基于GMRES算法的弹性结构强耦合小变形流激振动分析

使用混合广义变分原理,将基于Lagrange表述的小位移变形结构振动问题与基于Euler描述的不可压缩粘性流动问题,统一在功率平衡的框架下建立流固系统的耦合控制方程．用有限元格式做空间离散后,再用广义梯形法将有限元控制方程转化为增量型的线性方程组,该方程组的系数矩阵具有非对称性,其中元素含对流效应和时间因子．将GMRES算法与振动分析的Newmark法和流动分析的Hughes预测多修正法结合,发展成一种基于GMRES-Hughes-Newmark的稳定算法,用于计算具有复杂几何边界的强耦合流激振动问题．以混流式水轮机叶道为数值算例的计算表明,模拟结果与试验实测结果吻合较好．     

斜拉桥拉索-阻尼器系统非线性瞬态响应分析

考虑索的抗弯刚度、垂度及几何非线性的影响,得出了索-阻尼器系统的空间非线性振动偏微分方程,用中心差分法将偏微分方程在空间内离散,导出了系统的非线性振动常微分方程组．结合Newmark法及虚拟力法提出了一种用于求解非线性振动瞬态响应的杂交分析算法．并以典型的斜拉桥拉索为研究对象,给出了数值算例,并与Runge-Kutta直接积分法进行了比较,说明了杂交算法的准确性及有效性．为大跨斜拉桥拉索的振动控制研究提供了一种简便、有效、快速的时程分析方法．     

带裂纹三点弯曲试样的动态应力强度因子分析

提出了计算带单边裂纹三点弯曲试样动态应力强度因子的新方法．首先由权函数的普遍形式和两种参考载荷下的应力强度因子,得到了带单边裂纹三点弯曲试样的权函数,然后考虑试样的转动惯性和剪切变形,根据振动理论推导出无裂纹梁内的动应力响应和分布,最后由权函数的思想推导出了带裂纹三点弯曲试样动态应力强度因子公式．通过有限元数值计算,验证了该方法的正确性,结果比较表明公式具有较高的精度．另外,还研究了冲击载荷下三点弯曲试样的动态应力强度因子随裂纹长度和加载速率的变化规律．     

柔长结构气固耦合的线性与非线性气动力理论

针对柔性结构与风在三方向相互作用的特点,在合理的结构节段力学模型的基础上,建立了新的气动力模型,即三分力系数C_i=C_i(β(t),θ),(#em/em#=D,L,M)不仅是瞬时攻角的函数,而且也是转速的函数,并依据“片条理论”与改进的“准静态理论”,提出了推导结构节段模型与风相互作用的线性与非线性气动力项的方法,从而将土木工程中柔性结构与风的相互作用的线性与非线性理论集中到一个模型中.对于线性气动力部分,给出了与经典气动力公式中相对应的颤振导数的半解析表达式.对于非线性气动力部分,给出了扭转气动耦合的非线性气动力表达式,并给出了Tacoma大桥扭转非线性运动的控制方程,其形式与结果与V.F.B-m的相吻合.     

Unwanted noise and vibration control using finite element analysis and artificial intelligence

A mechatronic approach integrating both passive and active controllers is presented in this study to deal with unwanted noise and vibration produced in an automobile wiper system operation. Wiper system is a flexible structure with high order, nonlinear model that is considered as a multi objective control problem since there is a conflict between its functionality quality in wiping and generated unwanted noise and vibration. A passive control technique using multi body system (MBS) model and finite element analysis (FEA) is introduced to identify the potential of the effectiveness of the physical parameters of wiper blade to give appropriate range to reduce the unwanted noise and vibration in the system. While, the significant contribution of active controller is to deal with uncertainties exerted to system within wiper operation. In passive control stage, natural frequencies of a uni-blade automobile wiper are determined using modal testing. Later, a 3-dimensional model of a wiper blade assembly is developed in multi body system design to investigate the good validation test and agreement of the physical behavior of the system in experiment with finite element analysis. Parametric modification via complex eigenvalue is adopted to predict instability of the wiper blade. In active control level, experimental data collected from the wiper system during its operation. A system identification model named nonlinear auto regressive exogenous Elman neural network (NARXENN) is developed for implying the active controller. A bi-level adaptive-fuzzy controller is brought in whose parameters are tuned simultaneously by a multi objective genetic algorithm (MOGA) to deal with the conflict interests in wiper control problem.     

Modeling large amplitude vibration of pretwisted hybrid composite blades containing CNTRC layers and matrix cracked FRC layers

A modeling of the large amplitude free vibration of pretwisted hybrid composite blades is studied by considering the laminated structure which is composed of carbon nanotube reinforced composite (CNTRC) layers and matrix cracked fiber reinforced composite (FRC) layers. Two assumptions are made to facilitate this vibration study of hybrid nanocomposite: (1) CNTs are distributed across the layer thickness uniformly or functionally graded, and (2) the parallel slit matrix cracks disperse in the matrix homogeneously. Based on the theory of differential geometry, a novel shell model for pretwisted hybrid nanocomposites blade is developed. The von Kármán strains are adopted to capture the geometrically nonlinear behaviors of blades. The established governing equations are solved accurately and efficiently via the IMLS-Ritz method. The proposed numerical model is verified by making comparison studies and then the influence of crack density, pretwisted angle, CNT distribution and volume fraction, aspect ratio, width-to-thickness ratio, and ply-angle on the large amplitude vibration characteristics of matrix cracked pretwisted hybrid composite blade are scrutinized systematically. The present study serves as a useful benchmark to researchers who intend do further research in this topic.     

Numerical analysis of dynamic behavior of stream turbine blade group

This paper considers the stream turbine blade group as a rotationally periodic structure and the complex constraint method has been induced. The effect of the centrifugal force to dynamic vibration frequency has been considered by introducing a nonlinear large deformation equation. A method has been given to introduce the special constraint between the fin heaves of every blade during dynamic analysis.     

Nonaxisymmetric thermal stress state of laminated rotational bodies of orthotropic materials under nonisothermic loading

A procedure for numerical investigation of nonaxisymmetric temperature fields and the elastic stress-strain state of laminated rotational bodies of cylindrically and rectilinearly orthotropic materials under nonisothermal loading is proposed. The deformation of orthotropic materials is described by the equations of anisotropic elasticity theory. The equations of state are written in the form of Hookes law for homogeneous materials, with additional terms which take into account the thermal deformation, changes in the mechanical properties of materials in the circumferential direction, and their dependence on temperature. A semianalytic finite-element method in combination with the method of successive approximations is used. An algorithm for numerical solution of the corresponding nonlinear boundary problem is elaborated, which is realized as a package of applied FORTRAN programs. Some numerical results are presented.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 731–752, November–December, 2004.     

大型水平轴风力机叶片气动弹性计算

给出了一种考虑几何非线性的大型风力机静、 动气动弹性一体化计算方法．采用涡尾迹方法进行风力机气动载荷计算．建立风力机风轮的三维壳模型．沿周向平均风力机叶片载荷并加载到结构模型进行非线性静气动弹性分析．基于动力学小扰动假设, 在静平衡构型下进行动力学线性化, 计算风轮固有振动特性．继而结合非定常涡尾迹方法计算风力机动气动弹性响应．计算了NH 1500叶片考虑几何非线性的静气动弹性位移和动气动弹性响应．结果表明,大型风力机叶片几何非线性较为明显地减小静气动弹性位移,同时降低动气动弹性的响应幅值．大型风力机气动弹性响应计算需要考虑几何非线性     

Aeroelastic analysis of large horizontal wind turbine baldes?

A nonlinear aeroelastic analysis method for large horizontal wind turbines is described. A vortex wake method and a nonlinear ?nite element method (FEM) are coupled in the approach. The vortex wake method is used to predict wind turbine aero-dynamic loads of a wind turbine, and a three-dimensional (3D) shell model is built for the rotor. Average aerodynamic forces along the azimuth are applied to the structural model, and the nonlinear static aeroelastic behaviors are computed. The wind rotor modes are obtained at the static aeroelastic status by linearizing the coupled equations. The static aeroelastic performance and dynamic aeroelastic responses are calculated for the NH1500 wind turbine. The results show that structural geometrical nonlinearities signi?cantly reduce displacements and vibration amplitudes of the wind turbine blades. Therefore, structural geometrical nonlinearities cannot be neglected both in the static aeroelastic analysis and dynamic aeroelastic analysis.     

Nonlinear free vibration analysis of functionally graded beams by using different shear deformation theories

This study investigates the nonlinear free vibration of functionally graded material (FGM) beams by different shear deformation theories. The volume fractions of the material constituents and effective material properties are assumed to be changing in the thickness direction according to the power-law form. The von Kármán geometric nonlinearity has been considered in the formulation. The Ritz method and Lagrange equation are adopted to yield the discrete formulations. A direct numerical integration method for the motion equation in matrix form is developed to solve the nonlinear frequencies of FGM beams. Comparing with the global concordant deformation assumption (GCDA), a new deformation assumption named as local concordant deformation assumption (LCDA) is proposed in this study. The LCDA fits with the real deformation of the vibrating beam better, thus more accurate results of the nonlinear frequency can be expected. In numerical results, the comparison study of the GCDA and LCDA is carried out. In addition, the effects of power-law index, slenderness ratio and maximum deflection for different shear deformation theories and boundary conditions on the nonlinear frequency of the beam are discussed.     

扁薄锥壳在周边弯矩和横向载荷共同作用下的非线性振动

从问题的变分方程和协调方程出发,选取扁锥壳中心最大振幅为摄动参数,采用摄动变分法,对周边简支的扁薄锥壳在周边弯矩和横向载荷共同作用下的非线性振动问题进行了求解.一次近似得到了扁薄锥壳在静载荷作用下的线性固有频率,二次近似得到了扁薄锥壳在静载荷作用下的精确度较高的非线性固有频率.并给出了小变形时固有频率与周边弯矩、横向载荷、振幅以及锥底角之间非线性关系的三次近似解析表达式,数值结果的图形反映了在一定范围内固有频率和各参数之间非线性关系的复杂性和规律性.     

Dynamic analysis of non-uniform taper bars in post-elastic regime under body force loading

This paper presents a simulation study of the free flexural vibration behavior of non-uniform taper bars of circular and rectangular cross-section under body force loading due to gravity. The loading is controlled statically to take the bar to its post-elastic state so as to predict its dynamic behavior in the presence of plastic deformation. Hence the analysis is carried out in two parts; first the static problem under axial gravity loading is solved, then the dynamic problem is solved in this loaded condition. Appropriate variational method is employed to derive the set of governing equations for both the problems. The formulation is based on unknown displacement field which is approximated by finite linear combinations of orthogonal admissible functions. The present method is validated successfully with a well-known finite element package. Results are presented to investigate the effect of shape and size on the dynamic behavior of non-uniform taper bars. The study can be extended to study the post-elastic dynamic behavior of other related problems such as rotating beams and rotating disks.     

Simulation of nonlinear properties of ferroelectric and piezoceramicmaterials

Ferroelectric and piezoelectric materials are becoming a very significant part of smart materials that are used widely as actuators, sensors and most common applications such as vibration control, precision positioning, precision cutting and microelectromechanical systems (MEMS). Piezoceramic materials show nonlinear characteristics when they are under high electromechanical loading. In this study, nonlinear behaviour of tetragonal perovskite type piezoceramic materials is simulated using micromechanical model. In the simulations uni‐axial loading is applied. The calculations which are based on a linear constitutive model, nonlinear domain switching model and a model of probability to switch are performed at each grain. The different domain switching effects (900 or 1800 domain switching for tetragonal perovskite structure) due to energy differences, different probability functions, different statistical random generators and material parameters are analyzed. Finally, simulation results are compared with the data of experiments are giving in literature. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A continuous model for investigation of physically nonlinear deformation of orthotropic sandwich plates

A phenomenological yield condition for quasi-brittle and plastic orthotropic materials with initial stresses is suggested. All components of the yield tensor are determined from experiments on uniaxial loading. The reliability estimates of the criterion suggested is discussed. For a plastic material without initial stresses, the given condition transforms into the Marin—Hu criterion. The defining equations of the deformation theory of plasticity with isotropic and “anisotropic” hardening, associated with the yield condition suggested, are obtained. These equations are used as the basis for a highly accurate nonclassical continuous model for nonlinear deformation of thick sandwich plates. The approximations with respect to the transverse coordinate take into account the flexural and nonflexural deformations in transverse shear and compression. The high-order approximations allow us to model the occurrence of layer delamination cracks by introducing thin nonrigid interlayers without violating the continuity concept of the theory. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. pp. 329–340, May–June, 2000.     

Application of non-smooth NES in vibration suppression of rotor-blade systems

The non-smooth nonlinear energy sink (NSNES) is used to suppress the vibration of the rotor-blade system. Firstly, the structure and working principle of the NSNES for rotor-blade system are introduced. Then, the dynamics model of the rotor-blade-NSNES system is established by Lagrangian method. And then, numerical simulations are applied to evaluate the vibration suppression ability of the NSNES on rotor and blade. The results show that the suppression rates of NSNES on the rotor and the blade can reach 81% and 74% in steady state resonance under given parameters, respectively; and for transient vibration of blade, a 1.85 times dissipating speed is obtained in rotor-blade system with NSNES than that without NSNES. In particular, NSNES has better vibration suppression capability than linear dynamic vibration absorber (LDVA) when both have the same vibration absorption mass.     

Large-amplitude free vibrations of functionally graded beams by means of a finite element formulation

The large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The Von-Karman type nonlinear strain–displacement relationships are employed where the ends of the beam are constrained to move axially. The effects of the transverse shear deformation and rotary inertia are included based upon the Timoshenko beam theory. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A statically exact beam element which devoid the shear locking effect with displacement fields based on the first order shear deformation theory is used to study the geometric nonlinear effects on the vibrational characteristics of functionally graded beams. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law exponent, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible. Some new results for the nonlinear natural frequencies are presented in both tabular and graphical forms which can be used for future references.     

基于分子动力学模拟的金属构件的弹-塑性分解方法

针对金属多晶材料构件的分子动力学（MD）模拟,本文提出了一种新的弹-塑性分解方法.文章将MD运动轨迹分解为结构变形和热振动,给出了计算结构变形的方法和近似公式;针对金属多晶材料构件的当前构型,给出了基于FCC|BCC晶胞和四原子占位的四面体单元相组合的连续变形函数及计算变形梯度的算法;利用原子-连续关联模型,发展了计算当前构型应力场和弹性张量的算法.分析了当构件承受过大载荷后在材料内部所产生的微观缺陷,并将其分类标定为位错、层错、挛晶界、晶界和空位等;对于层错和挛晶界讨论了在弹性卸载过程中应满足的刚体运动约束方程;利用极小势能原理构造了基于当前构型的弹性卸载算法,进而给出了完整的基于MD模拟的计算弹-塑性应变的算法.最后,针对单晶铜纳米线拉伸的MD模拟,计算了弹-塑性应变场,验证了本文方法的合理性.
本文提出的基于MD模拟的弹-塑性分解方法,为从微观到宏观的多尺度和多模型耦合计算提供了算法支撑.