刚体单元及其在多体系统动力学中的应用

多体系统动力学分析软件要求人工输入形状复杂物体的质量、质心位置和转动惯量,而实际上这些参量并不容易获得。本文探索了一种以组成物体的刚体单元为基本要素的新方法,并结合实际需要具体构造了刚性四面体和刚性梁单元。以刚体单元为基础并内嵌网格剖分模块的分析软件能够自动获得这些参数,从而具备处理任何复杂系统的能力。仿真结果的对比分...     

Towards linear modal analysis for an L-shaped beam: Equations of motion

We consider an L-shaped beam structure and derive all the equations of motion considering also the rotary inertia terms. We show that the equations are decoupled in two motions, namely the in-plane bending and out-of-plane bending with torsion. In neglecting the rotary inertia terms the torsional equation for the secondary beam is fully decoupled from the other equations for out-of-plane motion. A numerical modal analysis was undertaken for two models of the L-shaped beam, considering two different orientations of the secondary beam, and it was shown that the mode shapes can be grouped into these two motions: in-plane bending and out-of-plane motion. We compared the theoretical natural frequencies of the secondary beam in torsion with finite element results which showed some disagreement, and also it was shown that the torsional mode shapes of the secondary beam are coupled with the other out-of-plane motions. These findings confirm that it is necessary to take rotary inertia terms into account for out-of-plane bending. This work is essential in order to perform accurate linear modal analysis on the L-shaped beam structure.     

Damage detection method in complicated beams with varying flexural stiffness

A damage detection method for complicated beam-like structures is proposed based on the subsection strain energy method (SSEM), and its applicability condition is introduced. For a beam with the continuously varying flexural stiffness and an edge crack, the SSEM is used to detect the crack location effectively by numerical modal shapes. As a complicated beam, the glass fiber-reinforced composite model of a wind turbine blade is studied based on an experimental modal analysis. The SSEM is used to calculate the damage index from the measured modal parameters and locate the damage position in the blade model successfully. The results indicate that the SSEM based on the modal shapes can be used to detect the damages in complicated beams or beam-like structures for engineering applications.     

Modal acoustic impedance force on a spherical source near a rigid interface

The modal acoustic radiation load on a spherical surface undergoing angularly periodic axisymmetric harmonic vibrations while immersed in an acoustic halfspace with a rigid (infinite impedance) planar boundary is analyzed in an exact fashion using the classical technique of separation of variables. The formulation utilizes the appropriate wave field expansions, the classical method of images and the appropriate translational addition theorem to simulate the relevant boundary conditions for the given configuration. The associated acoustic field quantities such as the modal impedance matrix and the modal acoustic radiation force acting on the spherical surface are determined. The analytical results are illustrated with a numerical example in which the spherical surface, excited in vibrational modes of various orders, is immersed near an impervious rigid wall. The presented solution could eventually be used to validate those obtained by numerical approximation techniques.     

Displacement modal identification method of elastic system under operational condition

Modal identification of engineering structure in operation deals with the estimation of modal parameters from vibration data obtained in working conditions rather than laboratory conditions. After one structure destruction during a flight test, it was strongly required to carry out full-scale model testing to acquire the low-frequency vibration acceleration data of the investigated rocket (its structural dynamic properties could be represented by a beam). These vibration data were used to assess the modal properties of the modified structure. In this paper, a new modal identification method based on vibration displacement is suggested. The displacements of the measured points on the rocket are obtained by the integration of the low-frequency vibration accelerations during free flight test. In the method, the data are filtered through wavelet transform. For comparison, several methods are used to extract the modal frequencies of the investigated beam. In terms of the results of standard deviation of identified frequencies, it is believed that the generalized displacement-based modal identification method is more practicable in modal identification for similar problems.     

PrandtlPlane Joined Wing: Body freedom flutter,limit cycle oscillation and freeplay studies

Dynamic aeroelastic behavior of a joined-wing PrandtlPlane configuration is investigated herein. The baseline model is obtained from a configuration previously designed by partner universities through several multidisciplinary optimizations and ad hoc analyses, including detailed studies on the layout of control architecture. An equivalent structural model has then been adopted to qualitatively retain similar aeroelastic properties.Flutter and post-flutter regimes, including limit cycle oscillations (LCOs), are studied. A detailed analysis of the energy transfer between fluid and structure is carried out; the areas in which energy is extracted from the fluid are identified to gain insights on the mechanism leading to the aeroelastic instability. Starting from an existing design of control surfaces on the baseline configuration, freeplay is also considered and its effects on the aeroelastic stability properties of the joined-wing system are investigated for the first time.Both cantilever and free flying configurations are analyzed. Fuselage inertial effects are modeled and the aeroelastic properties are studied considering plunging and pitching rigid body modes. For this configuration a positive interaction between elastic and rigid body modes yields a flutter-free design (within the range of considered airspeeds).To understand the sensitivity of the system and gain insight, fuselage mass and moment of inertia are selectively varied. For a fixed pitching moment of inertia, larger fuselage mass favors body freedom flutter. When the moment of inertia is varied, a change of critical properties is observed. For smaller values the pitching mode becomes unstable, and coalescence is observed between pitching and the first elastic mode. Increasing pitching inertia, the above criticality is postponed; meanwhile, the second elastic mode becomes unstable at progressively lower speeds. For larger inertial values “cantilever” flutter properties, having coalescence of first and second elastic modes, are recovered.     

Scaling Mode Shapes in Output-Only Systems by a Consecutive Mass Change Method

In operational modal analysis (OMA) mode shapes can be obtained only with arbitrary normalization. There are many applications where mass normalized mode shapes are required, such as response prediction and stress analysis. A method to scale the mode shapes in OMA is to modify the dynamic behaviour of the structure by adding masses and then to use the modal parameters of both the original and modified structure. Several mass change methods have been proposed in recent years for estimating the scaling factors, where a distributed array of added masses are needed to obtain good results. In this work a new mass change approach based on performing several individual mass changes is presented. This approach requires only a small number of masses that are located at different points in each individual experiment. The results of the individual tests are then combined to estimate the scaling factors. The approach is developed and validated by measurements carried out on a 15-tonne prestressed concrete slab strip and a steel cantilever beam. The results show that a good accuracy can be obtained by this method when a proper mass change strategy is used.     

An Experimental Evaluation of Two Potential Improvements for 3D Laser Vibrometer Based Operational Modal Analysis

The use of scanning laser doppler vibrometers (SLDV) is common practice in the context with experimental modal analysis. In recent years, commercial 3D SLDV have been developed, where three laser heads simultaneously point to the same measuring point and an input reference signal is used to combine the results of consecutive records. If the input reference signal is replaced by an additional output reference signal, an operational modal analysis (OMA) can be performed. However, in this case the use of single-point measurements may lead to difficulties identifying certain vibrational modes. Two improvements to reduce these issues were developed in this study: the application of pre-estimation multi-setup merging methods and the use of multi-point measurements with post-estimation coordinate transformation. An enhancement for the application of OMA methods is shown in both cases. In this context there are different possibilities to obtain output reference signals: a) from additional accelerometers or vibrometers and b) from the scan heads of the 3D SLDV itself. Their suitability is investigated in terms of data acqusition, modal analysis and multi-setup merging. Additionally, the feasibility of a “no-reference” measurement is shown. The developed methods have been applied to experimental data using the stochastic subspace identification (cov/ref) and three multi-setup merging methods.     

计及剪切变形的Timoshenko梁的刚-柔耦合动力学

研究带中心刚体的Timoshenko梁的刚-柔耦合动力学问题。从力学的基本原理出发,基于Timoshenko梁假设,用虚功原理建立了带中心刚体的柔性梁的刚-柔耦合动力学方程。仿真计算结果表明,随着梁的惯量矩和横截面积比逐渐增大,剪切变形对梁的刚-柔耦合动力学性态产生了一定的影响。此外,本文还对不计剪切变形的Euler-Bernoulli梁假设的适用性进行了研究。     

Control structure interaction in the nonlinear analysis of flexible mechanical systems

The effect of the control structure interaction on the feedforward control law as well as the dynamics of flexible mechanical systems is examined in this investigation. An inverse dynamics procedure is developed for the analysis of the dynamic motion of interconnected rigid and flexible bodies. This method is used to examine the effect of the elastic deformation on the driving forces in flexible mechanical systems. The driving forces are expressed in terms of the specified motion trajectories and the deformations of the elastic members. The system equations of motion are formulated using Lagrange's equation. A finite element discretization of the flexible bodies is used to define the deformation degrees of freedom. The algebraic constraint equations that describe the motion trajectories and joint constraints between adjacent bodies are adjoined to the system differential equations of motion using the vector of Lagrange multipliers. A unique displacement field is then identified by imposing an appropriate set of reference conditions. The effect of the nonlinear centrifugal and Coriolis forces that depend on the body displacements and velocities are taken into consideration. A direct numerical integration method coupled with a Newton-Raphson algorithm is used to solve the resulting nonlinear differential and algebraic equations of motion. The formulation obtained for the flexible mechanical system is compared with the rigid body dynamic formulation. The effect of the sampling time, number of vibration modes, the viscous damping, and the selection of the constrained modes are examined. The results presented in this numerical study demonstrate that the use of the driving forees obtained using the rigid body analysis can lead to a significant error when these forces are used as the feedforward control law for the flexible mechanical system. The analysis presented in this investigation differs significantly from previously published work in many ways. It includes the effect of the structural flexibility on the centrifugal and Coriolis forces, it accounts for all inertia nonlinearities resulting from the coupling between the rigid body and elastic displacements, it uses a precise definition of the equipollent systems of forces in flexible body dynamics, it demonstrates the use of general purpose multibody computer codes in the feedforward control of flexible mechanical systems, and it demonstrates numerically the effect of the selected set of constrained modes on the feedforward control law.     

Experiments on a beam-rigid body structure repetitively impacting a rod

This paper investigates the experimental dynamics of a beam structure that supports an attached rigid body and that can impact a comparatively compliant base structure. The problem area is motivated by impact phenomena that are observed in certain structures internal to nuclear reactors. The assembly is subjected to base excitation at specified frequency and acceleration, and the resulting displacement and velocity time histories are recorded and used to obtain spectra, phase diagrams, and Poincaré sections. The measurements validate simulation results obtained by using a constraint and modal mapping method based on the two sets of modes when the structure is in-contact, and when it is not-in-contact. Generalized coordinates are mapped across the impact discontinuities in the modal representation. The forced response simulation predicts the test specimen’s response over a range of excitation frequencies. The specimens are fabricated as single integral structures from acrylnitrile butadene styrene plastic through rapid prototyping technology in order to eliminate the undesirable dissipation and flexibility arising from joints and connections. The experimental system can exhibit complex response characteristics, and the influences on complexity of deadband clearance and of asymmetry in the point of impact are examined in the experiments.     

钢筋混凝土深梁频率特性的近似计算方法

讨论了纵向通长钢筋对等截面钢筋混凝土深梁自振频率的影响。首先建立了钢筋混凝土深梁的求解方程,然后提出了求解Timoshenko梁特征值问题的模态摄动法,最后通过算例,说明不同含钢率下钢筋混凝土深梁的自振特性的变化情况。算例表明,若忽略纵向通长钢筋的影响,计算所得的钢筋混凝土深梁的振动特征值将产生较大的误差。     

Timoshenko固端梁特征值问题近似计算方法

利用模态摄动法将Timoshenko梁特征值问题的求解转化为一组非线性代数方程组的求解，不仅可以简化计算过程，而且计算结果具有较高的精度，对同一类问题具有适用性。通过算例，计算了在不同长细比条件下，剪切变形和转动惯量对固端梁的各阶主频率的影响。     

Experimental and numerical investigations of the responses of a cantilever beam possibly contacting a deformable and dissipative obstacle under harmonic excitation

In this paper, the dynamics of a cantilever beam subjected to harmonic excitations and to the contact of an obstacle is studied with the help of experimental and numerical investigations. The steel flexible structure is excited close to the free end with a shaker and may come into contact with a deformable and dissipative obstacle. A technique for modeling contact phenomena using piece-wise linear dynamics is applied. A finite-dimensional modal model is developed through a Galerkin projection. Concentrated masses, dampers and forces are considered in the equations of motion in such a way that the boundary conditions are those of a cantilever beam. Numerical studies are conducted by assuming finite-time contact duration to investigate the frequency response of the impacted beam for different driving frequencies. Experimental results have been extrapolated through a displacement laser sensor and a load cell. The comparison between numerical and experimental results show many qualitative and quantitative similarities.The novelty of this paper can be synthetized in (a) the development of experimental results that are in good agreement with the numerical implementation of the introduced model; (b) the development of a comprehensive contact model of the beam with an unilateral, deformable and dissipative obstacle located close to the tip; (c) the possibility of accounting for higher modes for the cantilever beam problem, and hence of analyzing how the response varies when moving the excitation (and/or the obstacle) along the beam, and of investigating the effect of the linearly elastic deformability of the built‐in end of the beam; (d) an easy and intuitive solution to the problem of accounting for spatially singular masses, dampers, springs and forces in the motion equations; (e) the possibility of accounting for finite gap and duration of the contact between beam and obstacle.     

Non-linear dynamic analysis of tensegrity structures using a co-rotational method

A new formulation is presented for the non-linear dynamic analysis of space truss structures. The formulation is based on the dynamics of 3D co-rotational rods. In the co-rotation method, the rigid body modes are assumed to be separated from the total deformations at the local element level. In this paper a new co-rotational formulation is proposed based on the direct derivation of the inertia force vector and the tangent dynamic matrix. A closed-form equation is derived for the calculation of the inertia force, the tangent dynamic matrix, the mass matrix and the gyroscopic matrix. The new formulation is used to perform dynamic analysis of example tensegrity structures. The developed formulation is applicable to tensegrity structures with non-linear effects due to internal mechanisms or geometric non-linearities, and is applied to two numerical examples. The efficiency of the proposed approach is compared to the conventional Lagrangian method, and savings in computation of about 55%, 54% and 37% were achieved.     

Elastic cables–rigid body coupled dynamics: asymptotic modeling and analysis

An elastic cables–rigid body coupled model is proposed for investigating dynamic interactions between cables’ nonlinear transversal vibrations and boundary tower’s torsional dynamics, arising in large transmission line–tower systems and suspended cable–bridge tower systems. By introducing a weak torsion assumption and a large moment of inertia for the tower, an asymptotic expansion of cables–tower coupled dynamics is conducted in a weakly nonlinear framework, and a cables–tower reduced coupled model is eventually established. After model’s validations using direct numerical simulations, two distinct kinds of coupled dynamics are fully investigated. The first is that an external torque is applied to the tower and the two cables would both be indirectly excited, asymmetrically, by the torsional/oscillating tower. The two cables’ responses are the same in this case. The second is that only one of the two cables, i.e., the leader cable, is directly excited, and the other cable, i.e., the follower one, is only indirectly excited through cables–tower dynamic interactions. In such kind of leader–follower dynamics, the leader cable is quite different from the follower one. Nonlinear coupled frequency response diagrams for both systems are constructed using numerical continuation algorithms, mainly focused on the coupled steady solutions’ stabilities and bifurcations. Furthermore, the dynamic effects of tower’s moment of inertia, wing span and damping are thoroughly investigated.

     

基于应变脉冲响应协方差的损伤识别方法研究

基于振动参数的结构损伤识别,是近年来土木工程的热点研究课题,振动参数包括频率、振型、频响函数、模态应变能、应变响应和加速度响应等,当结构损伤时,损伤位置附近将产生应力重分布,从而引起应变的变化,因此对比损伤前后的应变或者应变响应参数,可以用来识别结构损伤.提出了一种应变脉冲响应协方差参数,它是应变脉冲响应在时间区间上的能量积分;推导并证明了该参数是结构模态参数(频率,位移模态,应变模态,阻尼等)的函数,可用来表征结构状态.相比于传统的模态参数识别方法,可以保留更高阶的模态参数,而且避免了模态识别可能引起的误差;基于简支钢梁的多种损伤工况,研究和展示了该参数的特性,通过数值模拟发现,该参数能简单直观地判定损伤发生和识别损伤位置,无需建立结构分析模型,只需比较结构损伤前后的应变脉冲响应协方差参数即可;该参数简便易算,具有较好的抗噪性能,对结构损伤敏感,而且对结构刚度减少呈现一致变化特性,所以适合实际工程结构的健康监测和损伤识别.     

Enhanced damping of a cantilever beam by axial parametric excitation

A uniform cantilever beam under the effect of a time-periodic axial force is investigated. The beam structure is discretized by a finite-element approach. The linearised equations of motion describing the planar bending vibrations of the beam structure lead to a system with time-periodic stiffness coefficients. The stability of the system is investigated by a numerical method based on Floquet’s theorem and an analytical approach resulting from a first-order perturbation. It is demonstrated that the parametrically excited beam structure exhibits enhanced damping properties, when excited near a specific parametric combination resonance frequency. A certain level of the forcing amplitude has to be exceeded to achieve the damping effect. Upon exceeding this value, the additional artificial damping provided to the beam is significant and works best for suppression of vibrations of the first vibrational mode of the cantilever beam.     

刚塑性自由梁中部在横向冲击下的初始变形模式

研究了均匀矩形截面刚塑性自由梁中部在小尺寸、平头、圆柱形刚性弹体撞击下的三种变形模式,即梁的刚体平动、单铰变形模式和三铰变形模式。考虑了刚性子弹冲击后在梁上形成的剪切冲塞,分析了子弹通过冲塞作用在梁中部的剪切力可能引起的梁的弯曲变形,找出了梁的初始变形模式对子弹大小、梁的尺寸和材料性能的依赖关系。