Forced response statistics of mistuned bladed disks: a stochastic reduced basis approach

This paper presents a stochastic reduced basis approach for predicting the forced response statistics of mistuned bladed-disk assemblies. In this approach, the system response in the frequency domain is represented using a linear combination of complex stochastic basis vectors with undermined coefficients. The terms of the preconditioned stochastic Krylov subspace are used here as basis vectors. Two variants of the stochastic Bubnov-Galerkin scheme are employed for computing the undetermined terms in the reduced basis representation, which arise from how the condition for orthogonality between two random vectors is interpreted. Explicit expressions for the response quantities can then be derived in terms of the random system parameters, which allow for the possibility of efficiently computing the response statistics in the post-processing stage. Numerical studies are presented for mistuned cyclic assemblies of mono-coupled single-mode components. It is demonstrated that the accuracy of the response statistical moments computed using stochastic reduced basis methods can be orders of magnitude better than classical perturbation methods.     

Numerical homogenization techniques applied to piezoelectric composites

With the recent availability of piezoelectric fibers, the design and the analysis of piezoelectric composites needs new modeling tools. Therefore, a numerical homogenization technique has been developed, based on the ATILA finite element code, that combines two techniques: one relying upon the representative volume element (RVE) the other relying upon the wave propagation (WP). The combination of the two methods allows the whole tensor of the homogenized properties of the piezoelectric composite to be found. Considering a fiber embedded in epoxy, the numerical results are compared to the results obtained using previous analytical models, thus validating the models. Even if the method is presented in a particular case, its extension to any piezoelectric composite is straightforward.     

A FEM-based method to determine the complex material properties of piezoelectric disks

Numerical simulations allow modeling piezoelectric devices and ultrasonic transducers. However, the accuracy in the results is limited by the precise knowledge of the elastic, dielectric and piezoelectric properties of the piezoelectric material. To introduce the energy losses, these properties can be represented by complex numbers, where the real part of the model essentially determines the resonance frequencies and the imaginary part determines the amplitude of each resonant mode. In this work, a method based on the Finite Element Method (FEM) is modified to obtain the imaginary material properties of piezoelectric disks. The material properties are determined from the electrical impedance curve of the disk, which is measured by an impedance analyzer. The method consists in obtaining the material properties that minimize the error between experimental and numerical impedance curves over a wide range of frequencies. The proposed methodology starts with a sensitivity analysis of each parameter, determining the influence of each parameter over a set of resonant modes. Sensitivity results are used to implement a preliminary algorithm approaching the solution in order to avoid the search to be trapped into a local minimum. The method is applied to determine the material properties of a Pz27 disk sample from Ferroperm. The obtained properties are used to calculate the electrical impedance curve of the disk with a Finite Element algorithm, which is compared with the experimental electrical impedance curve. Additionally, the results were validated by comparing the numerical displacement profile with the displacements measured by a laser Doppler vibrometer. The comparison between the numerical and experimental results shows excellent agreement for both electrical impedance curve and for the displacement profile over the disk surface. The agreement between numerical and experimental displacement profiles shows that, although only the electrical impedance curve is considered in the adjustment procedure, the obtained material properties allow simulating the displacement amplitude accurately.     

A new electrical to mechanical coupling effect for nonlinear piezoelectric solids

A new electrical to mechanical coupling mechanism is identified whereby electric field rates across discontinuities in strain are shown to induce strain gradients across the discontinuity.     

用于同步辐射的压电变形镜控制策略数值模拟北大核心CSCD

为了提高同步辐射中压电变形镜的控制自由度和面形精度,解决压电致动单元数量过多引起的解算电压受噪声影响异常波动(过拟合)问题,建立了变形镜模型并进行仿真控制。通过有限元仿真获得36组压电响应方程,构建面形与电压的数学模型;为补偿重力造成的镜面畸变,以获得的椭圆面形分析并比较了使用最小二乘法和Tikhonov正则化两种电压解算方案的控制效果。结果表明:采用Tikhonov正则化算法反演后,面形控制误差相比最小二乘法降低了21.7%,相邻极板间电压波动极大值从1.019 kV下降为0.174 kV,反演结果符合工程实际要求;系统对测试噪声具有鲁棒性,相比最小二乘法有更加优越的应用价值。     

Acoustic microscopy applied to nonlinear characterization of biological media

The use of an acoustic microscope as a method for nonlinear characterization of biological media is evaluated. The method consists of measuring the second harmonic signal generated in a sample located at the focus of the acoustic lens. Two experimental configurations were compared: The first is the simple case where the sample is a liquid mixture filling the space between the lens cavity and the receiver; in the second case, the liquid mixture is confined to a thin layer at the focal plane, in order to simulate a real tissue layer. Aqueous solutions of ethylene glycol and methanol were used as liquid samples. Simple theoretical models are presented for each configuration and the predictions show good qualitative agreement with experimental measurements. These results confirm our belief that the acoustic microscope is potentially a good tool for nonlinear B/A imaging of biological systems.     

Surface-enhanced raman scattering and nonlinear optics applied to electrochemistry

The most recently developed diagnostic technique in metal-electrolyte and metal-gas interfaces adapts spontaneous Raman scattering and nonlinear optical generation, techniques normally applied to bulk media, to surface science investigation. For certain metallic surfaces, an enormous increase exists in the Raman (as much as 10⁶ to 10⁸ times) and nonlinear optical signals resulting from submonolayer coverage of molecular adsorbates at the interface. Spontaneous Raman scattering and nonlinear optical scattering are well developed in both theory and practice for the analysis of molecular structure and concentration in bulk media. Instrumentation to generate and detect these inelastically scattered signals is readily available and is adequate for adaption to surface science. However, the mechanism (or mechanisms) giving rise to such a large enhancement at the interfaces is still being actively researched and remains controversial. Theoretical and experimental investigations related to the underlying physics of this enhancement and the application of such surface enhancement as a vibrational probe for adsorbates on the metal surface have been labeled “surface-enhanced Raman scattering” (SERS) and “surface-enhanced nonlinear optics”. Soon after the recognition that molecules adsorbed onto metal electrodes under certain conditions exhibit an anomalously large Raman scattering efficiency,^1–3 it became evident that such a phenomenon makes possible an in situ diagnostic probe for detailed and unique vibrational signatures of adsorbates in the ambient phase (electrolyte and atmospheric gas surroundings). Optical spectroscopy in the visible range has a much higher energy resolution (e.g., 0. I cm-I) than is presently available in electron energy loss spectroscopy (EELS), as well as the capability to measure much lower frequency modes (e.g., as low as 5 cm^?1) than is possible in infrared spectroscopy. Perhaps the most significant attribute of SERS and surface-enhanced nonlinear optical scattering is that the surrounding media in front of the interface (e.g., several meters of gas and several centimeters of liquid) do not introduce optical loss or overwhelmingly large signals. The recognition that SERS is capable of performing vibrational spectroscopy with this resolution, frequency range, and in such dense surroundings has therefore brought an explosion of activity to the field since 1977.     

Modelling nonlinearity in piezoceramic transducers: From equations to nonlinear equivalent circuits

Quadratic nonlinear equations of a piezoelectric element under the assumptions of 1D vibration and weak nonlinearity are derived by the perturbation theory. It is shown that the nonlinear response can be represented by controlled sources that are added to the classical hexapole used to model piezoelectric ultrasonic transducers. As a consequence, equivalent electrical circuits can be used to predict the nonlinear response of a transducer taking into account the acoustic loads on the rear and front faces. A generalisation of nonlinear equivalent electrical circuits to cases including passive layers and propagation media is then proposed. Experimental results, in terms of second harmonic generation, on a coupled resonator are compared to theoretical calculations from the proposed model.     

A simplified fuzzy model to mimic a nonlinear system, applied to aplasma source

This paper develops a fuzzy model to simulate the behaviour of a nonlinear system, in particular a plasma source, with a view to developing a control system for processing plasmas employing a helicon source. Genetic algorithms are employed to optimize fuzzy rules related to the parameters of the fuzzy model which contain a set of variable zeros and poles of the nonlinear system as well as its time delay. A practical application of the fuzzy model is to estimate the electron number density of a low-temperature plasma. Based on the membership functions of the input and output, a set of fuzzy rules by which the variable zeros and poles are identified is derived and optimized using a genetic algorithm. The principal reason for investigating the proposed fuzzy model is the subsequent computer-aided design of a fuzzy controller to control the nonlinear system. Two experimental results are presented to validate the fuzzy model method. One shows a computer simulation and the other predicts the real-time behaviour of the plasma source as its input parameters are varied     

An analysis of modulated molecular beam mass spectrometry applied to nonlinear systems

We have extended a formalism, developed previously to describe linear systems [H.-C. Chang and W.H. Weinberg, J. Chem. Phys. 66 (1977) 4176; Surface Sci. 65 (1977) 153], to the case of nonlinear reaction models in an analysis of modulated molecular beam mass spectrometry. The formalism is derived explicitly for the case of nonlinear surface reactions, adsorption with a coverage dependent sticking probability, and coupled bulk diffusion and nonlinear reaction. Specific examples illustrating how the formalism may be applied include the catalytic decomposition of formic acid on platinum and the reaction of fluorine with tantalum.     

三维非线性Schr(o)dinger方程的直接微扰方法

将直接微扰方法应用于含微扰的三维非线性Schrodinger方程,获得了该方程的包括零阶和一阶修正的近似解析解.借助得到的解析解,分析了微扰对孤子参数的影响.     

A hybrid WKB–Galerkin method applied to a piezoelectric sandwich plate vibration problem considering shear force effects

This paper deals with the problem of dynamic loading of a piezoelectric sandwich plate. The objective of the analysis is to obtain a closed form approximate analytical solution for the equilibrium equations of the loaded plate considering time variant damping, and to discuss the shear force effect for the problem. The solution to the problem is obtained using a hybrid WKB–Galerkin method.     

Nonsingular terminal sliding mode approach applied to synchronize chaotic parameters and systems with unknown nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchro-nization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master＇s and the slave＇s system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.     

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchronization of two different chaotic systems with fully unknown parameters and nonlinear inputs.We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero.We assume that both the master’s and the slave’s system parameters are unknown in advance.Proper adaptation laws are derived to tackle the unknown parameters.An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time.We prove that both reaching and sliding mode phases are stable in finite time.An estimation of convergence time is given.Two illustrative examples show the effectiveness and usefulness of the proposed technique.It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.     

Internal electric fields due to piezoelectric and spontaneous polarizations in CdZnO/MgZnO quantum well with various applied electric field effects

The strain-induced piezoelectric polarization and the spontaneous polarization can be reduced effectively using the applied electric field in the CdZnO/ZnMgO quantum well (QW) structure with high Cd composition. That is, optical properties as a function of internal and external fields in the CdZnO/ZnMgO QW with various applied electric field result in the increased optical gain due to the fact that the QW potential profile is flattened as a result of the compensation of the internal field by the reverse field as confirmed. These results demonstrate that a high-performance optical device operation can be realized in CdZnO/MgZnO QW structures by reducing the droop phenomenon.     

Time averaging and fitting of nonlinear metabolic changes: the issue of the time index choice applied to 31P MRS investigation of muscle energetics

We present an exact analytical method dedicated to fitting time-dependent exponential-like changes in MR spectra. As an illustration, this method has been applied to fitting metabolic changes recorded by 31P MRS in human skeletal muscle occurring during a rest-exercise-recovery protocol. When recording metabolic changes with the accumulative method, the time averaging of the MR signals implies the choice of a time index for fitting any changes in the features of the associated MR spectra. A critical examination of the different ways (constant, linear, and exponential) of choosing the time index is reported. By numerical analysis, we have calculated the errors generated by the three methods and we have compared their sensitivity to noise. In the case of skeletal muscle, both constant and linear methods introduce large and uncontrolled errors for the whole set of metabolic parameters derived from [PCr] changes. In contrast, the exponential method affords a reliable estimation of critical parameters in muscle bioenergetics in both normal and pathological situations. This method is very easy to implement and provides an exact analytical solution to fitting changes in MR spectra recorded by the accumulative method.