声学黑洞结构应用中的力学问题

声学黑洞(acoustic black hole,ABH)效应是利用薄壁结构几何参数或者材料特性参数的梯度变化,使波在结构中的传播速度逐渐减小,理想情况下波速减小至零从而不发生反射的现象.实现声学黑洞效应的主要方法是将薄板结构的厚度按照一定规律裁剪,利用声学黑洞可以将结构中传播的波动能量聚集在特定的位置.声学黑洞对波的聚集具有宽频高效、实现方法简单灵活等特点,在薄壁结构的减振降噪、能量回收等应用中具有明显的优势.本文介绍声学黑洞效应的基本原理、相关力学问题的研究进展和有待进一步探究的问题,包括声学黑洞结构的建模与分析方法、实验研究方法及进展、声学黑洞结构中波的传播与操控,以及声学黑洞在工程应用中的相关问题.     

计算气动声学的问题、方法与进展

本文简要介绍了气动声学理论的发展和现状,探讨了用数值方法处理气动声学问题的必要性和必然性,指出此方面研究急待解决的问题是建立准确模拟波运动特征的差分方程和无反射边界条件处理,最后讨论了在有限条件下可作先行研究的数值方法和理论问题．     

柔性电子器件的应用、结构、力学及展望

新的结构布局在延展性要求极高的器件中具有很大的应用潜力, 而使用较成熟的刚性技术制成的器件很难达到延展性要求. 将柔性技术应用到刚性电路中产生具有相同性能且能拉伸、压缩和弯曲的柔性集成电路, 这在健康监测器和表皮电子系统等领域具有重要的应用. 优化柔性电路结构, 研究其力学性能能提高系统的延展性. 本文对这些系统的应用、柔性电路的结构布局、力学行为进行总结概述. 最后, 就柔性电子器件未来研究的方向提出几点观点.     

层状弹性体系力学及其应用

层状弹性体系力学是弹性力学的一个分支。首先介绍层状弹性体系力学的发展历史。其次介绍$N$层弹性体系的力学分析与计算,内容包括基本假定、应力和位移分量的表达式、定解条件、根据定解条件建立求解积分常数的线性代数方程组、由线性代数方程组求解积分常数、贝塞尔函数的计算、积分计算公式、数值积分、后续的力学计算以及计算算例。最后介绍层状弹性体系力学在科学研究和工程设计中的应用。     

谈谈弹塑性力学中的简化问题

讨论了弹塑性力学中的基本假设、本构模型和简化分析方法. 指出在这一领域中, 简化是非常重要的和必需的.     

岩土力学与地下工程结构分析计算的若干进展

本文扼要介绍了岩土力学和地下工程结构分析计算方面近年来的若干进展，主要只对作者在课题研究中所接触到的一些工作进行综合性阐述，而未求涉猎该一子学科领域中所有问题。本文的主要内容包括：岩土力学学科的若干进展；几种有前景的数值方法；计算机科学在岩土力学与地下工程中的采用和地下结构的抗震动力分析计算研究。     

粘接双材料界面微区内力学行为的细观实验分析

本文将显微光栅与显微测距技术结合起来，实现了物体表面位移场的细观测量。应用这一方法，本文定量地测量了高分子粘接结构界面及周围区域的变形和应变，实验发现界面两侧存在着一个影响区，在影响区内材料的力学性质发生了变化。本文在实验结果的基础上讨论和分析了这一变化并对界面的力学模型进行了讨论。     

非饱和土土力学工程应用方法

通过引入文[1]提出的广义朗肯土压力计算公式,本文针对非饱和土主动(被动)土压力计算问题提出了工程应用方法,能够把非饱和土土压力理论应用于实际工程。该方法可以推广到非饱和土地基承载力、边坡稳定等其他领域,从而为非饱和土土力学理论应用于工程实践提供了一个新的思路。     

弹性力学问题复变函数解法的应用与发展

对利用复变函数法求解弹性力学问题在过去100年中的发展进行了简要综述,介绍了自1909年Kolosov提出复应力函数法以来的弹性力学复变函数解法相关的几本具有影响的经典专著或教科书、复变函数方法在弹性问题壳体和空间问题的拓展,以及近些年来在解决更多力学问题上的新发展和新应用等.     

几种逻辑方法在力学竞赛辅导中的应用

针对力学竞赛内容不同于学校考试型题目的特点,在力学竞赛辅导中采用科学方法论中的几种逻辑方法, 不仅可以提高辅导质量, 激发学生的学习兴趣;而且学生能熟练地利用这些方法来解决实际计算问题.     

Mechanics problems in application of acoustic black hole structures

声学黑洞(acoustic black hole,ABH)效应是利用薄壁结构几何参数或者材料特性参数的梯度变化,使波在结构中的传播速度逐渐减小,理想情况下波速减小至零从而不发生反射的现象.实现声学黑洞效应的主要方法是将薄板结构的厚度按照一定规律裁剪,利用声学黑洞可以将结构中传播的波动能量聚集在特定的位置.声学黑洞对波的聚集具有宽频高效、实现方法简单灵活等特点,在薄壁结构的减振降噪、能量回收等应用中具有明显的优势.本文介绍声学黑洞效应的基本原理、相关力学问题的研究进展和有待进一步探究的问题,包括声学黑洞结构的建模与分析方法、实验研究方法及进展、声学黑洞结构中波的传播与操控,以及声学黑洞在工程应用中的相关问题.     

Improvement of the acoustic black hole effect by using energy transfer due to geometric nonlinearity

Acoustic Black Hole effect (ABH) is a passive vibration damping technique without added mass based on flexural waves properties in thin structures with variable thickness. A common implementation is a plate edge where the thickness is locally reduced with a power law profile and covered with a viscoelastic layer. The plate displacement in the small thickness region is large and easily exceeds the plate thickness. This is the origin of geometric nonlinearity which can generate couplings between linear eigenmodes of the structure and induce energy transfer between low and high frequency regimes. This phenomenon may be used to increase the efficiency of the ABH treatment in the low frequency regime where it is usually inefficient. An experimental investigation evidenced that usual ABH implementation gives rise to measurable geometric nonlinearity and typical nonlinear phenomena. In particular, strongly nonlinear regime and wave turbulence are reported. The nonlinear ABH beam is then modeled as a von Kármán plate with variable thickness. The model is solved numerically by using a modal method combined with an energy-conserving time integration scheme. The effects of both the thickness profile and the damping layer are then investigated in order to improve the damping properties of an ABH beam. It is found that a compromise between the two effects can lead to an important gain of efficiency in the low frequency range.     

The mutual variational principle of free wave propagation in periodic structures

By taking infinite periodic beams as examples, the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propagation constant in the present paper, and the corresponding hierarchical finite element formulation is then derived. Thus, it provides the numerical analysis of that problem with a firm theoretical basis of variational principles, with which one may conveniently illustrate the mathematical and physical mechanisms of the wave propagation in periodic structures and the relationship with the natural vibration. The solution is discussed and examples are given. Supported by Doctorate Training Fund of National Education Commission of China     

柱状药包爆炸应力场及在地下中深孔爆破中的应用

针对球形集中药包理论指导中深孔爆破设计时与实际情况严重不符的现状,设计了2种实验模型,采用全息激光动光弹法进行了模型实验,研究了球形药包与柱状药包爆炸应力场、柱状药包在不同起爆位置时的爆炸应力场.将实验结果与现场实际情况相结合,通过对排距(最小抵抗线)、孔底距和炸药在孔内起爆位置进行的44排拟水平现场正交实验,确定了合...     

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

In this research, vibration and wave propagation analysis of a twisted microbeam on Pasternak foundation is investigated. The strain-displacement relations (kinematic equations) are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory (SGT) is used to implement the size dependent effect at microscale. Finally, using an energy method and Hamilton’s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave propagation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is inversely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.     

动态存储方法在气相爆轰波数值模拟中的应用

为减少反应流计算花费的时间,采用动态存储建立热力学数据表（In situ adaptive tabulation, ISAT）的方法来取代反应流计算中化学反应的直接积分（Direct integral, DI）,并针对气相H2/O2爆轰波的传播过程进行了数值模拟。采用两种不同的ISAT误差放大判据对一维爆轰波的压力、温度及组分变化进行了计算,并和DI的结果进行了比较以考察其计算精度。此外,还探讨了ISAT方法的效率。计算结果表明,和DI方法相比,在爆轰波传播计算中ISAT方法计算误差小于3％,化学反应计算速度提高了8倍。     

非均质变截面杆中弹性波的反射和透射

基于一维弹性波理论，本文对应力波在非均质变截面杆中传播问题进行了一维简单波分析，并把分析结果与二维轴对称有限元分析结果进行了比较，表明一维简单波分析是非常有效和实用的。利用一维简单波分析方法，本文还揭示了应力波在非均质变截面杆中的传播规律，特别对含有内部交界面的非均质变截面杆（带有连接段）进行了一维等效简化分析，研究了连接段对应力波传播的影响。     

The application of the Lattice Boltzmann method to the one-dimensional modeling of pulse waves in elastic vessels

The one-dimensional nonlinear equations for the blood flow motion in distensible vessels are considered using the kinetic approach. It is shown that the Lattice Boltzmann (LB) model for non-ideal gas is asymptotically equivalent to the blood flow equations for compliant vessels at the limit of low Knudsen numbers. The equations of state for non-ideal gas are transformed to the pressure-luminal area response. This property allows to model arbitrary pressure-luminal area relations. Several test problems are considered: the propagation of a sole nonlinear wave in an elastic vessel, the propagation of a pulse wave in a vessel with varying mechanical properties (artery stiffening) and in an artery bifurcation, in the last problem Resistor–Capacitor–Resistor (RCR) boundary conditions are considered. The comparison with the previous results shows a good precision.     

Some applications of semi-analytical finite element method in static and dynamic analysis of structures

In this paper a kind of semi-analytical finite element method based on the transfer matrix analysis of shells of revolution is briefly formulated. Some recent investigations on its application are presented: (1) a reanalysis algorithm for improving the accuracy of free vibration analysis; (2) a kind of semi-analytical ring element for the stress analysis of a curved pipe of the slender torus shell type.