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We consider the inverse problem of identifying the density and elastic moduli for three-dimensional anisotropic elastic bodies, given displacement and traction measurements made at their surface. These surface measurements are modelled by the dynamic Dirichlet-to-Neumann map on a finite time interval. For linear or nonlinear anisotropic hyperelastic bodies we show that the displacement-to-traction surface measurements do not change when the density and elasticity tensor in the interior are transformed tensorially by a change of coordinates fixing the surface of the body to first order. Our main tool, a new approach in inverse problems for elastic media, is the representation of the equations of motion in a covariant form (following Marsden and Hughes, 1983) that preserves the underlying physics.In the case of classical linear elastodynamics we then investigate how the type of anisotropy changes under coordinate transformations. That is, we analyze the orbits of general linear, anisotropic elasticity tensors under the action by pull-back of diffeomorphisms that fix the surface of the elastic body to first order, and derive a pointwise characterization of parts of the orbits under this action. For example, we show that the orbit of isotropic elastic media, at any point in the body, consists of some transversely isotropic and some orthotropic elastic media. We then derive the first uniqueness result in the inverse problem for anisotropic media using surface displacement-traction data: uniqueness of three elastic moduli for tensors in the orbit of isotropic elasticity tensors.
†Partially supported by an MSRI Postdoctoral Fellowship. Research at MSRI is supported in part by NSF grant DMS-9850361. This work was conducted while the first author was a Gibbs Instructor at Yale University.
‡Partially supported by an MSRI Postdoctoral Fellowship, and by NSF grant DMS-9801664 (9996350). 相似文献
64.
通过轿车副车架橡胶支承的动态特性试验和理论分析,实现橡胶支承迟滞特性的数学建模和参数识别。利用所建模型重构恢复力-位移迟滞回线,并与试验结果比较表明所建模型的正确性。介绍了具有线性和非线性连接子结构的自由界面模态综合法的基本原理,并采用该方法建立了考虑副车架橡胶支承迟滞特性的整车非线性动力学模型,用所建模型对汽车动力特性进行了数值仿真,并通过试验对仿真结果进行验证。 相似文献
65.
W. Silva 《Nonlinear dynamics》2005,39(1-2):25-62
The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in computational and experimental aeroelasticity are reviewed. Computational results include the development of computationally efficient reduced-order models (ROMs) using an Euler/Navier–Stokes flow solver and the analytical derivation of Volterra kernels for a nonlinear aeroelastic system. Experimental results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the active aeroelastic wing (AAW) aircraft. 相似文献
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Antonio Doménech‐Carbó María Teresa Doménech‐Carbó Francisco López‐López Francisco Manuel Valle‐Algarra Laura Osete‐Cortina Estrella Arcos‐Von Haartman 《Electroanalysis》2013,25(12):2621-2630
The solid state voltammetric response of Egypt blue, Han blue and ploss blue pigments upon attachment to graphite electrodes in contact with aqueous phosphate buffer at pH 7.0 is studied by voltammetry of microparticles and scanning electrochemical microscopy. Such voltammetric responses, combined with those for synthetic specimens consisting of binary mixtures of the pigment and SiO2 or CaCO3 as well as ternary ones of CaCO3 and SiO2 mixtures allow for the identification of the pigment and the support in samples from wall paintings using different electrochemical parameters, in particular upon performing the Tafel and modified Tafel analysis of voltammetric peaks. Identification of Egypt blue in microsamples of murals from a Roman archaeological site in Castulo (Jaén, Spain) is discussed. 相似文献
68.
Dr. Roberta Pievo Brigitta Angerstein Dr. Alistair J. Fielding Dr. Christian Koch Prof. Dr. Ivo Feussner Prof. Dr. Marina Bennati 《Chemphyschem》2013,14(18):4094-4101
Electron paramagnetic resonance (EPR) spectroscopy in combination with the rapid freeze‐quench (RFQ) technique is a well‐established method to trap and characterize intermediates in chemical or enzymatic reactions at the millisecond or even shorter time scales. The method is particularly powerful for mechanistic studies of enzymatic reactions when combined with high‐frequency EPR (ν≥90 GHz), which permits the identification of substrate or protein radical intermediates by their electronic g values. In this work, we describe a new custom‐designed micro‐mix rapid freeze‐quench apparatus, for which reagent volumes for biological samples as small as 20 μL are required. The apparatus was implemented with homemade sample collectors appropriate for 9, 34, and 94 GHz EPR capillaries (4, 2, and 0.87 mm outer diameter, respectively) and the performance was evaluated. We demonstrate the application potential of the RFQ apparatus by following the enzymatic reaction of PpoA, a fungal dioxygenase producing hydro(pero)xylated fatty acids. The larger spectral resolution at 94 GHz allows the discernment of structural changes in the EPR spectra, which are not detectable in the same samples at the standard 9 GHz frequency. 相似文献
69.
Rolling bearings act as key parts in many items of mechanical equipment and any abnormality will affect the normal operation of the entire apparatus. To diagnose the faults of rolling bearings effectively, a novel fault identification method is proposed by merging variational mode decomposition (VMD), average refined composite multiscale dispersion entropy (ARCMDE) and support vector machine (SVM) optimized by multistrategy enhanced swarm optimization in this paper. Firstly, the vibration signals are decomposed into different series of intrinsic mode functions (IMFs) based on VMD with the center frequency observation method. Subsequently, the proposed ARCMDE, fusing the superiorities of DE and average refined composite multiscale procedure, is employed to enhance the ability of the multiscale fault-feature extraction from the IMFs. Afterwards, grey wolf optimization (GWO), enhanced by multistrategy including levy flight, cosine factor and polynomial mutation strategies (LCPGWO), is proposed to optimize the penalty factor C and kernel parameter g of SVM. Then, the optimized SVM model is trained to identify the fault type of samples based on features extracted by ARCMDE. Finally, the application experiment and contrastive analysis verify the effectiveness of the proposed VMD-ARCMDE-LCPGWO-SVM method. 相似文献
70.
在数据驱动的建模中,通过测量或模拟得到时空数据,我们发现基于拉普拉斯先验的贝叶斯稀疏识别方法能有效地恢复时变偏微分方程的稀疏系数。本文将贝叶斯稀疏识别方法运用于各种时变偏微分方程模型(KdV方程、Burgers方程、Kuramoto-Sivashinsky方程、反应-扩散方程、非线性薛定谔方程和纳维-斯托克斯方程)的方程系数恢复,将贝叶斯稀疏恢复结果与PDE-FIND稀疏恢复算法进行比较,证实贝叶斯稀疏识别方法对偏微分方程具有非常强的稀疏恢复能力。同时,研究中发现贝叶斯稀疏方法对噪声更敏感,可以识别更多的附加项。此外,贝叶斯方法可以直接得到稀疏恢复解的误差方差,由此可以直接判定稀疏恢复的效果和可靠性。 相似文献