NONLINEAR VIBRATION FOR MODERATE THICKNESS RECTANGULAR CRACKED PLATES INCLUDING COUPLED EFFECT OF ELASTIC FOUNDATION

Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack＇s continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.

Nonlinear Dynamic Characteristics of a Simple Blade with Breathing Crack Using Ansys Software

Nonlinear dynamic response represents the most important studies for structures subjected to a dynamic mo-tion so that it provides the researcher by an excellent information especially at critical design levels. The un-predictable nonlinearity in the structure appears when damage is inherited. Most times, the failure of the structure is related to the dynamic nonlinearity. With regard to the breathing phenomena for nonlinear struc-tural systems, very little is known about how the nonlinearities influence the response and the dynamic char-acteristics of cracked structures. In this research, dynamic nonlinearity is presented in damaged structure due to presence of a crack. The crack is assumed to be open and close simultaneously and then breathing. Effect of breathing phenomenon was studied deeply. Crack breathing is simulated at the crack surfaces using con-tact elements. The contact, geometrical, penalty, and spin stiffnesses are taken in consideration. In addition, effect of several important parameters such as rotor angular velocity and crack ratio are studied. The study showed that the breathing natural frequency of any structure is ranged between opened (no contact) and closed crack natural frequencies. The larger crack length, the more nonlinear disturbance in the dynamic re-sponse behavior. Also, at a critical crack length, some mode shapes tend to exchange and pass over with other modes. The presence of the mode interchanging and mode crossover was a guide on the nonlinear re-sponse for the cracked structure. The numerical modeling is achieved using ANSYS finite element program. Experimental data are used for validating the accurate use of contact elements in ANSYS environment.

Micro-crack detection of nonlinear Lamb wave propagation in three-dimensional plates with mixed-frequency excitation

We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures.Simulation models of three-dimensional(3D)aluminum plates and composite laminates are established by ABAQUS software,where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage.The interactions between the S0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method.Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes,and sum and difference frequencies are extracted and simulated.Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes.There is a positive correlation among crack length,height,and sum and difference frequency amplitudes for an aluminum plate,with both amplitudes decreasing as crack thickness increased,i.e.,nonlinear effect weakens as the micro-crack becomes thicker.The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates.Furthermore,amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional ?bre rein- forced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are es- tablished. By applying the ?nite di?erence method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial di?erential gov- erning equations are solved. Some examples are given and the results are compared with available data.

NONLINEAR DYNAMICS OF A CRACKED ROTOR IN A MANEUVERING AIRCRAFT

The nonlinear dynamics of a cracked rotor system in an aircraft maneuvering with constant velocity or acceleration was investigated. The influence of the aircraft climbing angle on the cracked rotor system response is of particular interest and the results show that the climbing angle can markedly affect the parameter range for bifurcation, for quasi-periodic response and for chaotic response as well as for system stability. Aircraft acceleration is also shown to significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for on-line rotor crack fault diagnosis.

CRACK PROPAGATION IN THE POWER-LAW NONLINEARVISCOELASTIC MATERIAL

An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The Creep incompressilility assumption is used Tosimulate fracture behavior of craze region. it is assumed that in the .fracture processzone near the crack tip, the cohesive stress fo acts upon the crack surfaces and resistscrack opening. Through a perturbation method i. e., by superposing the Mode-Iapplied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelasticproblem is reduced to linear problem. For weak nonlinear materials, for which thepower-law index n=1, the expressions of stress and crack surface displacement arederived. Then, the fracture process zone local energy criterion is proposed and basedon which the formulas of crucking incubation time t. and crack slow propagationvelocity a are derired.

POWER LAW NONLINEAR VISCOELASTIC CRACK-TIP FIELDS

The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields.For the requirement of later derivation,the HRR singular fields and the high-order asymp- totic fields are first examined.That they are essentially the isotropic,incompressible,power law type nonlinear elastic crack-tip fields is illustrated.After a concise review of the elasticity recov- ery correspondence principle for solving the nonlinear viscoelastic problems,the correspondence principle for solving the crack problems of power law type nonlinear viscoelastic materials under the first type boundary condition is proposed.The solution of the crack-tip stress,strain fields for the power law type nonlinear viscoelastic materials,especially for the modified polypropylene, is obtained.

近表面疲劳裂纹的水浸式非共线横波混频检测方法研究

针对近表面疲劳裂纹检测问题,开展了水浸式非共线横波混频检测方法研究。在材料非线性、水/试件界面和疲劳裂纹不同非线性源情况下,分析相互作用角和频率比对混频非线性效应的影响规律。在此基础上,对有无近表面疲劳裂纹试件沿着深度方向进行扫查检测。结果表明,在不同非线性源情况下,混频特征图具有显著差异,根据混频特征图中和频纵波峰值及其对应相互作用角可对试件近表面疲劳裂纹进行检测;水/试件界面对近表面疲劳裂纹非共线横波混频检测具有一定影响,去参考检测方法可显著降低水/试件界面的影响,实现对近表面疲劳裂纹的有效检测。

耦合故障转子系统的非线性动力学分析

为研究多故障耦合对转子系统动力学的影响,建立刚性支承下的裂纹-碰摩耦合故障转子系统动力学模型,采用四阶Runge-Kutta方法对方程进行数值求解,对比分析系统在定子刚度以及裂纹深度等参数变化下转子系统的动力学响应。借助系统的分岔图对其非线性动力学行为以及系统稳定性进行分析,得到故障和转速之间的作用规律。结果表明,随着参数的改变,系统会呈现出丰富的动力学行为,包括单周期、多周期、拟周期和混沌等,该研究结果为汽车中驱动电机转子系统的设计和故障诊断提供了理论依据。

含裂纹缺陷的预扭壳结构非线性振动特性研究

基于扩展等几何方法和一阶壳体剪切变形理论建立了含裂纹缺陷的功能梯度预扭壳结构的非线性振动控制方程。控制方程中考虑了预扭壳结构的预扭角度及几何非线性,应用扩展等几何方法,采用反映位移变化的富集函数来描述裂纹的位置及长度,一方面可以提高计算精度,另一方面可以避免在裂纹处的网格加密,提高计算效率。采用了直接迭代法求解非线性振动控制方程。通过与现有文献结果对比,证明了本文方法的正确性和稳定性。在此基础上,探究裂纹对功能梯度预扭壳结构非线性振动频率的影响,研究了预扭角度、裂纹位置及长度和材料的功能梯度指数等参数对预扭壳非线性振动特性的影响规律。

基于小波时频分析的疲劳损伤定量表征

许多机械部件中的圆管结构长期在交变应力的工况下服役,容易出现疲劳裂纹,最终导致材料失效酿成事故。非线性超声能够表征疲劳裂纹的损伤程度,而表征损伤程度的非线性系数的提取方法尤为重要。提出一种基于小波变换的时频信号处理方法用以提取疲劳裂纹产生的非线性信号并以此计算非线性系数。首先,分析了多种小波基进行小波变换处理后得到的非线性系数间的量化关系;其次,利用仿真得到带有疲劳裂纹的圆管中的非线性超声导波信号,比较各类非线性系数提取方法得到的不同频率分量幅值随时间变化的信息;最后,建立疲劳裂纹损伤程度与各类方法得到的非线性系数间的量化关系。试验结果表明,所提方法得到的非线性系数能够更好地表征疲劳裂纹的损伤程度。

含呼吸裂纹的旋转扭型变截面叶片的动态接触特性

航空发动机叶片经常发生裂纹故障失效,从而引发一系列事故。以往的研究主要集中在裂纹引起的非线性振动上,而裂纹呼吸过程中裂纹表面的接触状态往往被忽略。然而,考虑裂纹表面的接触行为是非常重要的,因为它会导致裂纹叶片的非线性振动。为了进一步研究裂纹诱发非线性振动的机理,本文提出了一种基于自编非协调六面体单元(SNCHE)的旋转叶片动态接触呼吸裂纹模型,并使用弹簧单元模拟呼吸效应。通过接触有限元模型验证了模型的有效性。此外,还研究了裂纹参数(裂纹深度和裂纹位置)及载荷参数(气动振幅和气动频率)对裂纹叶片动态接触特性的影响。在此基础上,提出了一个呼吸裂纹量化指标(BCQI)来表征呼吸裂纹的非线性水平。结果表明,在裂纹呼吸过程中,裂纹面从叶片侧面向裂纹尖端中心方向闭合。并且BCQI随裂纹深度、气动幅值和转速的增加而增大,随裂纹位置越靠近叶尖而减小。

Analysis of the electromechanical behavior of ferroelectric ceramics based on a nonlinear finite element model

A nonlinear finite element （FE） model based on domain switching was proposed to study the electromechanical behavior of ferroelectric ceramics. The incremental FE formulation was improved to avoid any calculation instability. The problems of mesh sensitivity and convergence, and the efficiency of the proposed nonlinear FE technique have been assessed to illustrate the versatility and potential accuracy of the said technique. The nonlinear electromechanical behavior, such as the hysteresis loops and butterfly curves, of ferroelectric ceramics subjected to both a uniform electric field and a point electric potential has been studied numerically. The results obtained are in good agreement with those of the corresponding theoretical and experimental analyses. Furthermore, the electromechanical coupling fields near （a） the boundary of a circular hole, （b） the boundary of an elliptic hole and （c） the tip of a crack, have been analyzed using the proposed nonlinear finite element method （FEM）. The proposed nonlinear electromechanically coupled FEM is useful for the analysis of domain switching, deformation and fracture of ferroelectric ceramics.

NONLINEAR BUCKLING BEHAVIOR OF DAMAGED COMPOSITE SANDWICH PLATES CONSIDERING THE EFFECT OF TEMPERATURE-DEPENDENT THERMAL AND MECHANICAL PROPERTIES

On the basis of the first-order shear deformation plate theory andthe zig-zag deformation as- sumption, an incremental finite elementformulation for nonlinear buckling analysis of the composite sandwichplate is deduced and the temperature-dependent thermal and mechanicalproperties of composite is consid- ered. A finite element method forthermal or thermo-mechanical coupling nonlinear buckling analysis ofthe composite sandwich plate with an interfacial crack damage betweenface and core is also developed.

ANALYSIS OF DAMAGE NEAR A CONDUCTING CRACK IN A PIEZOELECTRIC CERAMIC

The finite element formulation for analyzing static damage near a conducting crack in a thin piezoelectric plate is established from the virtual work principle of piezoelectricity.The damage fields under various mechanical and electrical loads are calculated carefully by using an effective iterative procedure.The numerical results show that all the damage fields around a crack tip are fan-shaped and the electric field applied has great influence on the mechanical damage, which is related to the piezoelectric properties.

Multi-objective modeling and optimization for scheduling of cracking furnace systems

Cracking furnace is the core device for ethylene production. In practice, multiple ethylene furnaces are usually run in parallel. The scheduling of the entire cracking furnace system has great significance when multiple feeds are simultaneously processed in multiple cracking furnaces with the changing of operating cost and yield of product. In this paper, given the requirements of both profit and energy saving in actual production process, a multi-objective optimization model contains two objectives, maximizing the average benefits and minimizing the average coking amount was proposed. The model can be abstracted as a multi-objective mixed integer non- linear programming problem. Considering the mixed integer decision variables of this multi-objective problem, an improved hybrid encoding non-dominated sorting genetic algorithm with mixed discrete variables （MDNSGA-II） is used to solve the Pareto optimal front of this model, the algorithm adopted crossover and muta- tion strategy with multi-operators, which overcomes the deficiency that normal genetic algorithm cannot handle the optimization problem with mixed variables. Finally, using an ethylene plant with multiple cracking furnaces as an example to illustrate the effectiveness of the scheduling results by comparing the optimization results of multi-objective and single objective model.

ANALYSIS OF THE CHAOTIC MOTION FOR A ROTOR SYSTEM WITH A TRANSVERSE CRACK

The chaotic motion of an elastic shaft-disk rotor system including thegeometric nonlinearity of the shaft with a transverse crack is investigated. The critical conditionfor the system to enter chaotic state is given by the Melnikov method. Meanwhile, whether the chaosoccurs is determined by the Poincare map, phase portrait and time-displacement history diagram.

Concrete damage diagnosed using the non-classical nonlinear acoustic method

It is known that the strength of concrete is seriously affected by damage and cracking. In this paper, six concrete samples under different damage levels are studied. The experimental results show a linear dependence of the resonance frequency shift on strain amplitude at the fundamental frequency, and approximate quadratic dependence of the am- plitudes of the second and third harmonics on strain amplitude at the fundamental frequency as well. In addition, the amplitude of the third harmonics is shown to increase with the increase of damage level, which is even higher than that of the second harmonics in samples with higher damage levels. These are three properties of non-classical nonlinear acoustics. The nonlinear parameters increase from 106 to 108 with damage level, and are more sensitive to the damage level of the concrete than the linear parameters obtained by using traditional acoustics methods. So, this method based on non-classical nonlinear acoustics may provide a better means of non-destructive testing （NDT） of concrete and other porous materials.

非线性应力作用下裂缝砂岩应力敏感性特征

为了实现和评价变围压应力敏感实验关系转换为变内压应力敏感实验的等效关系,进而获取储层岩石渗透率与地层压力的关系,采用室内实验的方法,针对含微裂缝和人造裂缝的致密砂岩开展了变围压应力敏感实验、变内压应力敏感实验和特殊应力敏感实验;基于变围压实验数据,结合有效应力方程计算得到了实验岩样的渗透率随地层压力的变化关系,并与实验测定结果进行了对比分析。结果表明,计算得到的渗透率大于实验直接测定的渗透率,这种差异源于气体滑脱效应;基于Terzaghi有效应力方程计算的无因次渗透率小于对应变内压实验测定的无因次渗透率;基于非线性有效应力方程计算的无因次渗透率与对应变内压实验的无因次渗透率一致。有效应力和气体滑脱效应影响地层条件下渗透率的确定。

Finite Element Formulation and Analysis of Fracture Resistance Effected by Near-Tip Nonlinearities in Piezoelectric Solids

Comsidering the fact there are no systematic study on crack effected by large-scale near--tip nonlinearitiesup to now, a nonlinear finite element formulation accounting for nonlinearities and elasticity coupled with piezoelectricity is derived and a finite element program is developed. Numerical examples are presented to show the effect of nonlinear fracture characteristics on fracture resistance. It is found that an electric field may give a negative driving forceto prevent crack propagation.