DYNAMIC RESPONSE OF ELASTIC RECTANGULAR PLATES BY SPLINE STATE VARIABLE METHOD

Application of spline element and state space method for analysis of dynamic response of elastic rectangular plates is presented. The spline element method is used for space domain and the state space method in control theory of system is used for time domain. A state variable recursive scheme is developed, then the dynamic response of structure can he calculated directly. Several numerical examples are given. The results which are presented to demonstrate the accuracy and efficiency of the present method are quite satisfactory.

THE GENERAL SOLUTION FOR DYNAMIC RESPONSE OF NONHOMOGENEOUS BEAM WITH VARIABLECROSSSECTION

In this paper by means of the exact analytic method [1], the general solution fordynamic response of nonhomogeneous beam with variable cross section is obtained un-der arbitrary resonant load and boundary conditions. The problem is reduced to solvea non-positive differential equation. Generally, it is not solved by variational method.By the present method, the general solution for this problem may be written as an ana-lytic form. Hence, it is convenient for structure optimizing problem. In this paper, itsconvergence is proved. Numerical examples are given at the end of the paper. which in-dicates satisfactory results can be obtained.

Quantum Mechanics: Harmonic Wave-Packets, Localized by Resonant Response in Dispersion Dynamics

From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.

λ-PDF AND GEGENBAUER POLYNOMIAL APPROXIMATION FOR DYNAMIC RESPONSE PROBLEMS OF RANDOM STRUCTURES

A bounded,mono-peak,and symmetrically distributed probability density function, called λ-PDF,together with the Gegenbauer polynomial approximation,is used in dynamic response problems of random structures.The λ-PDF can reasonably model a variety of random parameters in engineering random structures.The Gegenbauer polynomial approximation can be viewed as a new extension of the weighted residual method into the random space.Both of them can be easily used by scientists and engineers,and applied to a variety of response problems of random structures.The numerical example shows the effectiveness of the proposed method to study dynamic phenomena in random structures.

Numerical Simulation of Dynamic Response of Supple Nets

A simulation method based on the lumped mass model is proposed for determining the dynamic behavior of nets exposed to a uniform current. Every mesh bar is modeled by a linear bar clement. The lumped mass point is set at the ends of each element. The net can be simulated by a discretized model consisting of many point masses and elements without mass. 3D shapes and the distribution of tensions of the net at different moments can be found from time integration of a set of motion equations with a computer program. Two nets are simulated according to reference experiments. Calculated results are in accordance with experimental results. The method is applicable and can be applied to improving design of, and research into other flexible structures, such as net cages.

Dynamic Response Analysis of the Equivalent Water Depth Truncated Point of the Catenary Mooring Line

The real-time computer-controlled actuators are used to connect the truncated parts of moorings and risers in the active hybrid model testing system. This must be able to work in model-scale real time, based on feedback input from the floater motions. Thus, mooring line dynamics and damping effects are artificially simulated in real time, based on a computer-based model of the problem. In consideration of the nonlinear characteristics of the sea platform catenary mooring line, the equations of the mooring line motion are formulated by using the lumped-mass method and the dynamic response of several points on the mooring line is investigated by the time and frequency domain analysis method. The dynamic response of the representative point on the mooring line is analyzed under the condition of two different corresponding upper endpoint movements namely sine wave excitation and random wave excitation. The corresponding laws of the dynamic response between the equivalent water depth truncated points at different locations and the upper endpoint are obtained, which can provide technical support for further study of the active hybrid model test.

Dynamic Analyses of a Simply Supported Double-Beam System Subject to a Moving Mass with Fourier Transform Technique

In order to study the dynamic characteristics of a simply supported double-beam system under a moving mass,the system of fourth-order dynamic partial differential equations of a simply supported double-beam system was transformed into a system of second-order dynamic ordinary differential equations relative to time coordinates by performing the finite sin-Fourier Transform relative to space coordinates.And the analytical solution of the dynamic response of the simply supported double-beam system under a moving mass was obtained by solving the system of dynamic ordinary differential equations.The analytical method and ANSYS numerical method were used to calculate the dynamic responses of several simply supported double-beam systems under a moving mass at different speeds.The influences of inertial effect,mass movement speed,and Winkler-layer spring stiffness and damping on the dynamic responses of simply supported double-beam systems were analyzed.According to the study results,the analytical calculation results in this paper fit well with the ANSYS finite element numerical calculation results,demonstrating the rationality of the analytical method.The inertial effect has a significant influence on the dynamic response characteristics of the simply supported double-beam system.The simply supported double-beam system underwent several resonant speeds under a moving mass,and the Winkler-layer spring stiffness has a relatively significant effect on the vibration of the first beam.

Dynamic discrete element method and its application in rock mass engineering

Based on conventional discrete element method, the idea and calculating method of dynamic discrete element (DDEM) was proposed, and a relevant program was developed. The application of the method is presented in rock mechanics and engineering, which indicates that the method can be widely used in dynamic response and stability analysis of jointed rockmass under dynamic load. [

The Vibration of Partially Filled Cylindrical Tank Subjected to Variable Acceleration

In this study, the vibration of a cylindrical tank partially filled with liquid under motion modeled as mass lumped is investigated. A three-dimensional quasi-static model of a partially-filled tank of circular cross-section is developed and integrated into a comprehensive three-dimensional vehicle model to study its dynamic performance as a function of acceleration, and the fill volume. The liquid load movement occurring in the roll and pitch planes of the tank is derived as a function of the longitudinal acceleration, and then the corresponding shifted load is expressed in terms of center of mass coordinates and mass moments of inertia of the liquid bulk, assuming negligible influence of fundamental slosh frequency and viscous effects. The vibration characteristics of the partially filled tank vehicle are evaluated in terms of load shift, forces and moments induced by the cargo movement, and dynamic load transfer in the longitudinal direction. The semi analytical response is obtained by means of SimuLink? Matlab Software. The effects of longitudinal acceleration of the tank system on the liquid surface inclination and consequently shifting of centroids and moment of inertia are illustrated.

Experimental Investigation of Multi-Mode Vortex-Induced Vibration of Flexible Risers with Different Mass Ratios

Experiments were conducted on risers with different mass ratios to study the effect of mode conversion and spanwise correlation. The slenderness ratio of the riser model was set as 169, and the Reynolds numbers are 1600-14400. The dynamic responses of riser models versus reduced velocity were analyzed, and the spanwise displacement, frequency,and trajectory of the mode conversion from the lower to the higher mode were explored. The results revealed that the riser model with a higher mass ratio excites a higher number of modes. The conversion region of multi-mode competition exists and narrows with the increasing mass ratio. Mode conversion is continuous and manifests as the transmission of peaks and troughs in mode shape: the peaks and troughs of mode shape move up in the mode stable development region and move down in the mode conversion region. The single-mode dominating vibration exhibits a standing wave feature, and the traveling wave feature is significant in the mode conversion region. Furthermore, the frequency jump is always transmitted from the trough to the peak of the mode shape, and finally, all the axial positions vibrate at the same frequency. The trajectory in the mode conversion region deviates from the 8-shape and recovers the standard8-shape at the middle and late stages of the mode stable development region.

地震作用下变截面钢管混凝土单桩动力响应

为了探讨桥梁位于软弱土层时,地震作用下变截面钢管混凝土桩基的动力响应,以翔安大桥为工程背景,利用FLAC3D有限元软件建立地震作用下桩-岩土体-钢管耦合作用的数值模型,研究在不同强度的地震作用下变截面钢管混凝土单桩和变截面普通混凝土单桩桩身加速度、桩身位移、桩身弯矩的动力响应差异.结果表明:变截面钢管混凝土单桩在地震作用下的桩身加速度、加速度放大系数、桩身位移最大值和桩身弯矩变化规律均同变截面普通混凝土单桩类似,但钢管使桩身加速度放大系数降低、桩基抵抗侧向变形能力和抗弯承载力提高.因此,钢管可以显著提升地震作用下桩基的抵抗变形能力和承载力.

液化场地大直径变截面单桩动力响应研究

为研究不同地震动强度下液化场地大直径变截面单桩的动力响应规律,基于振动台试验,选取5010波,在地震动强度0.10g~0.45g作用下,研究液化场地砂土孔压比和大直径变截面单桩桩顶水平位移、桩身弯矩、桩身加速度时程响应及桩基损伤等变化规律.试验结果表明:饱和砂土孔压比随着地震动强度的增大上升明显,地震动强度≥0.30g时,饱和砂土孔压比稳定值在0.9附近,此时砂土完全液化;在0.45g地震动强度作用下,桩身加速度、桩顶水平位移及桩身弯矩均达到最大;桩身不同位置处加速度峰值出现时刻均滞后于输入地震波加速度峰值出现时刻,且桩顶及变截面的加速度响应比桩端的响应更弱;不同地震动强度作用下,桩身弯矩最大值均出现在液化土层和非液化土层分界处,且变截面处弯矩小于土层分界面处;地震动强度达到0.30g时,大直径变截面单桩桩身发生损伤.因此,液化场地下大直径变截面桥梁单桩基础抗震设计时,应该重点考虑饱和砂土层分界处、变截面处的抗弯能力,以确保单桩桩身强度满足抗震要求.

震陷土层变化下变截面单、群桩动力响应差异

为研究地震动作用下震陷土层厚度不同时大直径变截面单桩与群桩基础的动力响应差异,依托厦门第二东通道翔安大桥,通过振动台模型试验,开展震陷土层厚度30、40、50 cm时,单桩与群桩基础桩周土震陷量、桩顶水平位移、桩身加速度及弯矩动力响应差异研究.结果表明:随着震陷层厚度增大,单桩与群桩基础桩周土震陷量、桩顶水平位移、桩身加速度及弯矩均逐渐增大,且加速度及弯矩在变截面处突变;同一震陷层厚度下,群桩基础桩周土震陷量较单桩大,但群桩基础加速度、桩顶水平位移及桩身弯矩均小于单桩.震陷场地桩基础设计时,应着重考虑变截面单桩与群桩动力响应差异,保证桩基础抗震性能.

小车运行状态下岸桥结构动力响应分析

本文对在役岸桥整机金属结构的动力学响应机理进行分析。基于Euler-Bernoulli梁理论建立起重机单梁结构数值模型,分析不同工况对梁结构动力响应的影响,并分析动力学方程中“离心加速度项”对岸桥的动力学响应的影响。利用一岸桥结构数据建立包含结构重要分析部位如铰点、轨道梁等结构的几何特征的整机精细化数值模型。以简化质量点模拟小车,将质量与板壳单元接触,实现小车与大梁的相互作用,并应用于岸桥结构动力学分析中,考虑轨道梁非中心受力,计算得到大梁铰点的加速度响应,与实测信号结果基本一致。经计算分析发现,岸桥大梁铰点处测点的加速度实测信号频谱和计算信号频谱均表明小车运行对岸桥结构的主要影响为经过轨道接头时产生的高频冲击。同时,岸桥模型大梁上10个测点及小车的位移结果表明,当小车带额定载荷以额定速度匀速运行时,岸桥前大梁前端产生垂向拟静态位移,位移频谱表明小车主要受到垂向强迫振动。

连续梁桥跳车冲击下车桥耦合振动响应分析

为研究车辆在不同工况下发生跳车对变截面连续梁桥动力响应的影响,文章选用1/4车辆模型,采用D’Alembert原理建立车辆振动平衡方程;基于Euler-Bernoulli梁理论将变截面连续梁划分成多个微段并进行受力分析,建立桥梁振动平衡方程,采用模态坐标法考虑振型的正交性对方程进行简化,与车辆振动方程联立得到车桥耦合振动方程,最终理论推导出跳车冲击过程中的车桥耦合振动平衡方程;利用MATLAB自编程序求解车桥耦合振动方程,得出车桥耦合动力响应。研究表明:当跳车高度不断增加时,桥梁动力响应持续加重,位移最大值逐渐增加;当不同桥跨跨中发生跳车时,跳车跨位移响应最大,距离跳车跨越远,位移响应越小。

基于变刚度悬臂梁的MEMS静电驱动器的动态响应优化

传统的微机电系统(MEMS)静电驱动器存在驱动电压高和超调振荡的问题,可动极板稳定在平衡位置前会发生持续的振荡,难以满足可变电容、光开关等应用领域的综合要求。针对上述问题,采用变刚度悬臂梁的设计,利用刚度随行程增大的特性抑制了极板吸合及释放过程的振荡现象,在缩短调节时间的同时,有效降低了器件的驱动电压。仿真和实验结果表明,当器件悬臂梁的刚度随位移由5N/m增大到35N/m时,在相同电压下,动态响应的调节时间减少了55.5%,在相同行程下,动态响应的调节时间减少了21%,对应的驱动电压减少了23%。

化零为整的宏观社会数据生成:基于潜变量模型和动态贝叶斯方法

对因果机制和对宏观检验的探寻催生了定量社会学研究对区群层面数据的需求,然而这类高质量的追踪数据资源相对稀缺。传统研究通常通过综合多个来源的个体社会调查数据来构建面板数据集以改善宏观数据匮乏现状,但其亦受制于社会调查在时间和空间分布上的稀疏性以及不同调查间的差异性。本文引介了一种可用于生成区群层面跨时空面板数据的动态贝叶斯潜变量建模框架,并通过应用实例展示了该方法的具体应用过程,比较了动态贝叶斯方法相较于几种常用的缺失值插补方法的优势。本文的示例结果表明,动态贝叶斯潜变量模型在跨时空、多维度的信息整合和参数不确定性探索方面具有重要的优势,可以实现对调查数据缺失年份或地区的估计和插补,大大缓解了社会学研究中面板数据不足的问题。

无砟轨道泡沫混凝土路基碎石夹层结构动力特性试验研究

为研究无砟轨道泡沫混凝土路基碎石夹层结构的动力特性和长期动力稳定性,建立夹层结构足尺试验模型,开展变频加载和循环加载试验。研究结果表明,在变频动载作用下,夹层结构的振动加速度、动位移和动土压力呈增大规律但无峰值出现,表明夹层结构未产生共振现象;为降低加载频率对比值系数的影响,建议采用底座板与路基面之间振动位移比值系数作为基床或级配碎石夹层对无砟轨道结构支承状态分析的判据。循环动载作用下,夹层结构的振动加速度、动位移和动土压力在加载至100万次后趋于稳定;相较传统土石填料路基,泡沫混凝土层能更好地均化上部荷载;经200万次动载作用后,试验模型总累积沉降为0.898 mm,碎石夹层的压缩变形占总累积沉降的82.9%。试验结果表明,在无砟轨道结构与泡沫混凝土层之间设置厚度为0.7 m的级配碎石夹层,可为线路提供平顺性和稳定性。

公路护栏中金属空心球泡沫铝防撞性能的研究

以泡沫铝应用于公路护栏,降低碰撞过程中的损害为背景,采用金属铝作为基体材料建立金属空心球泡沫的计算模型,通过数值模拟计算方法分析了金属空心球泡沫的动力学响应特性。重点讨论了冲击载荷作用下,不同密度金属空心球在空间的不同分布形式对金属空心球泡沫铝载荷一致性的影响。研究结果表明,将不同密度金属空心球在空间合理分布,即高密度质量和低密度质量交替排列分布的方式不会影响金属空心球泡沫的基本力学性能,同时能够有效提高金属空心球泡沫的载荷一致性。

质量参数对空爆荷载梁构件振动位移的影响

为研究质量参数对空爆荷载梁构件振动位移的影响,以等效单自由度法为基本方法,理论推导了柔性及刚性2类梁构件含质量参数在弹性、塑性各阶段的振动位移解,选择矩形截面、圆截面为梁构件典型截面,设计并计算了质量参数在1.00~1.20范围内的13种典型工况。结果表明:对于空爆荷载柔性及刚性2类梁构件,增大其截面面积后,仅考虑质量参数计算振动位移时误差较大,应按质量参数及产生的附加刚度参数耦合效应分析;对于矩形截面梁构件,采用质量参数与刚度参数耦合计算时,其最大弹性位移、最大弹塑性位移和残余变形降低幅度分别约为仅采用质量参数计算结果的4.75、3.28和2.96倍;对于圆截面梁构件,则分别为3.57、2.56和2.32倍;该结论在柔性梁构件及刚性梁构件均适用且无明显差异。