圆柱壳中圆盘状晶体压力传感器的厚度剪切振动

以电弹性体中叠加于偏场之上的小增量场理论为基础,研究了固定在圆柱壳中的圆盘状晶体谐振器的厚度剪切振动问题,得到了环境压力所诱导的谐振器频率漂移的表达式,该表达式可用于指导压力传感器的优化设计．数值结果表明:频率漂移与环境压力成正比,并且外壳的刚度越小或者压电晶片与外壳厚度之比越小,则压力传感器的灵敏度越高．     

汽车电磁悬架系统的Noether对称性及其应用

研究了含有电磁悬架汽车振动系统的Noether对称性,给出了系统的守恒量,并通过守恒量求得系统的对称性解.以能量形式,建立汽车不同振动形式下的Lagrange(拉格朗日)方程.选取位移坐标为广义坐标,研究了各种振动形式下系统的Noether对称性,并给出相应的Noether恒等式、Killing方程和广义Noether定理.研究系统守恒量,运用存在的守恒量,给出一种新的求解汽车振动系统响应的方法;并应用到具体的车体振动系统计算中,给出了系统在转弯、制动或加速等情况下的位移响应和速度响应曲线.     

Ultra-low frequency passive vertical vibration isolation system

An ultra-low frequency passive vertical vibration isolator is constructed by mounting a couple of additional masses on the crank-arms of the torsion spring. The theoretical analysis and experimental results show that the system with additional masses can achieve better vertical vibration isolation and longer resonant period. Measured displacement response of the test mass under seismic excitation reaches 3 x 10^{-12 m/√ Hz} around 10 Hz, and the isolation ratio comes to about 60 dB attenuation at 6 Hz, which is about 30 dB lower than that of the system without additional masses.     

横观各向同性层状弹性场地格林函数的数值解

采用横观各向同性层状弹性模型模拟半空间之上的层状场地,用人工透射边界代替半空间以吸收能量。利用薄层元素法给出任意节面上环形垂直及水平简谐荷载作用下场地的位移公式,并由此导出官类场地任意节面上在垂直及水平简谐集中荷作用下的位移响应显式解。算例表明本文方法与理论解相近,横观各向同性性质对格林函数有明显的影响。     

The nonlocal frequency behavior of nanomechanical mass sensors based on the multi-directional vibrations of a buckled nanoribbon

Considering the potential applications of the buckled structures as nanomechanical mass sensors, this paper presents an analytical method to solve the frequency shifts of the first-order transverse and longitudinal vibration modes when a mass attaches on the surface of a buckled nanoribbon based on the nonlocal elastic theory and the Lagrange's motion equation. The first-order transverse and longitudinal vibration modes of the buckled nanoribbon are introduced. A comparison between the analytic solution and the finite element analysis (FEA) is presented. Then, the effects of the compressive strain, the magnitude and location of attached mass, the nonlocal parameter, and attached mass numbers on the frequency shifts are presented. From example calculations, it is seen that the magnitude of attached mass increases the frequency shifts of the first-order modes, except the first-order transverse vibration mode at the location Z1=0. The frequency shifts for the first-order transverse and longitudinal vibration modes are different, and could be used as important principles in mass sensing. What's more, the compressive strain and the nonlocal parameter play significant roles on the sensing process of the buckled nanoribbon. The results could serve as useful references for the fabrications and applications of buckled structures based nanomechanical mass sensors.     

Mathematical modeling and numerical simulation of yarn behavior in a modified ring spinning system

In the paper, yarn dynamical behavior and twist distribution in a modified ring spinning system are investigated. Equations of motion and twist wave propagation are used to obtain the numerical solutions of yarn path, yarn tension and twist distribution in steady state. It is observed that yarn path in the twisting zone has several classic modes corresponding to the yarn tension, and all of the yarn paths are approximately planar curves rather than spatial curves. The angular velocities of yarn at the twisting device are given as well as the twist of yarn in the modified ring spinning system. Experiments are conducted to evaluate the yarn paths and twist distributions under consideration. The theoretical and experimental results have a good agreement.     

Ultra-low frequency passive vertical vibration isolation system

An ultra-low frequency passive vertical vibration isolator is constructed by mounting a couple of additional masses on the crank-arms of the torsion spring. The theoretical analysis and experimental results show that the system with additional masses can achieve better vertical vibration isolation and longer resonant period. Measured displacement response of the test mass under seismic excitation reaches 3 x 10^{-12 m/√ Hz} around 10 Hz, and the isolation ratio comes to about 60 dB attenuation at 6 Hz, which is about 30 dB lower than that of the system without additional masses. Project supported by the National Natural Science Foundation of China (Grant Nos. 19425008, 49674246 and 59678032).     

A finite element solution of an added mass formulation for coupled fluid-solid vibrations

Summary. A finite element method to approximate the vibration modes of a structure in contact with an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of an added mass formulation, which is one of the most usual procedures in engineering practice. Gravity waves on the free surface of the liquid are also considered in the model. Piecewise linear continuous elements are used to discretize the solid displacements, the variables to compute the added mass terms and the vertical displacement of the free surface, yielding a non conforming method for the spectral coupled problem. Error estimates are settled for approximate eigenfunctions and eigenfrequencies. Implementation issues are discussed and numerical experiments are reported. In particular the method is compared with other numerical scheme, based on a pure displacement formulation, which has been recently analyzed. Received August 31, 1998 / Published online July 12, 2000     

Electroelastic thickness vibrations of a quartz SC-cut plate

Analytic solutions are obtained of the boundary value problem of steady motions of a thick piezocrystalline SC-cut quartz plate describing thickness modes of harmonic elastic vibrations. The plate endfaces have no electrodes and adjoin a vacuum or a rarefied gas. The measure of the difference between the found values of the five lowest eigenfrequencies of the thickness vibrations of a plate without electrodes and the values of the corresponding frequencies of a plate whose endfaces are covered by massive short-circuited electrodes is determined.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 83–85, 1988.     

Free vibration multiquadric boundary elements applied to plane elasticity

This paper presents a new boundary element formulation for free vibration analysis of two-dimensional elastic structures. The dual reciprocity method (DRM) is introduced using the multiquadric radial basis functions (MQ). The required particular solution kernels for displacement and traction are derived and smoothed using simple mathematical trick; hence the limiting values of these kernels are computed. The eigen-problem of displacement is formulated and solved to obtain the required frequencies of different vibration modes. Finally, several numerical problems are studied to demonstrate the validity and accuracy of the developed formulation. The results are compared to those obtained from other interpolation functions, and finite element analysis to demonstrate the validity and superiority of the present formulation.     

Solutions of nonlinear thickness-shear vibrations of an infinite isotropic plate with the homotopy analysis method

As a preliminary attempt for the study on nonlinear vibrations of a finite crystal plate, the thickness-shear mode of an infinite and isotropic plate is investigated. By including nonlinear constitutive relations and strain components, we have established nonlinear equations of thickness-shear vibrations. Through further assuming the mode shape of linear vibrations, we utilized the standard Galerkin approximation to obtain a nonlinear ordinary differential equation depending only on time. We solved this nonlinear equation and obtained its amplitude–frequency relation by the homotopy analysis method (HAM). The accuracy of the present results is shown by comparison between our results and the perturbation method. Numerical results show that the homotopy analysis solutions can be adjusted to improve the accuracy. These equations and results are useful in verifying the available methods and improving our further solution strategy for the coupled nonlinear vibrations of finite piezoelectric plates.     

Determination of stresses and displacements in a thin annular disk subjected to diametral compression

Results of an analysis of the plane stress state of a thin annular disk subjected to uniform pressure on two diametrically opposite segments of the rim are presented. Some features of the stress distribution are investigated by means of both theoretical technique and experimental testing. Analytical expressions for the components of the displacement vector that correspond to the stress state of a ring under the action of diametral compression are established.     

A fifth-order polynomial that serves as both buckling and vibration mode of an inhomogeneous structure

This paper studies vibration of inhomogeneous beams in the presence of the distributed axial loads. We postulate the mode shape to be a fifth-order polynomial that represents the static displacement of the associated homogeneous beam under the linear loading. The beam is reconstructed such that it possesses the postulated modes of vibration and of loss of stability. It must be noted that the reconstruction is possible in most of the considered cases.     

Vibration analysis of rectangular plates coupled with fluid

The approach developed in this paper applies to vibration analysis of rectangular plates coupled with fluid. This case is representative of certain key components of complex structures used in industries such as aerospace, nuclear and naval. The plates can be totally submerged in fluid or floating on its free surface. The mathematical model for the structure is developed using a combination of the finite element method and Sanders’ shell theory. The in-plane and out-of-plane displacement components are modelled using bilinear polynomials and exponential functions, respectively. The mass and stiffness matrices are then determined by exact analytical integration. The velocity potential and Bernoulli’s equation are adopted to express the fluid pressure acting on the structure. The product of the pressure expression and the developed structural shape function is integrated over the structure-fluid interface to assess the virtual added mass due to the fluid. Variation of fluid level is considered in the calculation of the natural frequencies. The results are in close agreement with both experimental results and theoretical results using other analytical approaches.     

弹性约束边界条件下矩形蜂窝夹芯板的自由振动分析

蜂窝夹芯板在飞行器、高速列车等领域有广泛的用途，对其开展振动分析具有明确的科学价值及工程意义.为区别于诸简支等传统约束边界，提出了弹性约束边界下蜂窝夹芯板结构的自由振动特性分析方法.具体来说，首先通过将蜂窝夹芯层等效为各向异性板，将夹芯板问题转变为三层板结构.进一步地，将板结构的位移场函数由改进的二维Fourier级数表示，并基于能量原理的Rayleigh Ritz法得到结构的固有频率和固有振型，理论预测结果与数值模拟分析吻合较好.提出的理论模型可用于系统讨论约束边界对蜂窝夹芯结构自由振动特性的影响，为此类结构的约束方案设计提供理论依据.     

The vibration of a rotating heavy non-uniform thread and its stability

The linear vibration of a heavy non-uniform thread is investigated for different boundary conditions at the ends and taking an arbitrary additional tension into account. The thread is assumed to be ideal and inextensible and the motion takes place in a plane which may rotate about the vertical axis at constant angular velocity. A general scheme for solving the initial- and boundary value problem is proposed. Attention is focused mainly on the effective computation of the natural frequencies and mode of vibration. Given specific parametric types of mass distribution for the thread, sufficiently complete families of solutions describing the principal modes of vibration are constructed. Based on these families, stability and instability domains are constructed effectively, in terms of the system parameters, for a plane vibration of a rotating heavy thread subject to concentrated tension. New mechanical effects, of possible interest in practice, are observed and discussed.     

微极热弹性无限板的轴对称自由振动

研究了在应力自由和刚性固定边界条件下,无能量耗散的均匀、各向同性微极热弹性无限板的轴对称自由振动波的传播,导出了相应的对称和斜对称模态波传播的闭合式特征方程和不同区域的特征方程.对短波的情况,应力自由热绝缘和等温板中对称和斜对称模态波传播的特征方程退化为Rayleigh表面波频率方程.根据导出的特征方程得到了热弹性、微极弹性和弹性板的结果.在对称和斜对称运动中计算了板的位移分量幅值、微转动幅值和温度分布,给出了对称和斜对称模式的频散曲线,并示出了位移分量和微转动幅值和温度分布的曲线.能够发现理论分析和数值结论是非常一致的.     

Finite element analysis of compressible and incompressible fluid-solid systems

This paper deals with a finite element method to solve interior fluid-structure vibration problems valid for compressible and incompressible fluids. It is based on a displacement formulation for both the fluid and the solid. The pressure of the fluid is also used as a variable for the theoretical analysis yielding a well posed mixed linear eigenvalue problem. Lowest order triangular Raviart-Thomas elements are used for the fluid and classical piecewise linear elements for the solid. Transmission conditions at the fluid-solid interface are taken into account in a weak sense yielding a nonconforming discretization. The method does not present spurious or circulation modes for nonzero frequencies. Convergence is proved and error estimates independent of the acoustic speed are given. For incompressible fluids, a convenient equivalent stream function formulation and a post-process to compute the pressure are introduced.

     

负压激励下含椭圆孔高弹体的屈曲分析

基于数值模拟与理论分析,研究了含周期性椭圆孔二维结构的屈曲行为。针对不同的屈曲模态,建立理论模型进行模态分析。结果表明,改变孔的几何参数,椭圆孔结构的屈曲模态会随之发生转换,理论分析与数值结果吻合良好。此外,在数值模拟中,与位移加载不同,负压激励下的单胞需要考虑力边界条件的修正,以确保其满足完备性条件。已有工作在单胞选择中常存在问题,导致错误结果。针对上述问题研究了不同单胞所对应的边界条件,并结合有限结构进行了分析与讨论。     

有色噪声激励下双稳态电磁式振动能量捕获器动力学特性研究

随着微机电科技的进步,利用环境振动进行系统自供电已经成为目前非线性动力学研究的热点.以附加线性振子的双稳态电磁式振动能量捕获器为研究对象,建立系统的动力学方程,通过数值仿真研究了有色噪声激励作用下双稳态能量捕获系统的动力学行为,分别从有色噪声强度、质量比和调频比3个方面研究了双稳态系统动力学响应,获得了上述参数对双稳态能量捕获系统动力学特性的影响规律,上述研究结果为双稳态电磁式振动能量捕获系统的相关研究提供理论基础.