Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases, The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Theoretical and Experimental Investigation of Flexural Vibration Transfer Properties of High-Pressure Periodic Pipe

According to the theory of phononic crystals, the hydraulic pipeline is designed to be a periodic structure composed of steel pipes and hoses to suppress the vibration of the hydraulic system with band gaps. We present theoretical and experimental investigations into the flexural vibration transfer properties of a high-pressure periodic pipe with the force on the inner pipe wall by oii pressure taken into consideration. The results show that the vibration attenuation of periodic pipe decreases along with the elevation of working pressure for the hydraulic system, and the band gaps in low frequency ranges move towards high frequency ranges. The periodic pipe has good vibration attenuation performance in the frequency range below 1000 Hz and the vibration of the hydraulic system is effectively suppressed. A11 the results are validated by experiment. The experimental results show a good agreement with the numerical calculations, thus the flexural vibration transfer properties of the high- pressure periodic pipe can be precisely calculated by taking the fluid structure interaction between the pipe and oil into consideration. This study provides an effective way for the vibration control of the hydraulic system.

Analysis of the flexural vibration of ship's tail shaft by transfer matrix method

A ship's tail shaft has serious flexural vibration due to the cantilevered nature of the propeller's blades.Analysis of the nature frequency of flexural vibration is vital to be able to provide effective shock absorption for a ship's tail shaft.A mathematic model of tail shaft flexural vibrations was built using the transfer matrix method.The nature frequency of flexural vibration for an electrically propelled ship's tail shaft was then analyzed,and an effective method for calculating it was proposed:a genetic algorithm(GA),which calculates the nature frequency of vibration of a system.Sample calculations,with comparisons by the Prohl method under conditions bearing isotropic support,showed this method to be practical.It should have significant impact on engineering design theory.

Effects of ramp vibrational states on flexural intrinsic vibrations inBesocke-style scanners

For both the vibrating and steady supporting surfaces of a scanning disk in a Besocke-style piezoelectric scanner, a theoretical model is given by considering the nonlinear lateral friction at the micro-contact interface between the positioning legs and the supporting surface. Numerical simulations demonstrate that unexpected flexural vibrations can arise from a vibrating ramp, and their frequencies are lower than the eigenfrequencies of the scanner in the linearly elastic regime. The vibrations essentially depend on 1） the vibrational states of the supporting ramp and the steel ball tips on the three piezo- electric positioning legs, and 2） the tribological characteristics of the contacts between the tips and the ramp. The results give an insight into the intrinsic vibrations of the scanners, and are applicable in designing and optimizing piezoelectric scanning systems.

Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners

Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners with nanometer resolution are studied by using an electro-mechanical coupling Timoshenko beam model. Meanwhile, the effects of friction, the first moment, and moment of inertia induced by mass loads are considered. The predicted resonance frequencies of the ceramic tubes are sensitive to not only the mechanical parameters of the scanners, but also the friction acting on the attached shaking ball and corresponding bending moment on the tubes. The theoretical results are in excellent agreement with the related experimental measurements. This model and corresponding results are applicable for optimizing the structures and performances of the scanners.

Uniform Exponential Stabilization for Flexural Vibrations of a Solar Panel

Here we study a problem of stabilization of the flexural vibrations or transverse vibrations of a rectangular solar panel. The dynamics of vibrations is governed by the fourth order Euler-Bernoulli beam equation. One end of the panel is held by a rigid hub and other end is totally free. Due to attachment of the hub, its dynamics leads to a non-standard equation. The exponential stabilization of the whole system is achieved by applying an active boundary control force only on the rigid hub. The result of uniform stabilization is obtained by means of an explicit form of exponential energy decay estimate.

HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF MATERIALS(Ⅲ)—FLEXURE AND FREE VIBRATION OF PLATES

The methodology presented in Part I is employed to deal with flexure and free vibration of anisotropic plates.

Stability and vibration of a helical rod with circular cross section in a viscous medium

The stability and vibration of a thin elastic helical rod with circular cross section in a viscous medium are discussed. The dynamical equations of the rod in the viscous medium are established in the Frenet coordinates of the centreline with the Euler angles describing the attitudes of the cross section as variables. We have proved that the Lyapunov and Euler conditions of stability of a helical rod in the space domain are the necessary conditions for the asymptotic stability of the rod in the time domain. The free frequencies and damping coefficients of torsional and flexural vibrations of the helical rod in the viscous medium are calculated.

Modeling and solving for transverse vibration of gear with variational thickness

A analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. Traverse displacement, rotation angle, shear force and fiexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. The influence of hole to diameter ratios, segment thickness ratios, segment location ratios, Poisson ratio on the vibration behavior of stepped circular Mindlin disk were calculated, tabletted and plotted. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is very good. The largest error for all frequencies is 5.46%, and less than 5% for most frequencies.

Stability and vibration of a helical rod constrained by a cylinder

The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.

Analytical Solution of Vibration Analysis on Fixed-Free Single-Walled Carbon Nanotube-Based Mass Sensor

Fixed-free single-walled carbon nanotubes (SWCNTs) have attracted a lot of interest in recent years due to their suitability for a wide range of applications, such as field emission and vacuum microelectronic devices, nanosensors, and nanoactuators. Based on a cantilever beam-bending model with a rigid mass at the free end and mode analysis, an analytical solution is developed in the present study to deal with the resonant frequency and mode shapes of a SWCNT- based mass sensor. The resonant frequency shift and mode shape of the fixed-free SWCNTs caused by the addition of a nanoscale particle to the beam tip are examined in order to explore the suitability of SWCNTs as a mass detector device. The simulation results reveal that the volume of the added particle has little effect on the first resonant frequency. In contrast, the second resonant frequency decreases with increasing the volume of the added particle. Furthermore, the resonant frequency shift of the first mode is very obvious for the amount of added mass, and the second resonant frequency decreases rapidly with increasing volume of added particle. Therefore, the first and second resonant frequencies can be used in the measurement of the mass of added particle and its volume, respectively.

Vibration analysis of steel structures including the effect of panel zone flexibility based on the energy method

New approximate formulas are proposed to determine the natural frequencies of structures considering the effects of panel zone flexibility and soil-structure interaction. Several structures with various earthquake resisting systems are idealized as prismatic cantilever flexural-shear beams. Floor masses are considered as lumped masses at each story level and masses of columns are evenly distributed along the cantilever beam. Soil-structure interaction is considered as axial and rotational springs, whose potential energy are formulated and incorporated into overall potential energy of the structure. Subsequently, natural frequency equations are derived on the basis of energy conservation principle. The effect of axial forces on natural frequency is also considered in the proposed formulas. Using the method presented in this study, natural frequencies are computed using a simplified method with no complex numerical modeling. The proposed formulas are verified via experimental and numerical methods. Close agreement between the results from these three approaches are observed. Furthermore, the effects of panel zone flexibility, continuity plates and doubler plates on the natural frequencies of buildings are investigated.

某大型水电站机组特定负荷区间厂房振动噪声成因分析与探讨

某大型水电站机组在低水头特定负荷区间运行时厂房出现低沉的轰鸣噪声,并伴随厂房楼板、楼梯明显振动的现象,参建各方对引起该异常现象的原因进行了逐一排查但至今尚未解决。对此进行了机组变水位稳定性和能量试验,根据试验成果对机组及厂房结构耦合振动成因进行了分析与推测,初步判断原因为固定导叶卡门涡激发了活动导叶的弯扭耦合共振,通过轴承和顶盖传导至混凝土,并导致母线层楼板及下方立柱发生共振。

基于空耦超声激励的微结构模态频率温度特性研究

为了研究微悬臂结构弯曲振动模态频率的温度特性,首先针对各向异性材料的等截面矩形微悬臂结构建立了其各阶模态频率温度系数的理论模型;然后搭建了包括激光测振单元、空耦超声激励单元和温度控制单元的非接触式微结构动态特性测试系统;最后利用所搭建的测试系统分别对等截面矩形单晶硅微悬臂梁在室温~300℃时的动态特性进行了测试,获得了微悬臂梁前三阶弯曲振动模态频率随温度的变化规律和频率温度系数。研究结果表明,单晶硅微悬臂梁前三阶弯曲振动模态频率随着温度的升高而呈近似线性的减小,并且微悬臂梁前三阶弯曲振动模态具有几乎相同的频率温度系数,其中一阶模态频率的温度系数为-2.18×10-5/℃,二阶模态频率的温度系数为-1.91×10^(-5)/℃,三阶模态频率的温度系数为-2.01×10^(-5)/℃,前三阶模态频率温度系数的测试结果与理论模型预测值的偏差分别3×10^(-7)/℃,3×10^(-6)/℃和2×10^(-6)/℃。

具有翻转层的铌酸锂梁弯曲振动研究

研究了一种具有翻转层的新型铌酸锂梁,其翻转层与常规层的压电系数具有相反的符号,在厚度方向上施加电场可激发铌酸锂梁做弯曲振动。将位移和电势表达为梁的厚度和宽度方向的幂级数形式,推导了该种铌酸锂梁弯曲运动的一维方程。利用此一维方程分析了波沿梁长度方向传播的色散关系,以验证其精确程度。结果表明,所推导的一维方程在小波数范围内的色散曲线与三维精确解结果吻合良好;再用所得一维方程分析了梁式压电俘能器的输出功率密度和输出效率,将所得结果与由二维理论、三维理论所得结果进行对比。结果表明,一维方程所得结果与三维方程的结果接近,说明其在压电器件领域极具应用潜力。

超材料梁的双阶耦合带隙调控设计与宽带减振特性

局域共振带隙和Bragg带隙可同时存在于超材料梁中,利用两种带隙之间的相互耦合效应可以实现超宽耦合带隙设计,在宽带减振领域极具应用潜力.以往研究通常考虑单振子超材料梁的单阶耦合带隙设计,因而只能实现单阶的超宽耦合带隙,无法满足双目标或多目标频带的宽带减振需求.为此,本文开展了双振子超材料梁的双阶耦合带隙调控设计研究,提出了一种实现双阶耦合宽带隙的设计方法,分析了所设计双阶耦合带隙相比传统单阶耦合带隙的带宽优势,并探究了双振子质量分配比对双阶耦合带隙总宽度的影响,进一步设计出最优的质量分配比,使得实现的双阶耦合带隙的总宽度最宽.此外,还采用谱元法研究了基于双阶耦合带隙设计的双振子超材料梁的减振特性,通过与有限元法进行对比,验证了谱元法的准确性,研究表明基于双阶耦合带隙设计可以实现两个宽频带范围的高效减振.

基于声阻抗匹配理论的弹性吸收体研究

基于时域耦合模型理论的吸收体研究,不适用于所有模型,且基于此理论的设计过程复杂,难以在工业工程得到广泛应用。因此提出一种基于声阻抗匹配理论的弹性吸收体的研究方法,并通过理论计算、数值仿真以及实验对吸收体的吸收曲线进行验证。结果表明:本文提出的方法能够快速、简便地实现弹性吸收体的结构设计,无需额外附加阻尼材料,更有利于满足航空工程中对于结构轻量化的要求,为振动波吸收领域,尤其是弯曲波的高效吸收和减振设计研究带来了新的可能性。

地铁周期性轨道-隧道弯曲振动波传播特性研究

为探究地铁振源系统中弯曲振动波传播特性,将轨道-隧道模拟为Timoshenko梁-Timoshenko梁-Flügge复合双层圆柱薄壳耦合系统,并基于能量法和周期结构理论对其弯曲波带隙特性和振动响应特性开展分析。研究结果表明:在0~300 Hz范围内,耦合系统仅存在一条弯曲波带隙——0~46.4 Hz,为局域共振带隙,且主要受隧道质量和土体刚度影响;钢轨、道床板和隧道的振动导纳函数峰值依次为212、188和46 Hz,分别对应于钢轨-扣件子系统、道床板-等效支撑子系统及隧道-土体子系统的第一阶共振频率;钢轨、道床板和隧道的振动衰减区依次为0~142 Hz、0~73Hz和0~46 Hz。相关研究结论可为今后地铁结构的精细化减振设计及减振装备开发提供新的思路和理论指导。

弯曲振动复合楔形超声聚能器的设计

为了建立楔形变截面弯曲超声振动系统的设计理论,该文基于Timoshenko梁弯曲振动理论,推导了复合楔形超声聚能器的弯曲振动共振频率方程和放大系数解析表达式。利用解析理论模型和有限元仿真对复合楔形聚能器的前4阶弯曲振动特性进行了计算分析。结果表明:复合楔形超声聚能器的高度比和长度比对各阶弯曲共振频率和放大系数均有较大的影响;解析理论计算的聚能器的各阶弯曲共振频率和位移放大系数与有限元仿真结果一致,两种方法计算的聚能器的各阶弯曲共振频率相对误差均小于3%。由此表明该解析理论模型具有较高的理论计算精度。最后,设计并制作了复合楔形聚能器实验样品并对其一阶共振频率实验测试,实验测试结果与理论计算结果和有限元仿真结果吻合较好。该文研究结果为弯曲振动复合楔形超声振动系统的工程设计提供解析理论参考。

基于动刚度法的水面船舶桨-轴-船体耦合系统

为分析在低频段内船体两侧螺旋桨激励相位差对船体振动的影响,基于动刚度法建立水面船舶桨-轴-船体耦合系统的横向振动3梁耦合模型。将动刚度法的计算结果与有限元法进行对比,表明动刚度法具有良好的精度。分析桨-轴-船体耦合系统的垂向固有振动特性。在低频段内该系统主要表现为船体梁的振动,推进轴系对船体梁的固有特性影响较小。对左右双桨分别施加不同相位差的单位垂向简谐力,计算由各轴承位置输入至船体梁的功率流。结果表明,双桨激励相位差的增大会使输入至船体梁的功率流变小。因此,在对桨-轴-船体耦合系统的横向振动控制方面,应重点关注双桨激励相位差较大时的工况。