Analysis of Dynamic Characteristics of Forced and Free Vibrations of Mill Roll System Based on Fractional Order Theory

In this paper,the main researches are focused on the horizontal nonlinear vibration characteristics of roll systems for rolling mill,mainly including the study of forced vibration and free vibration of the roller.Firstly,the nonlinear damping parameters and nonlinear stiffness parameters within interface of the rolling mill are both considered,and a fractional-order differential term is also introduced to model the horizontal nonlinear vibration.Secondly,the averaging method is introduced to solve the forced vibration system of the mill roll system,and the amplitude-frequency characteristic curves of the system are obtained for different orders,external excitation amplitudes,stiffness and fractional order coefficients.Thirdly,the amplitude-frequency and phasefrequency characteristics of the free vibration of the mill roll system are investigated at different fractional orders.Then,the accuracy of the averaging method for solving the dynamic characteristics of the system is verified by numerical analysis,and the effect of the fractional differential term coefficients and order on the dynamic characteristics of the roll system are investigated.Finally,the time-frequency characteristics and phase-frequency characteristics of free vibration systems at different fractional orders are studied.The validity of the theoretical study is also verified through experiments.

Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.

An isogeometric analysis approach for dynamic response of doubly-curved magneto electro elastic composite shallow shell subjected to blast loading

For the first time, the isogeometric analysis(IGA) approach is used to model and analyze free and forced vibrations of doubly-curved magneto-electro-elastic(MEE) composite shallow shell resting on the visco-Pasternak foundation in a hygro-temperature environment. The doubly-curved MEE shallow shell types include spherical shallow shell, cylindrical shallow shell, saddle shallow shell, and elliptical shallow shell subjected to blast load are investigated. The Maxwell equation and electromagnetic boundary conditions are used to determine the vary of the electric and magnetic potentials. The MEE shallow shell's equations of motion are derived from Hamilton's principle and refined higher-order shear theory. Then, the IGA method is used to derive the laws of natural frequencies and dynamic responses of the shell under various boundary conditions. The accuracy of the model and method is verified through reliable numerical comparisons. Aside from this, the impact of the input parameters on the free and forced vibration of the doubly-curved MEE shallow shell is examined in detail. These results may be useful in the design and manufacture of military structures such as warships, fighter aircraft, drones and missiles.

Dynamic Response Analysis of A 5 MW NREL Wind Turbine Blade under Flap-Wise and Edge-Wise Vibrations

A wind turbine is subjected to a regime of varying loads.For example,each rotor revolution causes a complete gravity stress reversal in the low-speed shaft,and there are varying stresses from the out-of-plane loading cycle due to fluctuating wind load.Consequently,wind turbine blade design is governed by fatigue rather than ultimate load considerations.Previous studies have adopted many different beam theories,using different techniques and codes,to model the National Renewable Energy Laboratory(NREL)5MWoffshore wind turbine blade.There are differences,from study to study,in the free vibration results and the dynamic response.The contribution of this study is to apply the code written by the authors to the different beam theories used with the aim of comparing the different beam theories presented in the literature and that developed by the authors.This paper reports the investigation of the effects of deformation parameters on the dynamic characteristics of the NREL 5 MW offshore wind turbine blades predicted by the different beam theories.The investigation of free vibrations is a fundamental step in the analysis of structural dynamics,and this study compares different computational structural methods and investigates their effect on the predicted dynamic response.The modal characteristics of every model examined have been combined with strip theory to determine the dynamic response of the blade.

Cross-sectional warping and precision of the first-order shear deformation theory for vibrations of transversely functionally graded curved beams

The warping may become an important factor for the precise transverse vibrations of curved beams.Thus,the first aim of this study is to specify the structural design parameters where the influence of cross-sectional warping becomes great and the first-order shear deformation theory lacks the precision necessary.The outof-plane vibrations of the first-order shear deformation theory are compared with the warping-included vibrations as the curvature and/or thickness increase for symmetric and asymmetric transversely-functionally graded(TFG)curved beams.The second aim is to determine the influence of design parameters on the vibrations.The circular/exact elliptical beams are formed via curved mixed finite elements(MFEs)based on the exact curvature and length.The stress-free conditions are satisfied on three-dimensional(3D)constitutive equations.The variation of functionally graded(FG)material constituents is considered based on the power-law dependence.The cross-sectional warping deformations are defined over a displacement-type FE formulation.The warping-included MFEs(W-MFEs)provide satisfactory 3D structural characteristics with smaller degrees of freedom(DOFs)compared with the brick FEs.The Newmark method is used for the forced vibrations.

Prediction Model for Vortex-Induced Vibration of Circular Cylinder with Data of Forced Vibration

A model based on the data from forced vibration experiments is developed for predicting the vortex-induced vibra- tions （VIV） of elastically mounted circular cylinders in flow. The assumptions for free and forced vibration tests are explored briefly. Energy equilibrium is taken into account to set up the relationship between the dynamic response of selfexcited oscillations and the force coemcients from forced vibration experiments. The gap between these two cases is bridged straightforwardly with careful treatment of key parameters. Given reduced mass m^# and material damping ratio of an elastically mounted circular cylinder in flow, the response characteristics such as amplitude, frequency, lock-in range, added mass coefficient, cross-flow fluid force and the corresponding phase angle can be predicted all at once. In- stances with different combination of reduced mass and material damping ratio are compared to investigate their effects on VIV. The hysteresis phenomenon can be interpreted reasonably. The predictions and the results from recent experiments carried out by Wifliamson＇ s group are in rather good agreement.

The Interface Stress Field in the Elastic System Consisting of the Hollow Cylinder and Surrounding Elastic Medium Under 3D Non-Axisymmetric Forced Vibration

The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.

Further Investigation for Nonlinear Free Vibration of Elastic Circular Plate with Large Amplitude

The nonlinear free vibrations of the elastic circular thin plate with large amplitude taking radial force of inertia into account are investigated by using method similar to modified iterative method.The algorithm and formulas finding its approximate analytical solution are provided,and the solution behaviors are also discussed through the calculating example.

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.

A vertical coupling dynamic analysis method and engineering application of vehicle–track–substructure based on forced vibration

Purpose–This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track and vehicle caused by local fastener failure.Design/methodology/approach–The track and substructure are decomposed into the rail subsystem and substructure subsystem,in which the rail subsystem is composed of two layers of nodes corresponding to the upper rail and the lower fastener.The rail is treated as a continuous beam with elastic discrete point supports,and spring-damping elements are used to simulate the constraints between rail and fastener.Forced displacement and forced velocity are used to deal with the effect of the substructure on the rail system,while the external load is used to deal with the reverse effect.The fastener failure is simulated with the methods that cancel the forced vibration transmission,namely take no account of the substructure–rail interaction at that position.Findings–The dynamic characteristics of the infrastructure with local diseases can be accurately calculated by using the proposed method.Local fastener failure will slightly affect the vibration of substructure and carbody,but it will significantly intensify the vibration response between wheel and rail.The maximum vertical displacement and the maximum vertical vibration acceleration of rail is 2.94 times and 2.97 times the normal value,respectively,under the train speed of 350 km$h
1.At the same time,the maximum wheel–rail force and wheel load reduction rate increase by 22.0 and 50.2%,respectively,from the normal value.Originality/value–This method can better reveal the local vibration conditions of the rail and easily simulate the influence of various defects on the dynamic response of the coupling system.

大型发电机端部绕组电磁力物理数字孪生建模

为了在“智慧汽轮机”中更好地结合物理信息模型先验知识与数据驱动模型,并向真实机组模型迁移试验模型,进一步实现可靠的实验室数值仿真数据和真实运行数据互相印证与混和建模驱动,以600 MW大型汽轮发电机为研究对象,建立融合演进因素的汽轮发电机定子绕组本体模型,提出集成数字孪生智能绕组研究框架,并提出智能绕组内涵的形式化定义。基于镜像法、气隙回转电流应用叠加法、毕奥-萨伐尔定律和安培力定律建立定子端部绕组电磁力的数学机理物理信息模型。对有限元电磁力和数字化电磁力进行了分析对比,验证了所建立电磁力数字化物理信息模型的合理性。对比分析振动响应结果,进一步验证了数字化电磁力物理信息建模的正确性以及有限元电磁力对比验证的正确性。研究将对“智慧汽轮机”运维的振动动态基于物理机理与数据驱动混和建模的数字孪生故障诊断与预测提供有力的支撑。

Experimental and numerical study of effecting core configurations on the static and dynamic behavior of honeycomb plate with aluminum material

The sandwich panel incorporated a honeycomb core,a widely utilized composite structure recognized as a fundamental classification of composite materials.Comprised a core resembling a honeycomb,possessing thickness and softness,and is flank by rigid face sheets that sandwich various shapes and materials.This paper presents an examination of the static and dynamic analysis of lightweight plates made of aluminum honeycomb sandwich composites.Honeycomb sandwich plate samples are 300 mm long,and 300 mm wide,the heights of the core have been varied at four values ranging from 10 to 25 mm.The honeycomb core is manufactured from Aluminum material by using a novel technique namely resistance spot welding(RSW)instead of using adhesive material,which is often used when an industrial flaw is detected.Numerical optimization based on response surface methodology(RSM)and design of experiment software(DOE)was used to verify the current work.A theoretical examination of the crashworthiness behavior(maximum bending load,maximum deflection)and vibration attributes(natural frequency,damping ratio,transient temporal response)of honeycomb sandwich panels with different design parameters was also carried out.In addition,the finite element method-based ANSYS software was used to confirm the theoretical conclusions.The findings of the present work showed that the relationship between the natural frequency,core height,and cell size is direct.In contrast,the relationship between the natural frequency and the thickness of the cell wall is inverse.Conversely,the damping ratio is inversely proportional to the core height and cell size but directly proportional to the thickness of the cell wall.The study indicates that altering the core height within 10-25 mm leads to a significant increase of 82%in the natural frequency and a notable decrease of 49%in the damping ratio.These findings are based on a specific cell size value of 0.01 m and a cell wall thickness of 0.001 m.Also,the results indicate that for a given set of cell wall thickness and size values,an increase in core height from(0.01-0.025)m,leads to a reduction of the percentage of maximum response approX imately 76%.Conversely,the increasing thickness of the wall of cell wall,ranging 0.3-0.7 mm with a constant core height equal to 0.015 m,resulted in a de crease of maximum transient response by 7.8%.

基于谐响应的大型异步电机电磁振动分析

大型异步电机的电磁振动是电机振动的主要构成部分,对电机振动等级的评估需要进行准确的电磁振动分析,本文以一台10 kV兆瓦级大型异步电机为对象进行电磁振动分析。首先对完整的电机模型进行模态分析,求解固有频率及对应振型,并实验测量了电机实际运行时的固有频率;然后将电磁场二维有限元计算得到的径向电磁力作为载荷,对该电机进行谐响应分析,最后与实验测得的振动速率对比。结果表明,基于电机整机模型的模态分析和谐响应分析可以较为准确地分析大型异步电机电磁振动,能够为电机的优化设计或电磁振动抑制提供理论依据。

双向恢复力模型对基础隔震建筑风振响应的影响

为明确MSS、Casciati和Harvey and Gavin这3种常用双向恢复力模型计算基础隔震建筑风振响应的差异,采用3种模型模拟铅芯橡胶支座在水平单向和双向位移下的恢复力,对比试验或有限元结果的差异,采用3种模型对一算例在双向风荷载下隔震层位移、顶点位移和顶点加速度3个指标的差异进行了分析。研究表明:3种模型模拟铅芯橡胶支座在单向循环位移、方形和偏置方形位移下恢复力的趋势基本一致;而模拟圆形和偏置圆形位移时,MSS模型双向恢复力形状与有限元结果不同,不能较为准确地模拟支座双向耦合行为,Casciati模型误差稍小于Harvey and Gavin模型。Casciati模型和Harvey and Gavin模型计算风振响应基本一致;对于横风向响应均方根,3种模型差距不大;对于顺风向隔震层位移、顶点位移和顶点加速度均方根,MSS模型稍小,而对于顺、横风向隔震层位移峰值因子,MSS模型稍大;对于顺、横风向顶点加速度峰值因子和双向与单向模型顶点加速度最值比值随风速变化规律,MSS模型与其他模型差异较大。基于双向耦合效应模拟及风振响应指标的差异,建议采用Casciati模型考虑双向恢复力模型对基础隔震建筑风振响应的影响。

附加阻尼环的航空齿轮强迫响应分析方法

为了避免航空齿轮振动过大导致齿轮辐板破裂,在齿轮外缘安装阻尼环是一种有效减振方法。针对工程中阻尼环设计时缺乏有效便捷的设计方法问题,基于能量法建立了航空齿轮节径型振动下阻尼环的等效参数模型。在给定模态振型下,将阻尼环的影响效果简化为依赖于齿轮振幅(振动应力)的等效阻尼、等效刚度和等效质量,实现了齿轮-阻尼环系统幅频响应快速求解。以某航空齿轮为例,分析了激励载荷、摩擦系数、转速以及结构固有阻尼对强迫响应的影响,结合许用振动应力进行了阻尼环优化设计。结果表明:阻尼环减振效果与振动应力具有强非线性,在本文给定的激励载荷及100 MPa许用振动应力下,阻尼环质量比不应大于5%,最佳摩擦系数为0.1,设计得当的阻尼环能够降低50%以上的振动应力。

岩体临空面块体振动响应规律研究

结构面是控制岩体工程局部稳定的关键因素之一,查明结构面赋存及组合状态是岩体稳定性分析的前提条件,目前常采用地质调察的方法,由于勘察手段的局限性,存在遗漏时常需要补充勘察,成本耗费高。通过开展室内试验,对结构面模型的表面振动响应规律进行了研究,研究表明:对于单结构面模型,结构面前方的质点振幅存在增幅效应,对于由两条结构面切割的块体模型,仅在远离动力输入侧的结构面前方存在振幅放大效应。在试验成果的基础上开展了数值模拟分析,分别对不同结构面倾角的岩体模型进行计算,结果表明:相对于萨道夫斯基经验公式得到的振动衰减规律,当结构面与爆源方向地面夹角θ值小于90°时,结构面前方的振动波入射区域质点振幅存在明显放大效应,结构面后方质点振动幅值则显著衰减。随着结构面与边界面夹角θ的减小,结构面前质点峰值振速增幅率逐渐增大,并在θ=20°时波幅放大2.8倍。通过合理布置爆破振动监测测点,这一规律为爆破工程中识别结构面及块体提供判据。

考虑液体晃荡的部分充液圆柱壳受迫振动分析

充液圆柱壳结构广泛存在于在工程中,在外部激励作用下,圆柱壳会与流体产生耦合振动,且未充满的液面也会产生晃荡,这种耦合振动响应分析在工程中具有重要意义。提出了一种求解考虑内部液体小幅晃荡的弹性圆柱壳振动响应的半解析法。首先分别在壳体建立结构坐标系、在自由液面建立液体坐标系,各自用来描述结构及内部液体的运动。基于Flügge壳体理论建立了圆柱壳的运动控制方程。将液体视为无黏、不可压缩的理想流体,根据线性水波理论和液体自由表面运动边界条件,得出了内部液体的速度势函数。通过流固耦合界面的连续性条件,结合坐标变换推导得到流固耦合系统的运动控制方程。研究了壳体在径向点力激励下振动响应,并得出了对应的液面晃荡响应。和有限元法对比验证了方法的正确性,然后改变相关参数讨论了考虑内部液体晃荡的弹性圆柱壳振动响应特性。

Reynolds and Mass-Damping Effect on Prediction of the Peak Amplitude of A Freely Vibrating Cylinder

The Reynolds effect and mass-damping effect on the peak amplitude of a freely vibrating cylinder is studied by using forced oscillating data from Gopalkrishnan＇ s research in 1993, in which all experimental cases were carried out at a fixed Reynolds and the tested cylinder was recognized as a body that had no mass and damping. However, the Reynolds and roass-damping are the very important parameters for the peak amplitude of a freely vibrating cylinder. In the present study, a function F is introduced to connect the forced oscillation and free vibration. Firstly the peak amplitude AG^＊ can be obtained from the function F using forced oscillation data of Gopalkrishnan＇ s experimental at Re = 10^4, and then the Reynolds effect is taken into account in the function f（Re）, while the mass-damping effect is considered in the function K（ α ）, where a is the mass-damping ratio. So the peak amplitude of a freely vibrating cylinder can be predicted by the expression： A ^＊ = K（ α ）f（ Re ）AG^＊ . It is found that the peak transverse amplitudes predicted by the above equation agree very well with many recent experimental data under both high and low Reynolds conditions while roass-damping varies. Furthermore, it is seen that the Reynolds number does have a great effect on the peak amplitude of a freely vibrating cylinder. The present idea in this paper can be applied as an update in the empirical models that also use forced oscillation data to predict the vortex induced vibration （VIV） response of a long riser in the frequency domain.

冰载荷激励下内河船推进轴系扭转振动研究

以一艘内河实船推进轴系为例,利用场矩阵法与霍尔兹表法研究系统自由扭振固有频率,根据1阶及2阶固有频率下的共振转速通过放大系数法及场矩阵法对比研究柴油机稳态激励下系统强制扭振,分析两种方法的频域结果.利用Newmark积分及编程计算求解冰载荷下轴系扭转应力的时域响应,对比分析冰载荷下轴系瞬时扭转应力与柴油机激励下的稳态扭转应力.结果表明:冰块撞击后轴系扭转应力超过许用应力值并远大于无冰块撞击时的扭转应力.