghua University.Investigation of natural circulation and parameter effect under heaving motion was carried out using the program and comparison of heaving,inclination and rolling on natural circulation respectively to reveal the influence mechanism.Results indicate that:(1)significant influence of heaving motion on natural circulation was observed,and heaving motion with high level of strength and long cycle would lead to severe flow fluctuation;(2)slight effect was caused by short cycle heaving motion which was completely different from long cycle heaving motion;(3)comprehensive action of alternating force and flow density distribution would result in natural circulation under heaving motion;(4)most severe accidents maybe result from the long cycle heaving motion rather than inclination and rolling motion.Investigation of influence of heaving motion on natural circulation could have important reference significance in the optimization design of nuclear reactors.     

Conformal analysis of fundamental frequency of vibration of simple-supported elastic ellipse-plates with concentrated substance

Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipseplates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant inplane stress, as well as the concentrated substance mass and positions are analyzed respectively.     

Conformal analysis of fundamental frequency of vibration of simple-supported elastic ellipse-plates with concentrated substance

Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elasticplates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipseplates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant inplane stress, as well as the concentrated substance mass and positions are analyzed respectively.     

轴向运动屈曲梁非线性振动研究

为解决屈曲梁在不同的激励条件下产生共振问题,基于哈密顿原理建立屈曲梁的振动模型以及非线性偏微分振动方程和边界条件,通过数值模拟分析了屈曲梁在相平面的动态特性.采用多模态伽辽金离散法预测静态弯曲参数,通过局部分析获得某一个弯曲附近处的非线性近似响应,并得出有效的非线性表达式和频率响应曲线.     

波节管固有频率计算方法的研究

将波节管简化成附有,1个集中质量且具有相同抗弯刚度的等截面直管,通过填补法对波节管进行单元离散化,采用旋转壳的分段积分法计算,利用里茨法进行波节管的特征值分析,计算得到波节管弯曲振动的前二阶固有频率．并用得到的结果与有关文献进行对比,结果证明该分析方法的有效性与准确性．     

带有集中质量矩形板的振动分析

工程实际中有许多附有集中质量薄板结构,如船舶甲板、悬挂油箱机翼及房屋建筑楼板等,针对这类结构动力学问题,建立了带有集中质量矩形薄板的力学模型,该模型可作用任何类型载荷.运用约束模态分析法分析了有集中质量矩形薄板特征值及振型,并给出了薄板振动响应计算公式.研究结果表明,集中质量在板上某些特定位置起到了刚度强化作用,提升了薄板振动自然频率,该结果可用于实际工程中薄板振动主动控制的研究.     

玻璃采光顶预应力索桁架支承体系动力特性

为了提供玻璃采光顶预应力索桁架支承体系抗风和抗震研究的理论基础,寻求其动力特性主要影响因素及影响量,采用连续化理论研究了其动力特性.以圆形平面玻璃采光顶预应力索桁架支承体系为例,考虑温度变化及几何非线性影响,基于动力学理论建立了该体系非线性振动方程.通过Galerkin方法,将偏微分方程转化为常微分方程,并采用LP法及KBM法对常微分方程进行了求解.结合算例讨论了温度变化、振幅、外激励等因素对玻璃采光顶预应力索桁架支承体系非线性振动的影响.算例表明,预应力索桁架支承体系固有频率随着温度的升高而减小,其自振频率随着振幅发生变化,非线性振动呈现“硬弹簧”特性,非线性自振频率高于线性振动频率,在简谐荷载激励下的稳态振动是稳定的周期运动.     

汽车喇叭膜片结构参数分析

针对解决汽车喇叭声级不足,喇叭膜片在寿命期内碎裂等问题,建立了汽车喇叭膜片组件的振动模型,并给出了通过调整膜片结构参数使膜片组件的固有频率及膜片工作时的应力分布达到理想状态的方法,研究了膜片工作中裂纹产生的原因,并给出了如何通过合理设计膜片结构参数来提高膜片使用寿命的方法,提出了对应膜片组件固有频率的结构参数合理范围和...     

材料及结构参数对基桩非线性纵向振动的影响

假设嵌岩桩桩身材料满足非线性弹性和线性粘弹性本构关系，桩周土为有阻尼非线性弹性土体，从而导出了分析基桩非线性纵向振动的偏微分方程；用Galerkin方法对方程进行简化，对简化后的系统进行了数值模拟计算，得到了一种典型参数情形时基桩运动的时程曲线、相平面图、功率谱图、Poincare截面图及分又混沌图，考察了各种材料及结构参数对基桩非线性纵向振动的影响。     

索结构风雨振的周期运动及混沌运动动力学

研究了带有运动上水线的两个自由度的索结构风雨振动力学模型。对原系统非线性部分进行5阶泰勒展开,得到了简化形式的常微分方程。利用多尺度法分析了索结构风雨振系统,得到了系统具有稳态解的条件,同时利用数值法得到了索结构和水线的运动相图及其随时间变化曲线。通过对系统李雅普诺夫指数的计算,发现了该系统存在倍周期、概周期运动以及混沌运动现象。借助计算机代数语言Mathematica程序研究了参数变化对系统的周期运动和混沌运动的影响。     

波浪荷载下粉质土动应变和动强度的试验研究

为寻找不同振动频率的波浪荷载作用下海底粉质土的动应变和动强度发展规律,进行了一系列的模拟不同振动频率的波浪荷载的动三轴试验.试验选用杭州湾地区分布较广的粉土,研究了振动频率的变化对粉土动应变和动强度的影响.试验结果表明,粉土的动应变和动强度的发展与土样所受的固结应力、围压、循环应力比和振动频率有关;在等向固结条件下围压对土样的累积轴向应变增长的影响作用是由波浪荷载振动频率的高低决定的;波浪荷载振动频率的改变对不同围压作用下粉土的动强度影响很大,并且在该类粉土中存在临界循环应力比.     

二阶效应的压弯构件振动分析

采用结构振动理论和二阶理论对压弯构件的振动进行了分析,求解构件的二阶自振频率和主振型,并对均匀简谐荷载作用下压弯构件的强迫振动进行了讨论。结果表明,二阶效应将对构件的位移和内力产生极为不利的影响。     

拱坝非线性全调整分载法研究

基于拱坝全调整拱梁分载法的基本原理,导出材料非线性条件下的拱梁刚度方程,给出了裂缝扩展的判别与跟踪方法,并在分载法框架下研究裂缝对拱,梁应力应变的影响,形成了非线性全调整分载法。算例表明文中所述方法可行,计算结果合理,该成果可模拟拱坝在超载或材料缺陷条件下的非线性变形,开裂,裂缝扩展直至压碎破坏的全过程,可用于评估拟建和已建拱坝的安全度。     

碳纤维斜拉索的动力参数特性分析

为探索碳纤维(CFRP carbon fiber reinforced polymer)索本身的动力学行为,寻求影响CFRP索自振频率的主要因素及影响量.采用悬链线索单元分析CFRP单索结构的自振频率与相应振型随单索的垂度及索结构参数的变化规律,在理论推导的基础上,通过具体算例将分析计算得到的结果与频率法测试索力的结果进行了对比。分析结果表明:CFRP斜拉索随着垂度的增大,一阶振型由单波正对称向反对称过渡;当斜拉索的垂跨比处在不同范围内时,CFRP索与钢索的自振频率差值也有所变化;因CFRP拉索垂度小,采用频率法计算索力产生的误差可以满足工程精度要求。因此,合理设置CFRP索身的垂度能有效地避免索身在外荷载作用下产生的一系列不利振动.     

单层球面网壳风振分析的多模态效应

为研究网壳结构风振响应的主要贡献模态分布规律及模态耦合效应,有利于提高结构风振响应的计算效率,利用Ritz-POD法,综合考虑各结构振型自身参振能力的强弱及其与脉动风压空间分布模式之间的关系来识别单层球面网壳风振的主要贡献模态;利用模态广义位移协方差矩阵的特性分析其模态耦合效应.结果表明,单层球面网壳存在高阶主要贡献模态,该高阶振型通常处于结构自振频率发生突变的位置;网壳结构的风振响应以模态自相关为主,模态耦合效应相对较弱,对结构动力响应的影响大致为10%.