Joining of components of complex structures for improved dynamic response

The goal of this work is to provide a method for choosing joining (e.g., bolt) locations for attaching structural reinforcements onto complex structures. The joining locations affect structural performance criteria such as the frequency response and the static compliance of the modified structure. One approach to finding improved/optimal joining locations is to place the joints such that the total amount of energy input into the structure (from external forces) is lowered/minimized, thus ensuring that the performance of the structure is least affected by the structural modifications. However, such an approach does not account for the stresses in the joints. Therefore, in this work, the amount of strain energy concentrated in the joints is also considered. The cost function for this optimization problem is then composed of two energies. These energies are different for the undamped and damped cases. Herein, the focus is on the (more realistic) damped case. The cost function is minimized by a modified optimality criteria method. This process is time consuming because it requires the calculation of sensitivities of the joint strain energy, which in turn requires the calculation of the displacements of all candidate joint locations by using the system-level mass and stiffness matrices and force vector (at each frequency in the range of interest). To address this issue, a series of complex algebraic manipulations and approximations are used to significantly reduce the computational cost. In addition, for the case where structural and geometrical variations are necessary, parametric reduced-order models are used to compute the cost function with further significant gains in computational speed. Numerical results for improved/optimal joining are presented for representative complex structures with structural variabilities.     

An efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems

The design of high-Q resonators such as Xylophone Bar Resonators (XBRs) capable of being fabricated using Micro-Electro-Mechanical Systems (MEMS) processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance. This paper is concerned with vibration analysis and Q optimisation of an XBR, with the method extending directly to other planar frames and straightforwardly to more complex structures. The Rayleigh–Ritz method is discussed in some detail, first treating the discrete case, followed by developing and applying a kinematical procedure to an L-frame structure. Attention is given to geometric interpretation of the Rayleigh–Ritz procedure and to developing an intuitive understanding the method before turning to the XBR case. Having developed an approximation for system dynamics, the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support Q factor. Natural frequencies, mode shapes, and support Q values are presented and compared to Finite Element models of the same problem, with excellent agreement observed at substantially lower computational cost. For the first time in the literature, the geometric impedance tuning principle underlying the XBR design is validated and quantified, including sensitivity to manufacturing error.     

Spectral finite elements for vibrating rods and beams with random field properties

The classical stochastic Helmholtz equation grasps, through the random field of the refraction index, the spatial variability in the mass density but not the variability in elastic moduli or geometric parameters. In contradistinction to this restriction, the present analysis accounts for the spatial randomness of mass density as well as those of elastic properties and cross-sectional geometric properties of rods undergoing longitudinal vibrations and of Timoshenko beams in flexural vibrations. All the material variabilities are described here by random Fourier series with a typical (average) characteristic size of inhomogeneity d, which is either smaller, comparable to, or larger than the wavelength. The third length scale entering the problem, but kept constant, is the rod or beam length. We investigate the relative effects of random noises in all the material parameters on the spectral stiffness matrices associated with rods and beams for a very wide range of frequencies.     

Lie Superalgebras Based on 𝔤𝔩n Associated to the Adjoint Representation, and Invariant Geometric Structures Defined on Them

Finite-dimensional real and complex Lie superalgebras whose underlying Lie algebra is ????_n and whose odd module is ????_n itself under the adjoint representation are classified up to isomorphism. It is shown that for n≥3 there are one-parameter families of nonisomorphic such Lie superalgebras, plus another set of finitely many different isomorphism classes. For n=2 there are 10 different isomorphism classes over the real field, and 8 different over the complex numbers. For n=1 there are 2 different isomorphism classes over either ground field. Representatives on each isomorphism class are given, and their automorphism groups are determined. The question as to which representatives admit ?₂-graded, ad-invariant geometric structures (of orthogonal or symplectic type) is also addressed, and a precise list of which of such geometric structures can be defined on each isomorphism class is given. In particular, it is shown that ?₂-homogeneous, orthogonal, ad-invariant geometric structures must be odd. The case of ????₂ over the real field is further analyzed in order to determine for which of the equivalence classes that admit such a structure, that structure can be induced by an underlying Minkowski metric on the 4-dimensional (nongraded) ????₂.     

ON THE RELATION BETWEEN COMPLEX MODES AND WAVE PROPAGATION PHENOMENA

This paper discusses the well-known, but often misunderstood, concept of complex modes of dynamic structures. It shows how complex modes can be interpreted in terms of wave propagation phenomena caused by either localized damping or propagation to the surrounding media. Numerical simulation results are presented for different kinds of structures exhibiting modal and wave propagation characteristics: straight beams, an L-shaped beam, and a three-dimensional frame structure. The input/output transfer relations of these structures are obtained using a spectral formulation known as the spectral element method (SEM). With this method, it is straightforward to use infinite elements, usually known as throw-off elements, to represent the propagation to infinity, which is a possible cause of modal complexity. With the SEM model, the exact dynamic behavior of structures can be investigated. The mode complexity of these structures is investigated. It is shown that mode complexity characterizes a behavior that is half-way between purely modal and purely propagative. A coefficient for quantifying mode complexity is introduced. The mode complexity coefficient consists of the correlation coefficient between the real and imaginary parts of the eigenvector, or of the operational deflection shape (ODS). It is shown that, far from discontinuities, this coefficient is zero in the case of pure wave propagation in which case the plot of the ODS in the complex plane is a perfect circle. In the other extreme situation, a finite structure without damping (or with proportional damping), where the mode shape (or the ODS) is a straight line on the complex plane, has a unitary complexity coefficient. For simple beam structures, it is shown that the mode complexity factor can also be calculated by curve-fitting the mode to an ellipse and computing the ratio of its radii.     

A novel simulation theory and model system for multi-field coupling pipe-flow system

Due to the lack of a theoretical basis for multi-field coupling in many system-level models, a novel set of system-level basic equations for flow/heat transfer/combustion coupling is put forward. Then a finite volume model of quasi-1D transient flow field for multi-species compressible variable-cross-section pipe flow is established by discretising the basic equations on spatially staggered grids. Combining with the 2D axisymmetric model for pipe-wall temperature field and specific chemical reaction mechanisms, a finite volume model system is established; a set of specific calculation methods suitable for multi-field coupling system-level research is structured for various parameters in this model; specific modularisation simulation models can be further derived in accordance with specific structures of various typical components in a liquid propulsion system. This novel system can also be used to derive two sub-systems: a flow/heat transfer two-field coupling pipe-flow model system without chemical reaction and species diffusion; and a chemical equilibrium thermodynamic calculation-based multi-field coupling system. The applicability and accuracy of two sub-systems have been verified through a series of dynamic modelling and simulations in earlier studies. The validity of this system is verified in an air–hydrogen combustion sample system. The basic equations and the model system provide a unified universal theory and numerical system for modelling and simulation and even virtual testing of various pipeline systems.     

一种便携式光电跟踪系统在线检测装置的设计与实现

某型光电跟踪系统在线检测是通过计算机模拟台实现的,而模拟台体积大、携带不便、安装复杂,为解决其在外场使用不便的问题,设计了一种便携式光电跟踪系统在线检测装置。该装置采用基于WinCE操作系统的ARM嵌入式平台,将工作状态检测分为一个系统级模块和多个部件级模块,可根据实际需要按模块进行检测,以此降低CPU的负荷及检测装置的功耗。通过实际验证,该装置能够对光电跟踪系统的详细状态实现实时在线检测,并准确地定位故障部位,达到快速修复故障的目的。     

Epidemic variability in hierarchical geographical networks with human activity patterns

Recently, some studies have revealed that non-Poissonian statistics of human behaviors stem from the hierarchical geographical network structure. On this view, we focus on epidemic spreading in the hierarchical geographical networks and study how two distinct contact patterns (i.e., homogeneous time delay (HOTD) and heterogeneous time delay (HETD) associated with geographical distance) influence the spreading speed and the variability of outbreaks. We find that, compared with HOTD and null model, correlations between time delay and network hierarchy in HETD remarkably slow down epidemic spreading and result in an upward cascading multi-modal phenomenon. Proportionately, the variability of outbreaks in HETD has the lower value, but several comparable peaks for a long time, which makes the long-term prediction of epidemic spreading hard. When a seed (i.e., the initial infected node) is from the high layers of networks, epidemic spreading is remarkably promoted. Interestingly, distinct trends of variabilities in two contact patterns emerge: high-layer seeds in HOTD result in the lower variabilities, the case of HETD is opposite. More importantly, the variabilities of high-layer seeds in HETD are much greater than that in HOTD, which implies the unpredictability of epidemic spreading in hierarchical geographical networks.     

On drift,diffusion and geometry

We present some reflections on the links between drift, diffusion and geometry. For this purpose, we examine different sources of “diffusion models”, in physics and in mathematics. We observe that diffusion processes may arise from original models either deterministic, or random but where dynamics and noise are clearly delineated. In the end, we get a diffusion process where noise and dynamics (“drift”) are generally intimately entangled in a second-order partial differential operator. We focus on the following questions. Are there implicit geometric structures to properly define a diffusion? How are drift/dynamics and diffusion mixed? Are there geometric structures needed to separate drift and diffusion? We stress the importance of recurrent differential geometric structures – connections and Riemannian metrics – needed to properly define a “diffusion term” and also to separate drift from diffusion.     

Investigation of dispersion characteristic in MI- and MII-type single mode optical fibers

Dispersion characteristic of MI and MII type single mode optical fibers is analytically investigated. For this purpose modal analysis of these fibers to obtain possible wave vectors for given system parameters are done. Then using numerical evaluation of the presented analytical relations, chromatic and waveguide dispersions are calculated. The effects of geometrical and optical parameters of the fibers on dispersion characteristics are investigated. In this analysis, we show that with increase of Δ (optical parameter) for MI structure the slope of dispersion curve is decreased and the case is reversed for MII structure. Also, with rising of Q (geometric parameter) for MI structure the slope of dispersion curve is decreased and the situation is reversed for MII structure. Finally, we show that with boosting of R₂ for MII structure the slope of dispersion is increased. As a final result, our simulations show that small values for optical parameters are better in MII structure for multi-channel optical communications. In MI structure to obtain small dispersion slope, Q can be increased that is easy for fabrication in practice. Finally, Q and R₂ are suitable parameters for control of dispersion in the proposed structures.     

Natural frequencies of two bubbles in a compliant tube: analytical, simulation, and experimental results

Motivated by various clinical applications of ultrasound contrast agents within blood vessels, the natural frequencies of two bubbles in a compliant tube are studied analytically, numerically, and experimentally. A lumped parameter model for a five degree of freedom system was developed, accounting for the compliance of the tube and coupled response of the two bubbles. The results were compared to those produced by two different simulation methods: (1) an axisymmetric coupled boundary element and finite element code previously used to investigate the response of a single bubble in a compliant tube and (2) finite element models developed in comsol Multiphysics. For the simplified case of two bubbles in a rigid tube, the lumped parameter model predicts two frequencies for in- and out-of-phase oscillations, in good agreement with both numerical simulation and experimental results. For two bubbles in a compliant tube, the lumped parameter model predicts four nonzero frequencies, each asymptotically converging to expected values in the rigid and compliant limits of the tube material.     

Bifurcation structures in two-dimensional maps: The endoskeletons of shrimps

Bifurcation structures for nonlinear dynamical systems in a space of two parameters often display geometric shapes resembling shrimps. For one-dimensional maps with two parameters and multiple extrema, the underlying structure of the shrimps can be elucidated by computing the locus of superstable cycles which form a “skeleton” that supports the shrimps. Here we use continuation methods to identify and compute structures in two-dimensional maps that play the same role as the skeleton in one-dimensional maps. This facilitates determining the complex geometries for situations in which there is multistability, and for which the regions of parameter space supporting stable orbits get vanishingly small.     

Photonic crystal with complex unit cell for large complete band gap

A novel two-dimensional complex photonic crystal with dielectric rods and veins in square and honeycomb lattice is presented to achieve large complete band gaps. The rods with different symmetries, shapes, orientations, and sizes are investigated numerically. The sizes of gaps are intensively affected by these geometric parameters. Extremely large gaps are realized by the parameter optimization with gallium arsenide material. The scattering of veins is more dominant than that of rods which demonstrates the validity of the complex photonic crystal structures. Furthermore, an excellent wide region of dielectric rods and veins, where the sizes of gaps are universally large, is found in square and honeycomb lattice, respectively.     

A model of the ethylene signaling pathway and its gene response in Arabidopsis thaliana: pathway cross-talk and noise-filtering properties

Dynamic models of molecular networks and pathways enable in silico evaluations of the consistency of proposed interactions and the outcomes of perturbations as well as of hypotheses on system-level structure and function. We postulate a continuous model of the activation dynamics of the ethylene response factor 1 (ERF1) gene in response to ethylene signaling. This activation elicits the response of the plant defensin 1 (PDF1) gene, which also responds to jasmonic acid, and the inhibition of the putative auxin responsive factor 2 (ARF2) gene, that also responds to auxin. Our model allows the effect of different ethylene concentrations in eliciting contrasting genetic and phenotypic responses to be evaluated allows the effect of different ethylene concentrations in eliciting contrasting genetic and phenotypic responses to be evaluated and seems to consider key components of the ethylene pathway because the ERF1 dose-response curve that we predict has the same qualitative form as the phenotypic dose-response curves obtained experimentally. Therefore, our model suggests that the phenotypic dose-response curves obtained experimentally could be due, at least in part, to ERF1 changes to different ethylene concentrations. Stability analyses show that the model's results are robust to parameter estimates. Of interest is that our model predicts that the ethylene pathway may filter stochastic and rapid chaotic fluctuations in ethylene availability. This novel approach may be applied to any cellular signaling and response pathway in plants and animals.     

An embedded sensitivity approach for diagnosing system-level vibration problems

In diagnosing a system-level vibration problem, the goals are to identify which component or components(s) are most responsible for the phenomenon and which changes to the system are most likely to mitigate the problem. The use of sensitivity analysis in diagnosing system-level vibration phenomena is examined in this work. It is shown that even if only a small subset of measured system input–output functions is available, an appropriate analytical parameterization of these functions leads to simple relationships between the measured data and the desired embedded sensitivity functions. These functions are then reformulated in terms of transmissibility functions with respect to a single input using a novel modal deflection chain technique in order to accommodate system-level operating response data in the absence of input measurements. The embedded sensitivity approach is used to examine two competing design modifications for reducing a structure-borne noise problem in an exhaust system. The sensitivity analysis shows that although both modifications mitigate the resonant vibration problem of interest, one of the modifications is more effective than the other because it introduces less overall change in the forced response characteristics at other frequencies.     

Two families of non-local scattering models and the weighted curvature approximation

There are several nonlocal scattering models available in the literature. Most of them are given with little or no mention of their expected accuracy. Moreover, high- and low-frequency limits are rarely tested. The most important limits are the low-frequency or the small perturbation method (SPM) and the high-frequency Kirchhoff approximation (KA) or the geometric optics (GO). We are interested in providing some insight into two families of non-local scattering models. The first family of models is based on the Meecham-Lysanov ansatz (MLA). This ansatz includes the non-local small slope approximation (NLSSA) by Voronovich and the operator expansion method by Milder (OEM). A quick review of this first family of models is given along with a novel derivation of a series of kernels which extend the existing models to include some more fundamental properties and limits. The second family is derived from formal iterations of geometric optics which we call the ray tracing ansatz (RTA). For this family we consider two possible kernels. The first is obtained from iteration of the high-frequency Kirchhoff approximation, while the second is an iteration of the weighted curvature approximation (WCA). In the latter case we find that most of the required limits and fundamental conditions are fulfilled, including tilt invariance and reciprocity. A study of scattering from Dirichlet sinusoidal gratings is then provided to further illustrate the performance of the models considered.     

Feature points extraction of different structure for industrial computed tomography image contour

In order to accurately obtain the physical structure and dimension, the feature points extraction must be carried out from the ICT (industrial computed tomography) image contour. Therefore, the discrete data could be transformed into CAD models, and different methods have been developed for the feature points extraction, according to geometric features, the function and shape of mechanical parts. We discussed the feature points extraction methods, and one method is not enough to all the structures, so we must first distinguish the structure as regular and irregular. For the regular structures, by using a positive–negative factor, the curvature estimation method was improved. This method was designed and verified for the actual part, and has an improved accuracy in the feature points extraction. While for the irregular structures we used the polygon approximation method in the feature points extraction. For a complex part composing of several regular structures and irregular structures in the same ICT contour, we divided the whole contour into the regular and irregular structures, then used the corresponding methods for each structure. Last all feature points were extracted. The actual examples showed that the used methods are practical and effective.     

Recurrence Times in Quasi-Periodic Motion: Statistical Properties,Role of Cell Size,Parameter Dependence

We investigate the probabilistic properties of recurrence times for the simplest form of aperiodic deterministic dynamics, quasi-periodic motion. Previous results using number theory techniques predict two fundamental recurrence times for uniform quasi-periodic motion on a two-dimensional torus, while no analogous analytic result seems to exist for higher dimensional tori. The two-dimensional uniform case is reanalyzed from a more geometric point of view and new, workable expressions are derived that enable us fully to understand and predict the recurrence phenomenon and to analyze its parameter dependence. Emphasis is placed on the statistical properties and, in particular, on the variability of recurrence times around their mean, in relation to local Farey tree structure. Higher-dimensional tori are considered, and seen to also display a high variability in their finite-time recurrence behavior. The results are finally extended to the non-uniform quasi-periodic case.