Effect of approximation fidelity on vibration-based elastic constants identification

Some applications such as identification or Monte Carlo based uncertainty quantification often require simple analytical formulas that are fast to evaluate. Approximate closed-form solutions for the natural frequencies of free orthotropic plates have been developed and have a wide range of applicability, but, as we show in this article, they lack accuracy for vibration based material properties identification. This article first demonstrates that a very accurate response surface approximation can be constructed by using dimensional analysis. Second, the article investigates how the accuracy of the approximation used propagates to the accuracy of the elastic constants identified from vibration experiments. For a least squares identification approach, the approximate analytical solution led to physically implausible properties, while the high-fidelity response surface approximation obtained reasonable estimates. With a Bayesian identification approach, the lower-fidelity analytical approximation led to reasonable results, but with much lower accuracy than the higher-fidelity approximation. The results also indicate that standard least squares approaches for identifying elastic constants from vibration tests may be ill-conditioned, because they are highly sensitive to the accuracy of the vibration frequencies calculation.     

Inplane vibration analysis of polar orthotropic annular plates with linearly varying thickness

The natural frequencies of inplane vibrations of polar orthotropic annular plates with linearly varying thickness have been analysed. A semi-analytical method of analysis has been used where the radial and tangential displacements are expanded in the circumferential direction as Fourier series and the radial behaviour is solved using the finite element method. For the sake of comparison, results have been obtained starting with two different kinds of displacement functions. The frequencies have been studied with respect to various boundary conditions. aspect ratios, thickness ratios, ratios of moduli, and two fibre directions.     

Uncertainty quantification in the damage assessment of a cable-stayed bridge by means of fuzzy numbers

Cables offer interesting possibilities in bridge design, but are rather susceptible to damage. Since damage in a cable changes its natural vibration frequency, it can be assessed with a vibration-based finite element updating procedure. However, the natural frequency of a cable is also influenced by the temperature, and the measured frequencies are prone to measurement errors. Therefore, it is useful to check the sensitivity of the identified damage with respect to these factors. This paper presents a methodology based on fuzzy numbers to investigate the propagation of measurement errors and uncertainty on the structural temperature throughout the updating procedure.     

微构件力学性能片外拉伸测试装置

微构件材料力学性能测试中,拉伸测试主要解决材料弹性模量、泊松比、屈服强度和断裂强度的测量问题。介绍了一种片外拉伸测试试验装置的设计过程及工作原理,试样放在动/静载物台上,压电陶瓷制动器驱动动载物台,从而拉动试样,直到试样被拉断。施加在试样上的力和试样被拉伸后的伸长量分别由微力检测传感器和位移检测传感器测出。分别介绍了每个部件的功能,给出了误差分析。结果表明:此装置设计合理,达到预期目标。     

Inverse method based on modal analysis for characterizing the constitutive properties of thick composite plates

This paper presents a powerful method for evaluating the constitutive properties of composite laminates through a mixed numerical–experimental identification procedure based on both the extracted mode shapes and the corresponding natural frequencies of the structure. The modal quantities are measured with a precise contact-free experimental technique and extracted numerically with an accurate shell element derived from the higher order shear deformation theory. The elastic properties are estimated with a nonlinear least squares algorithm applied to modal identification criteria. With this novel approach of combining frequency and mode based error norms, the proposed identification method allows an accurate identification of both in-plane and transverse elastic properties with a single non-destructive test. The effectiveness of the procedure is highlighted by test cases on moderately thick to thick plates.     

Subspace identification with guaranteed stability using constrained optimization

In system identification, the true system is often known to be stable. However, due to finite sample constraints, modeling errors, plant disturbances and measurement noise, the identified model may be unstable. We present a constrained optimization method to ensure asymptotic stability of the identified model in the context of subspace identification methods. In subspace identification, we first obtain an estimate of the state sequence or extended observability matrix and then solve a least squares optimization problem to estimate the system parameters. To ensure asymptotic stability of the identified model, we write the least-squares optimization problem as a convex linear programming problem with mixed equality, quadratic, and positive-semidefinite constraints suitable for existing convex optimization codes such as SeDuMi. We present examples to illustrate the method and compare to existing approaches.     

A multiple test arbors-based calibration method for a hybrid machine tool

Kinematic calibration is a necessary way to guarantee the accuracy of hybrid machine tools. The traditional calibration methods have high requirements for the measuring instruments and the measurement environment, and the measurement is extremely complex. The contradiction between measurement complexity and identification accuracy is an important problem in calibration. In this paper, a multiple test arbors-based calibration method for a hybrid machine tool is presented. The tool center point (TCP) position errors of multiple test arbors are measured sequentially by virtual TCP position constraints. The error parameters can be accurately identified based on these position errors without orientation measurement. The corresponding measurement scheme is described in detail according to whether the ball diameters of the test arbors are the same. The influence of the length and number of test arbors on the calibration results is investigated, and the basic principle for the selection of test arbors is given. Finally, the proposed method is validated by simulations and experiments. The proposed method can achieve overall high-accuracy calibration with simple measurement devices and convenient measurement steps, which provides a basis for automated calibration.     

Numerical analysis of single-layered graphene sheets by a mesh-free approach

The paper presents a numerical analysis of the behavior of single-layered graphene sheet (SLGS) using a mesh-free approach based on a nonlocal continuum plate model (NCPM). The adopted NCPM constructed by incorporating the nonlocal elasticity theory into the first order shear deformation elastic plate theory is able to capture small length scale effects. Through the NCPM, the SLGS is modeled as a continuous orthotropic nanoplate. the obtained nonlocal nonlinear partial differential equations completed by boundary conditions are solved numerically by a mesh-free approach associating the asymptotic numerical method with the mesh-free collocation method based on moving least square approximation. The effects of the small-scale parameter and aspect ratio on the nonlinear bending and post-buckling behaviors of SLGS are considered. Good agreement has been established between the obtained results and those of the literature.

     

Vortex shedding from confined micropin arrays

The hydrodynamics in microcavities populated with cylindrical micropins was investigated using dynamic pressure measurements and fluid pathline visualization. Pressure signals were Fourier-analyzed to extract the flow fluctuation frequencies, which were in the kHz range for the tested flow Reynolds numbers (Re) of up to 435. Three different sets of flow dependent characteristic frequencies were identified, the first due to vortex shedding, the second due to lateral flow oscillation and the third due to a transition between these two flow regimes. These frequencies were measured at different locations along the chip (e.g. inlet, middle and outlet). It is established that vortex shedding initiates at the outlet and then travels upstream with increase in Re. The pathline visualization technique provided direct optical access to the flow field without any intermediate post-processing step and could be used to interpret the frequencies determined through pressure measurements. Microcavities with different micropin height-to-diameter aspect ratios and pitch-to-diameter ratios were tested. The tests confirmed an increase in the Strouhal number (associated with the vortex shedding) with increased confinement (decrease in the aspect ratio or the pitch), in agreement with macroscale measurements. The compact nature of the microscale geometry tested, and the measurement technique demonstrated, readily enabled us to investigate the flow past 4,420 pins with various degrees of confinements; this makes the measurements performed and the techniques developed here an important tool for investigating large arrays of similar objects in a flow field.     

Combined CI-MD approach in formulation of engineering moduli of single layer graphene sheet

An evolutionary approach of multi-gene genetic programming (GP) is used to study the effects of aspect ratio, temperature, number of atomic planes and vacancy defects on the engineering moduli viz. tensile and shear modulus of single layer graphene sheet. MD simulation based on REBO potential is used to obtain the engineering moduli. This data is then fed into the paradigm of a GP cluster comprising of genetic programming, which was specifically designed to formulate the explicit relationship of engineering moduli of graphene sheets loaded in armchair and zigzag directions with respect to aspect ratio, temperature, number of atomic planes and vacancy defects. We find that our MGGP model is able to model the engineering moduli of armchair and zigzag oriented graphene sheets well in agreement with that of experimental results. We also conducted sensitivity and parametric analysis to find out specific influence and variation of each of the input system parameters on the engineering moduli of armchair and zigzag graphene sheets. It was found that the number of defects has the most dominating influence on the engineering moduli of graphene sheets.     

Nonlinear solution adaptive structured grids via heat-conduction analogies

This paper discusses an adaptive grid approach, developed using Fortran 77, on quadrilateral meshes for the Euler and Navier-Stokes solvers. Solution adaptation is through two nonlinear heat-conduction analogies applied directly on a two-dimensional surface using the finite volume method. Clustering of the grid generated is controlled by the conductivity in the computational domain, which is related arbitrarily to the geometrical curvature and flow gradient. Three levels of “multigrid” approach are implemented to accelerate convergence as a grid refinement process. The grid quality is accessed by a histogram analysis of maximum angle and aspect ratio distributions within the computational domain. This work assumes that interpolation errors due to numerical approximation of fluxes across the surfaces of a control volume should become significant as the skew angle and aspect ratio increases. Detailed computational results and comparisons with measured data are presented for steady transonic flow over a NACA0012 airfoil, supersonic flow through a DFVLR rotor, and a 15° ramp.     

Crack detection in beam-like structures using genetic algorithms

A fault diagnosis method based on genetic algorithms (GAs) and a model of damaged (cracked) structure is proposed. For modeling the cracked-beam structure an analytical model of a cracked cantilever beam is utilized and natural frequencies are obtained through numerical methods. Our method utilizes genetic algorithms to monitor the possible changes in the natural frequencies of the structure. The identification of the crack location and depth in the cantilever beam is formulated as an optimization problem, and binary and continuous genetic algorithms (BGA, CGA) are used to find the optimal location and depth by minimizing the cost function which is based on the difference of measured and calculated natural frequencies. Also we present a new cost function based on natural frequencies. The average values of location and depth prediction errors are 1.02% and 1.98%, respectively, using the BGA. These values become 0.73% and 1.11% for the CGA. To validate the proposed method and investigate the modeling and measurement errors some experimental results are also included. The average values of experimental location and depth prediction errors are 10.57% and 11.19%, respectively, for the BGA. These values become 10.21% and 10.39% for the CGA.     

Error estimation of load identification based on linear sensitivity analysis and interval technique

This paper applies interval perturbation approach to load identification in the statistical energy analysis (SEA) framework, and the influence of the measurement errors of parameters on identified loads is revealed. By considering the damping loss factors and coupling loss factors with measurement errors as interval variables, the errors in identified loads can finally be estimated. The presented interval approach is demonstrated through the simulated study for a two-plate coupling structure and the simulated study for a plate-shell coupling structure. Meanwhile, the identified load with considering the measurement errors of the damping loss factors and coupling loss factors is compared with that without considering the measurement errors of the damping loss factors and coupling loss factors. The results show that the measurement errors of damping loss factors and coupling loss factors have a large effect on identified load, so the measurement errors of damping loss factors and coupling loss factors are non-ignorable when the high-frequency load identification based on SEA is carried out.     

随机逼近自适应滤波在捷联惯导系统初始对准中的应用

对于测量噪声方差未知的捷联惯导系统(SINS),采用常规Kalman滤波进行初始对准会造成较大状态估计误差,甚至使滤波器发散。为了解决系统测量噪声方差未知或不确切知道时SINS的误差估计问题,提出一种基于随机逼近的自适应滤波方法。该方法将Robbins-Monro算法与Kalman滤波相结合,通过简化求逆运算,解决了系统观测噪声特性未知情况下SINS的误差估计问题,并提高了算法的数值稳定性。仿真结果表明,该方法能在系统测量噪声方差未知情况下有效实现SINS初始对准。     

Viscoelastic material design with negative stiffness components using topology optimization

An application of topology optimization to design viscoelastic composite materials with elastic moduli that soften with frequency is presented. The material is a two-phase composite whose first constituent is isotropic and viscoelastic while the other is an orthotropic material with negative stiffness but stable. A concept for this material based on a lumped parameter model is used. The performance of the topology optimization approach in this context is illustrated using three examples.     

超声弹性模量测量中声时测量精度的提高方法

超声脉冲回波法是一种高精度的弹性模量声速测量法。实验测定由声耦合界面引起声时测量相对误差达0. 3%,延时相对误差在0. 2%左右。为减小声时测量误差,提高超声脉冲回波法弹性模量的测量精度,采用了台阶轴试样,避免了由声耦合界面引起的声时测量相对误差;利用试样后端面的二次回波,变相的改变声程,消除了由各种延时引起的声时测量误差。     

利用电子束曝光系统制作高深宽比图形的研究

为了加工具有高深宽比的器件,采用能量连续递减近似模型,运用蒙特卡罗方法分析高能电子束曝光领域的电子散射轨迹及背散射电子对曝光分辨力的影响,探讨了制作高深宽比图形的工艺条件。计算机模拟结果与实验结果吻合得很好,表明在其它实验条件不变的情况下,较高的加速电压能提高图形的高深宽比,提供了制作高深宽比图形的一种方法。     

Large errors in approximate decoupling of nonclassically damped linear second-order systems under harmonic excitations

A simple and commonly used approximate technique of solving the normalized equations of motion of a nonclassically damped linear second-order system is to decouple the system equations by neglecting the offdiagonal elements of the normalized damping matrix, and then to solve the decoupled equations. This approximate technique can result in a solution with large errors, even when the off-diagonal elements of the normalized damping matrix are small. Large approximation errors can arise in lightly damped systems under harmonic excitations when some of the undamped natural frequencies of the system are close to the excitation frequency. In this article, a rigorous analysis of the approximation error in lightly damped systems is given. Easy-to-check conditions under which neglecting the off-diagonal elements of the normalized damping matrix can result in large approximation errors are presented.     

Structural damage identification by adding virtual masses

This paper presents a method for damage identification by adding virtual masses to the structure in order to increase its sensitivity to local damages. The main concept is based on the Virtual Distortion Method (VDM), which is a fast structural reanalysis method that employs virtual distortions or pseudo loads to simulate structural modifications. In this paper, the structure with an added virtual mass is called the virtual structure. First, the acceleration frequency response of the virtual structure is constructed numerically by the VDM using local dynamic data measured only by a single excitation sensor and a single acceleration sensor. Second, the value of the additional mass is determined via sensitivity analysis of the constructed frequency responses of the virtual structure with respect to damage parameters; only the natural frequencies with high sensitivity are selected. This process is repeated for all the considered placements of the virtual mass. At last, the selected natural frequencies of all the virtual structures are used together for damage identification of the real structure. A finite element (FE) model of a plane frame is used to introduce and verify the proposed method. The damage can be identified precisely and effectively even under simulated 5 % Gaussian noise pollution.