楔形杆轴纵、扭固有振动的修正摄动解

将含大参数的二阶线性方程的修正摄动解应用于楔型杆轴的固有纵振和扭振的研究,得到了其作固有纵振、扭振时的修正摄动解。并通过实例计算,比较了这种方法得出的解与Bessel方法一级近似解之间的误差。可以证明该修正摄动解具有相当高的精度。     

求强非线性振动系统的新摄动法

对强非线性振系统进行参数变换,把强非线性振动系统转化为弱非线性振动系统,同时再把振动系统的解展开为傅立叶级数,利用参数待定法即可方便求出非线性振动系统的主精度摄动解。     

耗能减震结构的摄动分析方法

针对用振型分解法对耗能减震结构进行反应分析中存在的计算精度差且耗时的问题,提出了求解振动方程特征值问题的改进一阶摄动的高精度模态展开法,并推导了强行解耦的振型分解的一阶摄动修正公式。最后通过算例证明,提出的摄动分析法是有效的。     

非牛顿润滑流的Maxwell模型的摄动解

对各种形式的Maxwell模型已有一些研究结果。Tichy讨论了粘弹性流体的Maxwell模型并对二维润滑流应用这一模型，使用以Deborah数为摄动量的正则摄动法，得到了模型的解。本文用双重正则摄动求解模型，得到了相应的解。顺便指出，所得速度的粘弹性修正项与Tichy的相应结果不同。     

弹丸膛内运动引起炮管振动的小参数解法

本文研究弹丸膛内运动引起的炮管横向振动问题,模型中同时计入了弹丸重力及炮管的静挠度和动挠度对炮管振动的影响。以弹丸与炮管的质量比作为小参数,用摄动法求得了单发射击时炮管振动整个过程的一般解。并利用叠加原理,将单发射击的分析结果进一步推广到连发射击的情况,从而建立了完整的弹丸膛内运动引起的炮管振动理论和分析方法。     

基于频率响应函数的动力学模型修正方法研究

概述了国内外动力学模型修正技术的研究状况，研究了近些年发展起来的基于频响函数的动力学模型修正方法；利用航天器振动试验测量所得的频响函数，从理论上介绍了频响函数残差法、设计参数型频响函数法和摄动型频响函数法三种基于频响函数的动力学模型修正方法，为动力学模型修正技术的发展提供参考。     

正切非线性包装系统跌落冲击的MSLP解EI北大核心CSCD

针对有阻尼正切型非线性包装系统在发生跌落冲击时的响应问题,基于摄动法(multi-scale Lindstedt-Poincare,MSLP)讨论了系统跌落冲击响应的一、二次近似解。并与龙哥库塔法(R-K)的数值结果及相关文献进行了对比,对比结果显示:对于正切型强非线性包装系统,MSLP计算的最大位移和加速度响应的一阶近似解与R-K数值结果对比的相对误差分别为1.35%和3.28%,二次近似阶的相对误差分别为0.62%和1.84%,在不进行能量修正的情况下,比同伦摄动法、牛顿谐波平衡法的精度更高。考虑阻尼系统能量修正的复杂性,所求有阻尼正切型非线性系统跌落冲击一次近似解析具有较好的精度和简洁的形式,为此类问题的求解及工程应用提供了参考。     

扭转弹簧约束复合材料层压梁的自由振动EI北大核心CSCD

基于伽辽金法推导了扭转弹簧约束复合材料层压梁自由振动的显式解析解。当复合材料层压梁两端的扭转弹簧刚度系数相等时,层压梁的横向挠度函数由两端简支梁的振动特征函数和两端固支梁修正的振动特征函数线性组合而成;当复合材料层压梁两端的扭转弹簧刚度系数不相等时,层压梁的横向挠度函数则由简支-固支梁的振动特征函数,固支-简支梁修正的振动特征函数和两端固支梁修正的振动特征函数线性组合而成。所构造的横向挠度函数可以避免扭转弹簧约束复合材料层压梁的经典振动特征函数在高阶(≥11)模态时出现的数值不稳定现象;研究表明,给出的显式解析表达式能有效地对扭转弹簧约束复合材料层压梁的自由振动进行分析。     

圆柱壳体的非线性磁弹性振动问题

导出了纵向磁场中圆柱薄壳体的非线性轴对称振动基本方程。利用多尺度法和摄动法求出了两端简支壳体振动的近似解析解,并对振动幅值和频率进行了讨论。     

L-P摄动法在跌落冲击问题中的应用

本文先是试探性地将L-P摄动法对杜芬方程的一次渐近解应用于跌落冲击问题，结果很不理想。因此，提出一种新的解法：将L-P摄动法与包装动力学的能量法相结合，以一次渐近解为基础，用一个初始条件和两个峰值条件确定积分常数。本文取了一个振幅修正系数，其作用是根据具体问题的具体情况调节基频与高频成分的比例关系。算例表明，用本文这种一次渐近解绘制的产品加速度时间曲线与椭圆积分法非常接近，在峰值、波形与冲击持续时间三个方面的准确性都能达到令人满意的程度。     

连续变密度圆形和环形薄膜的轴对称振动

本文采用打靶法数值分析了质量密度沿径向连续变化的圆形和环形薄膜的轴对称横向自由振动。针对密度以半径的二次函数变化的情形,计算了系统的一阶大有频率,并与文献（７）中分别用Ｄｉｆｆｅｒｅｎｔｉａｌ Ｑｕａｄｒａｔｕｒｅ Ｍｅｔｈｏｄ和Ｒａｙｌｅｉｇｈ’ｓ Ｑｕｏｔｉｅｎｔ Ｍｅｔｈｏｄ所得结果进行了比较,显示出本文结果的精确性和方法的优越性。然后,数值求解了密度沿半径以指数函数变化的非均匀圆形和环形膜     

Longitudinal vibrations of a silica fiber segment characterized using a fiber Bragg grating

A modulator assembly that excites longitudinal vibrations in a short (19 cm) silica fiber segment is described. A physical model of the modulator assembly is used to theoretically predict the behavior of longitudinal vibrations in the fiber segment. The longitudinal vibrations are experimentally characterized using an intrinsic fiber Bragg grating. Experimental results are compared to theoretical predictions.     

水流作用下悬浮隧道锚索的动力响应

为研究涡激振动和参数振动共同作用下锚索的横向振动响应,在考虑锚索垂度效应基础上建立了悬浮隧道锚索-管体耦合非线性模型,并通过伽辽金法和龙格-库塔法进行了数值求解和分析。结果表明:锚索的涡激振动可以激发系统的参数振动,系统的初始扰动对锚索的瞬态振幅影响很大,锚索的稳态振动振幅最终由涡激振动决定,涡激振动和参数振动共同作用下的系统响应比任何一种单独作用时都要大。     

Behavior of a Light Solid in a Rotating Horizontal Cylinder with Liquid Under Vibration

Dynamics of a cylindrical body in a rotating cavity is experimentally studied under transversal translational vibrations of the cavity rotation axis. Experiments are run at high rotation rate, when under the action of centrifugal force the body shifts to the rotation axis (the centrifuged state). In the absence of vibrations, the lagging rotation of the body is observed, due to the body radial shift from the axis of rotation caused by gravity. The body average rotation regime depends on the cavity rotation rate. The vibrations lead to the excitation of different regimes of body differential rotation (leading or lagging) associated with the excitation of its inertial oscillations. The dependence of the differential speed of the body rotation on the vibration frequency is investigated. The body dynamics has a complex character depending on the dimensionless vibration frequency. The analysis of body oscillation trajectory revealed that the body oscillatory motion consists of several modes, which contribute to the averaged dynamics of the body and the flows in the cavity.     

多跨连续长索的横振固有频率

采用LAPLACE变换求得了多跨连续长索固有横振振型的解析解,利用此振型解析解即可以方便地取得其固有横振的频率方程,并通过实例计算说明了该方法的应用。     

波浪场中水中悬浮隧道动力响应的研究

针对水中悬浮隧道在波浪力作用下动力响应的问题,通过Hamilton原理推导得到了悬浮隧道管段和锚索的运动控制方程,同时考虑了锚索横向和轴向变形之间的耦合作用,建立了悬浮隧道的动力响应模型,在时间域内采用逐步积分法迭代求解其运动控制方程。波浪力采用Airy线性波理论和Morison方程计算。计算结果表明:当锚索长细比较大时,锚索的自振模态会被激发,其横向和轴向变形之间的耦合作用不可忽略。随着入射波高或悬浮隧道重浮比的增加,悬浮隧道的横荡位移以及横摇角增大,但结构的垂荡位移以及锚索中的应力受波浪的影响较小。     

Design and realization of the microwave cavity in the PTB caesium atomic fountain clock CSF1

At the Physikalisch-Technische Bundesanstalt (PTB), the caesium atomic fountain clock CSF1 was developed. One key element of it is its microwave cavity, which was designed to have a low transversal phase variation across the cavity opening. This usually is achieved by using a cylindrical cavity with a TE011 field mode, having a high intrinsic quality factor, and by feeding the cavity symmetrically via two apertures at opposite position in the cavity wall. In contrast to other solutions, the CSF1 cavity is tightly coupled to the microwave feeds (Q _load≈2000). Therefore, detuning of the cavity resonance frequency has a reduced impact on the microwave field amplitude in the cavity compared to the case of weak coupling. Thus, a temperature stabilization of the cavity can be avoided. The extent to which the tight coupling may have an impact on the transversal phase distribution was studied. This question was solved analytically for a simplified cavity model. The results were applied to define the coupling geometry of the CSF1 cylindrical cavity in such a manner that the transversal phase distribution should become minimized. The key parameter is the electric length of the waveguides that constitute the junction to the coupling apertures. The theoretical studies are presented in some detail, and steps of the practical realization of the cavity are described     

Thickness vibration of an electroelastic plate under biasing fields

We study thickness vibrations of an electroelastic plate under uniform but otherwise arbitrary thermoelectromechanical biasing fields in a manner more general than previous studies of thickness vibrations of plates. An exact solution is obtained for materials with general anisotropy. Special attention is paid to the case of thickness-shear vibrations of plates of monoclinic crystals. The special cases of unidirectional extension and free thermal expansion are discussed in detail. Simple and useful formulas for frequency shifts and capacitance change versus biasing fields are obtained.     

Computation of moments and stresses in laminated composite plates by the boundary element method

This paper presents a boundary element formulation for the computation of moments and stresses at internal and boundary points of laminated composite plates. Integral equations for second transversal displacement derivatives are developed and all derivatives of the fundamental solution are computed analytically. These integral equations are used to compute moments and stresses at internal points. Stresses on the boundary are computed by a procedure that uses integral equations for the first transversal displacement derivatives, derivatives of shape functions, and constitutive relations. The obtained results are in good agreement with finite element results available in literature.