压电智能环形板的主动控制

对在不同位置粘有任意多组压电传感器和压电执行器的轴对称弹性环形薄板的振动控制进行了研究．根据压电执行元件的等效作用量得到了压电智能环板的振动控制方程和传感方程,再利用分离变量法以及由传感器测得的电量和作用在执行器上电压之间的控制模式得到振动方程的全解．实行了对整体结构的主动控制．对不同的压电片布置进行了数值计算．结果表明：当离散分布压电元件布置越密,振动衰减的效果越佳     

Stochastic response determination of structural systems modeled via dependent coordinates: a frequency domain treatment based on generalized modal analysis

Generalized independent coordinates are typically utilized within an analytical dynamics framework to model the motion of structural and mechanical engineering systems. Nevertheless, for complex systems, such as multi-body structures, an explicit formulation of the equations of motion by utilizing generalized, independent, coordinates can be a daunting task. In this regard, employing a set of redundant coordinates can facilitate the formulation of the governing dynamics equations. In this setting, however, standard response analysis techniques cannot be applied in a straightforward manner. For instance, defining and determining a transfer function within a frequency domain response analysis framework is challenging due to the presence of singular matrices, and thus, the machinery of generalized matrix inverses needs to be employed. An efficient frequency domain response analysis methodology for structural dynamical systems modeled via dependent coordinates is developed herein. This is done by resorting to the Moore–Penrose generalized matrix inverse in conjunction with a recently proposed extended modal analysis treatment. It is shown that not only the formulation is efficient in drastically reducing the computational cost when compared to a straightforward numerical evaluation of the involved generalized inverses, but also facilitates the derivation and implementation of the celebrated random vibration input–output frequency domain relationship between the excitation and the response power spectrum matrices. The validity of the methodology is demonstrated by considering a multi-degree-of-freedom shear type structure and a multi-body structural system as numerical examples.

     

Stability case study of the ACROBOTER underactuated service robot

The dynamics of classical robotic systems are usually described by ordinary differential equations via selecting a minimum set of independent generalized coordinates. However, different parameterizations and the use of a nonminimum set of (dependent) generalized coordinates can be advantageous in such cases when the modeled device contains closed kinematic loops and/or it has a complex structure. On one hand, the use of dependent coordinates, like natural coordinates, leads to a different mathematical representation where the equations of motion are given in the form of differential algebraic equations. On the other hand, the control design of underactuated robots usually relies on partial feedback linearization based techniques which are exclusively developed for systems modeled by independent coordinates. In this paper, we propose a different control algorithm formulated by using dependent coordinates. The applied computed torque controller is realized via introducing actuator constraints that complement the kinematic constraints which are used to describe the dynamics of the investigated service robotic system in relatively simple and compact form. The proposed controller is applied to the computed torque control of the planar model of the ACROBOTER service robot. The stability analysis of the digitally controlled underactuated service robot is provided as a real parameter case study for selecting the optimal control gains.     

基于对称性的三维车辆轨道耦合系统随机振动虚拟激励方法

基于结构的对称性提出了用于三维车辆轨道耦合系统高效随机动力响应分析的虚拟激励方法.车辆采用刚体动力学模型,轨道结构利用三维轨道广义单元建模,车辆与轨道通过线性轮轨关系耦合.采用虚拟激励法将高低、方向和水平三类轨道不平顺转化为一系列筒谐的虚拟不平顺;考虑车辆及轨道结构的对称性,分别推导了耦合系统的对称和反对称凝聚矩阵,提出了用于车辆轨道耦合系统动力响应计算的自由度凝聚方法,将耦合系统的自由度缩减至原来的一半以下,并在此基础上实现了耦合系统随机振动的高效分析.数值算例将本文方法与传统有限元方法进行对比,验证了本文方法的正确性和有效性.     

空间结构耦合模态控制及实验研究

智能结构以主动元件为传感器和驱动器,根据结构的动态响应和控制要求,自适应地改变结构的动态性能,实现结构特性的自调节功能,以增强结构适应于外界环境变化的能力.结构振动主动控制方法中常用的模态空间控制方法,就是将系统方程转化到模态坐标下,从而得到内部解耦的以模态坐标表示的方程组,然后根据一定的控制方法,计算出模态控制力,实现实时控制.该方法计算简单,效率高,能满足实时控制的需要.本文根据一个三层智能结构主动控制实验,介绍了耦合模态控制理论及实现方法,设计并阐述了压电主元杆件的工作原理,根据Riccati方程得到了主元杆件的最优布置.通过对实验数据运用五点滑动平均平滑法进行处理分析及频谱分析可以看到,智能结构通过主动控制,对相应的控制模态位移及加速度有很大的抑制作用,对应的模态阻尼系数得到了不同程度的提高.     

On the equations of motion for accelerated frames

In this communication we present the equations of Euler generalized for the motion of a body in an accelerated reference frame using the generalized work-energy principle. The equivalence among the generalized Euler equation, the generalized Lagrange equation, and the generalized Kane equation are shown when applied to the motion of a body of a holonomic system that depend onn generalized coordinates. Therefore when the generalized coordinates can be reduced to two sets of independent coordinates, the generalized Euler equation can be split into two uncoupled equations that are not independent of each other.Universidade da Beira Interior, Covilhã, Portugal. Published in Prikladnaya Mekhanika, Vol. 31, No. 9, pp. 79–89, September, 1995.     

二维含裂纹结构与声耦合问题研究

应用分形有限元方法结合边界元方法研究了二维含裂纹结构和声耦合问题.采用二级分形有限元方法对含裂纹的弹性结构体进行离散处理,这样可以使得自由度数大大地减少;无限大外域声场的计算使用边界元方法,可以自动满足无穷远辐射条件.数值仿真算例结果表明:结构声耦合系统的共振频率随着裂纹深度的增加而下降;裂纹附近的声场所受的影响较为明显.     

The normal modes of non-linear symmetric systems by group representation theory

Group representation theory is applied to analyze a symmetric spring mass system of finite degree of freedom for non-linear normal modes of vibration. A set of symmetry operations constituting a group characterises the symmetry of a system. The symmetry adapted basis vectors, corresponding to the irreducible representations present in the reducible representation, are determined. The equations of motion in the symmetry adapted coordinates have a lower order of coupling. An equipotential surface in each invariant subspace is determined from which the normal mode vectors are evaluated in terms of the symmetry adapted basis vectors.     

框架结构振动控制系统可靠性研究

振动控制系统的可靠性可以反映出主动控制的效果,本文提出了一种适合于确定框架结构控制系统可靠性的计算方法。该方法利用模态变换,把系统变为模态独立的振动方程,根据Field提出的假设,先定义阈值,假设控制后系统响应对阈值的穿阈率服从泊松分布,然后根据各模态的控制结果确定相应的可靠性,最后根据Veneziano提出的方法给出系统的可靠性。文中提出针对框架最大位移的控制输出来确定系统可靠性概念;此外,在系统降阶和控制方法方面,选择了基于系统可控性的平衡降阶法和针对系统不确定性具有较好控制效果的广义预测控制,最后给出了计算实例,算例表明这一方法是有效的。     

正交各向异性功能梯度材料开口圆柱壳的自由振动分析

区别于一般圆柱壳,开口圆柱壳沿周向是不封闭的,因此具有四个边界,本文根据轴向梁式振动和轴向曲拱振动特性对各种端部与侧边边界条件下的壳体提出统一的位移振型函数,并根据哈密顿原理建立了材料参数与空间坐标相关的正交各向异性开口圆柱壳的动力变分方程,求出了不同材料属性下开敞圆柱壳固有频率与振型解的一般解析表达式,适用于任意边界条件下不同材料的开敞圆柱壳自由振动分析．     

广义Hamilton系统的保结构算法

基于广义Hamilton系统微分方程解析解理论。给出了构造保持系统真解典则性的高阶显式积分格式的方法,并说明其可推广到广义Hamilton控制系统。该方法保持了原系统的几何定性特征,因而是稳定的。数值例子说明了算法的有效性。     

Analysis of the structure of generalized forces in the Lagrange equations

Stability of mechanical systems in the sense of Thomson and Tait [1] can be judged from the type of forces applied to them. The forces are usually divided into potential (conservative), circular, dissipative, accelerating, gyroscopic, etc. The decomposition itself of generalized positional forces into conservative and properly nonconservative forces is well known for the case in which these forces linearly depend on the generalized coordinates (e.g., see [1–5]). Such a decomposition is associated with the unique representation of an arbitrary matrix of these forces as the sum of symmetric and skew-symmetric parts. Generalized forces linearly depending on the velocities can in a similar way be divided into dissipative and gyroscopic parts. In the present paper, we show how the same decomposition can be performed in the general nonlinear case.     

考虑时滞的框架结构控制可靠性研究

提出了一种适合于确定框架结构可靠性计算方法．利用模态变换，把系统变为模态独立的振动方程，根据Field提出的假设，先定义阈值，假设控制后系统响应对阚值的穿阚率服从泊松分布，然后根据各模态的控制结果确定相应的可靠性．最后根据Veneziano提出的方法给出系统的可靠性。本文提出针对框架重点部位的控制输出来确定系统可靠性概念。考虑到实际情况，在控制方法选择针对系统不确定性具有较好控制效果的广义预测控制并考虑时滞影响。本文最后给出了计算实例。     

完全笛卡尔坐标描述的多体系统动力学

用完全笛卡尔坐标描述多体系统的运动学和动力学在提高计算效率方面有突出优点．导出用完全笛卡尔坐标表示的刚体及多体系统的动量和动量矩的解析式，给出与之对应的广义惯量矩阵概念，建立无力矩状态下用完全笛卡尔坐标描述的多体系统动力学的一阶微分方程组，用于多体航天器的姿态运动分析     

随机振动问题的广义坐标合成法

工程中的随机振动分析多采用完全二次型组合法(CQC)及其改进算法,如虚拟激励法(PEM)和谐波激励法(HEM)。广义坐标合成法(GCS)提出了一种计算随机响应的新思路,其基本原理是将物理空间的计算转移到自由度较小的振型空间进行,从而缩减了计算量和计算规模。对于较大规模结构体系的随机振动问题,GCS方法计算响应协方差矩阵的计算量只相当于PEM的2r/sT,其中s、r和T分别为激励功率谱矩阵的秩、振型总数和离散频率点数。此外,对于给定激励时程的问题,由于GCS方法直接求解广义坐标运动方程,因而可以方便得出响应时程。通过对几种方法的详细对比,说明对于大多数只需要求解响应方差的随机振动问题,GCS是最优的计算方法。PEM只有在s相似文献   

The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets

Traditional rotor dynamics mainly focuses on the steady- state behavior of the rotor and shafting. However, for systems such as hydro turbine generating sets (HTGS) where the control and regulation is frequently applied, the shafting safety and stabilization in transient state is then a key factor. The shafting transient state inevitably involves multiparameter domain, multifield coupling, and coupling dynamics. In this paper, the relative value form of the Lagrange function and its equations have been established by defining the base value system of the shafting. Taking the rotation angle and the angular speed of the shafting as a link, the shafting lateral vibration and generator equations are integrated into the framework of generalized Hamiltonian system. The generalized Hamiltonian control model is thus established. To make the model more general, additional forces of the shafting are taken as the input excitation in proposed model. The control system of the HTGS can be easily connected with the shafting model to form the whole simulation system of the HTGS. It is expected that this study will build a foundation for the coupling dynamics theory using the generalized Hamiltonian theory to investigate coupling dynamic mechanism among the shafting vibration, transient of hydro turbine generating sets, and additional forces of the shafting.     

基于质量阵Cholesky分解的发动机悬置系统优化

根据拉格朗日方程,建立发动机悬置系统的动力学模型;基于广义坐标下质量矩阵的Cholesky分解,设计正则模态矩阵;结合悬置系统的能量分布矩阵和工程约束条件,在最小二乘原则下,对支撑参数进行优化求解;在发动机的振动激励源分析的基础上,通过对悬置系统进行动力学仿真,证明了基于质量阵Cholesky分解的发动机悬置系统优化方法的可行性及有效性。     

A modified incremental harmonic balance method for rotary periodic motions

The determination of periodic solutions is an essential step in the study of dynamic systems. If some of the generalized coordinates describing the configuration of a system are angular positions relative to certain reference axes, the associated periodic motions divide into two types: oscillatory and rotary periodic motions. For an oscillatory periodic motion, all the generalized coordinates are periodic in time. On the other hand, for a rotary periodic motion, some angular coordinates may have unbounded magnitude due to the persistent circulation about their pivots. In this case, although the behaviour of the system is periodic physically, those angular coordinates are not periodic in time. Although various effective methods have been developed for the determination of oscillatory periodic motion, the rotary periodic motion can only be determined by brute force integration. In this paper, the incremental harmonic balance (IHB) method is modified so that rotary periodic motions can be determined as well as oscillatory periodic motions in a unified formulation. This modified IHB method is applied to a practical device, a rotating disk equipped with a ball-type balancer, to show its effectiveness.     

A version of the finite element method for frictional contact problems

We propose a method for solving frictional contact problems which is based on including the generalized coordinates of absolutely rigid bodies in the degrees of freedom of the system under study and on varying the functional of the variational problem with respect to these coordinates. As a result, one can include the generalized coordinates or the energy-conjugate generalized forces directly in the right-hand side of the resolving system of equations, which permits easily taking into account any laws of motion or loading of absolutely rigid bodies.     

Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate

The constitutive relations and field equations for anisotropic generalized thermoelastic diffusion are derived and deduced for a particular type of anisotropy, i.e. transverse isotropy. Green and Lindsay (GL) theory, in which, thermodiffusion and thermodiffusion–mechanical relaxations are governed by four different time constants, is selected for study. The propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, elastic plate of finite width is studied, in the context of generalized theory of thermoelastic diffusion. According to the characteristic equation, three quasi-longitudinal waves namely, quasi-elastodiffusive (QED-mode), quasi-massdiffusive (QMD-mode) and quasi-thermodiffusive (QTD-mode) can propagate in addition to quasi-transverse waves (QSV-mode) and the purely quasi-transverse motion (QSH-mode), which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew symmetric modes of the plate are derived. The amplitudes of displacements, temperature change and concentration for symmetric and skew symmetric modes of vibration of plate are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient and amplitudes of wave propagation are presented graphically in order to illustrate and compare the analytically results. Some special cases of frequency equation are also deduced from the existing results.