含间隙弹簧振动系统的非线性模态特性

针对含间隙的两自由度弹簧-质量分段振动系统的非线性模态开展了研究.首先,解析确定了分段保守自治系统发生同相和反相模态运动的初始位移,并采用加权平均方法确定了分段振动系统的模态频率,及其在位形空间模态曲线.然后,采用数值方法求解了系统的非线性模态曲线和模态频率,与本文获得的解析模态频率比较,说明本文的结果较等效模态频率有更好的精度.研究结果表明:在一定的参数条件下,系统的非线性模态个数会高于系统的自由度数目,系统可能发生内共振,而产生多余模态.多余模态运动是两振子同向振动中含有异向振动,说明多余模态是在同相模态运动和反相模态运动之间转换的模态.     

空间相机桁架结构模态相关性分析

为有效地预示空间相机桁架结构的动态特性，需要对其进行模态相关性分析，目的在于检验分析结果的有效性和准确度，发现结构中的薄弱部位，但由于桁架结构是一复杂的杆板组合结构，计算结果中存在着大量次模态，从而无法与试验结果进行对比。基于上述问题，提出一种利用模态应变能比值来定量区分的方法，从密集的计算模态群中识别出桁架结构的主模态。主模态经模态向量缩减后与试验结果进行比较，鉴定它们之间的总体相关程度，若误差超过规定的界限，则通过调整模型参数、修改模型构型来寻找可能的误差源，反复这一过程，直到有限元模型能够很好地模拟实际结构的主要动态特性为止。分析结果预示了较好的试验和计算模态相关性，验证了有限元模型的有效性，为进一步的响应分析和振动控制设计提供了依据。     

火箭结构系统纵向模态自动辨识方法

针对工程中需要从火箭结构系统的整体模态中识别纵向模态,根据模态有效质量理论,提出了一种识别火箭结构系统纵向模态的自动辨识方法.以具有集中质量系统的振动特性作为算例,通过有限元软件,建立了具有集中质量系统的梁模型,利用自动辨识的方法,自动辨识出系统的纵向模态,并与应用模态分析法所计算的系统模态信息相比较,这种自动辨识方法不仅能准确的辨识出振动系统的纵向模态,而且还具有自动高效的识别特点.为准确快速建立液体火箭POGO振动系统的动力学模型等工程系统的模型提供理论依据.     

Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures

Non-linear normal modes (NNMs) are used in order to derive accurate reduced-order models for large amplitude vibrations of structural systems displaying geometrical non-linearities. This is achieved through real normal form theory, recovering the definition of a NNM as an invariant manifold in phase space, and allowing definition of new co-ordinates non-linearly related to the initial, modal ones. Two examples are studied: a linear beam resting on a non-linear elastic foundation, and a non-linear clamped–clamped beam. Throughout these examples, the main features of the NNM formulation will be illustrated: prediction of the correct trend of non-linearity for the amplitude-frequency relationship, as well as amplitude-dependent mode shapes. Comparisons between different models—using linear and non-linear modes, different number of degrees of freedom, increasing accuracy in the asymptotic developments—are also provided, in order to quantify the gain in using NNMs instead of linear modes.     

Inessential Features, Ineliminable Features, and Modal Logics for Model Theoretic Syntax

While monadic second-order logic (MSO) has played a prominent role in model theoretic syntax, modal logics have been used in this context since its inception. When comparing propositional dynamic logic (PDL) to MSO over trees, Kracht (1997) noted that there are tree languages that can be defined in MSO that can only be defined in PDL by adding new features whose distribution is predictable. He named such features “inessential features”. We show that Kracht’s observation can be extended to other modal logics of trees in two ways. First, we demonstrate that for each stronger logic, there exists a tree language that can only be defined in a weaker logic with inessential features. Second, we show that any tree language that can be defined in a stronger logic, but not in some weaker logic, can be defined with inessential features. Additionally, we consider Kracht’s definition of inessential features more closely. It turns out that there are features whose distribution can be predicted, but who fail to be inessential in Kracht’s sense. We will look at ways to modify his definition.     

Raising natural frequencies of a structure via surface-grooving technique

Structural dynamics modification (SDM) is a very effective technique to improve a structure’s dynamic characteristics by adding or removing auxiliary structures, changing material properties and shape of structure. Among the SDM techniques, changing or modifying structure shape to raise its natural frequencies has been mostly relied on engineer’s experience and time-consuming trial-and-error process. To develop a systematic method to modify structure shape, surface-grooving technique is studied. In this work, the shape of base structure is modified to improve its dynamic characteristics such as natural frequencies via surface-grooving technique. Grooving shape is formed by merging the neighboring small embossed elements after analyzing frequency increment sensitivities of all the surrounding embossed elements. All this process is targeted to pack in a software to get an optimum grooving shape automatically. In this package, the initial grooving position starts from the element having the highest modal strain energy then it expands into neighboring elements. The range of grooving area for checking its frequency sensitivities is restricted only to their surrounding elements to reduce its computation effort. The developed algorithm was tested with an L-shaped plate and hard disk drive (HDD) cover to raise its natural frequency by giving some groove on its surface. Also, the grooved HDD cover design was manufactured using rapid prototyping and tested to prove the effectiveness of the surface grooving as a SDM tool.     

Dynamic Modeling and Experimental Validation of a 3-PRR Parallel Manipulator with Flexible Intermediate Links

This paper presents the development of structural dynamic equations of motion for a 3-PRR parallel manipulator with three flexible intermediate links, based on the assumed mode method. Lagrange’s equation is used to derive the dynamic model of the manipulator system. Flexible intermediate links are modeled as Euler–Bernoulli beams with pinned–pinned boundary conditions. Dynamic equations of motion of a 3-PRR parallel manipulator with three flexible links are developed by adopting the assumed mode method. The effect of concentrated rotational inertia at both ends of intermediate links is included in this model. Numerical simulations of vibration responses, coupling forces and inertial forces are presented. The corresponding frequency spectra analysis is performed using the Fast Fourier Transform (FFT). Experimental modal tests are performed to validate the theoretical model through comparison and analysis of modal characteristics of the flexible manipulator system.     

侧碰传感器安装点频率响应优化分析

系统介绍频率响应分析方法的基本理论,并通过MSC Nastran对侧碰传感器安装点进行频率响应分析,在初始设计结构不能满足要求的情况下,通过结构优化提高侧碰传感器局部安装点的模态频率,满足设计要求.该优化对结构动态特性的改进有重要指导意义.     

Modal synthesis method of lateral vibration analysis for rotor-bearing system

Rigid coupling and flexible connection made up of elastic coupling units are widely applied to rotor-bearing system with multi-branched shafting system. This paper proposes a modal synthesis method of lateral vibration analysis for such kind of rotor-bearing system. When the proposed approach is developed, the elastic coupling unit is defined as “flexible substructure” which is treated individually and the other parts are partitioned into some substructures which are analyzed by finite element method. The lower-frequency normal modes of the substructures are retained; whereas the higher-frequency normal modes are neglected by a frequency truncation criterion and the residual flexibility of those omitted modes is considered. The lower-frequency normal modes and residual flexibility are considered to be the assumed modes of Rayleigh–Ritz analysis of whole structure. The approach to the treatment of higher-frequency modes leads to a great reduction in the calculation time and a significant improvement in the efficiency of modal synthesis. Examples show that the proposed approach is very effective for the vibration analysis of rotor-bearing system with multi-branched shafting system and the results derived from this approach are in a good agreement with those from transfer matrix method.     

A method for topology optimization of structures under harmonic excitations

This paper deals with topology optimization of large-scale structures with proportional damping subjected to harmonic excitations. A combined method (CM) of modal superposition with model order reduction (MOR) for harmonic response analysis is introduced. In the method, only the modes corresponding to a frequency range which is a little bigger than that of interest are used for modal superposition, the contribution of unknown higher modes is complemented by a MOR technique. Objective functions are the integral of dynamic compliance of a structure, and that of displacement amplitude of a certain user-defined degree of freedom in the structure, over a range of interested frequencies. The adjoint variable method is applied to analyze sensitivities of objective functions and the accuracy of the sensitivity analyses can also be ensured by CM. Topology optimization procedure is illustrated by three examples. It is shown that the topology optimization based on CM not only remarkably reduce CPU time, but also ensure accuracy of results.