Semi-analytical hybrid approach for the simulation of layered waveguide with a partially debonded piezoelectric structure

This paper presents an efficient semi-analytical hybrid approach for simulating the dynamic interaction of perfectly bonded or damaged piezoelectric structures with a layered elastic waveguide. In the proposed approach, the frequency domain spectral element method is utilized for the discretization of the finite-sized surface mounted piezoelectric structure, and the semi-analytical boundary integral method is employed for the evaluation of wave phenomena in the host laminate structure. While the spectral element method allows cost-effective simulation of dynamics of a complex-shaped transducer (e.g. curvilinear or with wrapped electrodes), the analytically-based technique reliably describes wave excitation and propagation in multi-layered structures. The coupling of these methods is achieved through the rigorous fulfillment of the boundary conditions at the area of waveguide-transducer contact. Three various combinations of approximation polynomials and surface-load interpolation functions are applied in order to obtain the solution in a frequency domain. The time-domain solution is evaluated employing the inverse Laplace transform. Convergence of the method is confirmed for different bonding conditions. The paper demonstrates the efficiency of the proposed method for the multi-parameter analysis of the dependence of the resonance characteristics on the debonding parameters and contact conditions. The approach can be used for such a crucial task as diagnosing failures of piezoelectric devices incorporated into a structural health monitoring system based on guided waves.     

A Coupled FE-BE Analysis of Smart Lightweight Structures for Active Noise and Vibration Control

Over the past years much research and development has been done in the area of active control in order to improve the acoustical and vibrational properties of thin–walled lightweight structures. An efficient technique for actively reducing the structural vibration and sound radiation is the application of smart structures. In smart structures piezoelectric materials are often used as actuators and sensors. The design of smart structures requires fast and reliable simulation tools. Therefore, the purpose of this paper is to present a coupled finite element–boundary element formulation, which enables the modeling of piezoelectric smart lightweight structures. The paper describes the theoretical background of the coupled approach in which the finite element method (FEM) is applied for the modeling of the passive vibrating shell structure as well as the surface attached piezoelectric actuators and sensors. The boundary element method (BEM) is used to characterize the corresponding sound field. In order to derive a coupled FE–BE formulation additional coupling conditions are introduced at the fluid–structure interface. Since the resulting overall model contains a large number of degrees of freedom, the mode superposition method is employed to reduce the size of the FE submodel. To validate the accuracy of the proposed approach, numerical simulations are carried out in the frequency domain and the results are compared with analytical reference solutions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic response analysis of the two stators hybrid transducer type piezoelectric ultrasonic motor using finite element simulation

This paper presents the finite element simulation with an aim to analyse the dynamic response of the two stators hybrid transducer type piezoelectric ultrasonic motor. The three dimensional–model which includes the effects of piezoelectric coupling are formulated. The dynamic behaviours of a motor stator are calculated and later compared to the experimental results measured from the prototype of this motor. The impedance characteristic of the complete stator is validated using HP4294A precision impedance analyzer. In addition to the electrical measurements, the mechanical displacement and the mechanical velocity of the stator are measured directly using a single point laser Doppler vibrometer. This is to verify that finite element modelling is an appropriate approach to analyse the dynamic behaviour of this piezoelectric ultrasonic motor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiphysics finite element model for the computation of the electro-mechanical dynamics of a hybrid reluctance actuator

ABSTRACT

In hybrid reluctance actuators, the achievable closed-loop system bandwidth is affected by the eddy currents and hysteresis in the ferromagnetic components and the mechanical resonance modes. Such effects must be accurately predicted to achieve high performance via feedback control. Therefore, a multiphysics electro-mechanical finite element model is proposed in this paper to compute the dynamics of a 2-DoF hybrid reluctance actuator. An electromagnetic simulation is adopted to compute the electromagnetic dynamics and the actuation torque, which is employed as input for a structural dynamic simulation computing the electro-mechanical frequency response function. For model validation, the simulated and measured frequency response plots are compared for two actuators with solid and laminated outer yoke, respectively. In both cases, the model accurately predicts the measurement results, with a maximum relative phase error of 1.7% between the first resonance frequency and 1 kHz and a relative error of 1.5% for the second resonance frequency..     

A stabilized finite element method based on local polynomial pressure projection for the stationary Navier–Stokes equations

This article considers a stabilized finite element approximation for the branch of nonsingular solutions of the stationary Navier–Stokes equations based on local polynomial pressure projection by using the lowest equal-order elements. The proposed stabilized method has a number of attractive computational properties. Firstly, it is free from stabilization parameters. Secondly, it only requires the simple and efficient calculation of Gauss integral residual terms. Thirdly, it can be implemented at the element level. The optimal error estimate is obtained by the standard finite element technique. Finally, comparison with other methods, through a series of numerical experiments, shows that this method has better stability and accuracy.     

AN ADAPTIVE INVERSE ITERATION FEM FOR THE INHOMOGENEOUS DIELECTRIC WAVEGUIDES

We introduce an adaptive finite element method for computing electromagnetic guided waves in a closed, inhomogeneous, pillared three-dimensional waveguide at a given frequency based on the inverse iteration method. The problem is formulated as a generalized eigenvalue problems. By modifying the exact inverse iteration algorithm for the eigenvalue problem, we design a new adaptive inverse iteration finite element algorithm. Adaptive finite element methods based on a posteriori error estimate are known to be successful in resolving singularities of eigenfunctions which deteriorate the finite element convergence. We construct a posteriori error estimator for the electromagnetic guided waves problem. Numerical results are reported to illustrate the quasi-optimal performance of our adaptive inverse iteration finite element method.     

Analysis of the stator/rotor-contact in a two stators hybrid transducer type ultrasonic motor

This paper presents the procedure to understand the contact mechanism of the hybrid transducer type piezoelectric ultrasonic motor with two stators by using finite element analysis. First, the vibration mode of a stator will be calculated and analyzed using the commercial finite element program package ANSYS. The computed resonance frequencies of the stator will be presented in the frequency domain, in term of input admittance analysis. After that the distribution of the elliptic path of motion of a particle on the stator surface area will be studied. Finally, the contact condition between the stator and the rotor will be addressed in the computation. The normal displacement, normal velocity and tangential velocity of a point on stator surface area will be calculated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A constrained optimization based method for acoustic finite element model updating of cavities using pressure response

A method based on constrained optimization for updating of an acoustic finite element model using pressure response is proposed in this paper. The constrained optimization problem is solved using sequential quadratic programming algorithm. Updating parameters related to the properties of the sound absorbers and the measurement errors are considered. Effectiveness of the method is demonstrated by numerical studies on a 2D rectangular cavity and a car cavity. It is shown that the constrained formulation, that includes lower and upper bounds on the updating parameters in the form of inequality constraints, is important for obtaining a correct updated model. It is seen that the proposed updating method is not only able to effectively update the model to obtain a close match between the finite element model pressure response and the reference pressure response, but is also able to identify the correction factors to the parameters in error with reasonable accuracy.     

A Note on a Nonlinear Model of a Piezoelectric Rod

If piezoceramics are excited by weak electric fields a nonlinear behavior can be observed, if the excitation frequency is close to a resonance frequency of the system. To derive a theoretical model nonlinear constitutive equations are used, to describe the longitudinal oscillations of a slender piezoceramic rod near the first resonance frequency. Hamilton's principle is used to receive a variational principle for the piezoelectric rod. Introducing a Rayleigh Ritz ansatz with the eigenfunctions of the linearized system to approximate the exact solution leads to nonlinear ordinary differential equations. These equations are approximated with the method of harmonic balance. Finally it is possible to calculate the amplitudes of the displacements numerically. As a result it is shown, that the Duffing type nonlinearities found in measurements can be described with this model.     

Application of inverse finite element method in tube hydroforming modeling

In tube hydroforming, the inverse finite element method (IFEM) has been used for estimating the initial length of tube, axial feeding and fluid pressure. The already developed IFEM algorithm used in this work is based on the total deformation theory of plasticity. Although the nature of tube hydroforming is three-dimensional deformation, in this paper a modeling technique has been used to perform the computations in two-dimensional space. Therefore, compared with conventional forward finite element methods, the present computations are quite fast with no trial and error process. In addition, the solution provides all the components of strain. Using the forming limit diagram (FLD), the components of strain can lead us to measure the potentials for failures or wrinkles during the deformation. The results of analysis for free bulging and square bulging have been compared with some published experimental data and the results obtained by conventional commercial software.     

Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces

In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.     

Nonlinear dynamics and stability analysis of piezo-visco medium nanoshell resonator with electrostatic and harmonic actuation

In this paper, nonlinear dynamics, vibration and stability analysis of piezo-visco medium nanoshell resonator (PVM-NSR) based on functionally graded (FG) cylindrical nanoshell integrated with two piezoelectric layers subjected to visco-pasternak medium, electrostatic and harmonic excitations is investigated. Nonclassical method of the electro-elastic Gurtin–Murdoch surface/interface theory with von-Karman–Donnell's shell model as well as Hamilton's principle, the assumed mode method combined with Lagrange–Euler's are considered. Complex averaging method combined with arc-length continuation is used to achieve a numerical solution for the steady state vibrations of the system. The stability analysis of the steady state response is performed. The parametric studies such as the effects of different boundary conditions, different geometric ratios, structural parameters, electrostatic and harmonic excitation on the nonlinear frequency response and stability analysis are studied. The results indicate that near the natural frequency of the nanoshell, it will lead to resonance and will have large motion amplitude and near the resonant frequency, the nanoshell shows a softening type of nonlinear behavior, and the nanoshell bandwidth increases due to nonlinear factors. In this range, nanoshell has three different ranges of motion, of which two are stable and the other unstable, and so the jump phenomenon and saddle-node bifurcation are visible in the behavior of the system. Also piezoelectric voltage influences on static deformation and resonant frequency but has no significant effect on nonlinear behavior and bandwidth and also system very sensitive to the damping coefficient and due to decrease of nano shell stiffness, natural frequency decreases. And also, increasing or decreasing of some parameters lead to increasing or decreasing the resonance amplitude, resonant frequency, the system's instability, nonlinear behavior and bandwidth.     

Variational Approach to Scattering by Inhomogeneous Layers Ab ove Rough Surfaces

In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.     

Simulation Based Determination of Piezoelectric Material Parameters

The exact numerical simulation of piezoelectric transducers needs the knowledge of all material tensors that occur in the piezoelectric constitutive relations. The determination of these tensors is achieved by a simulation based algorithm which adjusts the 3D - FEM simulated data with electrical measurements of a piezoelectric transducer. Its advantage compared to the standards (see [1], [2]) lies in the fact that a determination of the complete set of material parameters from one arbitrarily shaped specimen with a high precision is possible. The reconstruction of the material tensors is formulated as a parameter identification problem for a system of PDEs. Since unique solvability of this inverse problem may hardly be verified, the system of equations we have to solve for recovering the material tensor entries can be rank deficient and therefore requires application of appropriate regularization strategies. For this purpose, we use inexact Newton methods. The material parameters are assumed to be complex-valued which allows to account for mechanical, dielectric and piezoelectric losses. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new dependence measure for importance analysis: Application to an environmental model

This paper presents a new dependence measure for importance analysis based on multivariate probability integral transformation (MPIT), which can assess the effect of an individual input, or a group of inputs on the whole uncertainty of model output. The mathematical properties of the new measure are derived and discussed. The nonparametric method for estimating the new measure is presented. The effectiveness of the new measure is compared with the well-known delta and extended delta indices, respectively, through a linear example, a risk assessment model and the Level E model. Results show that the proposed index can produce the same importance rankings as the delta and extended delta indices in these three examples. Yet the computation of the proposed measure is quite tractable due to the univariate nature of MPIT. The results also show that the established estimation method can provide robust estimate for the new measure in a quite efficient manner.     

Eigenstates of the quantum Penning-Ioffe nanotrap at resonance

We discuss the choice of physical parameters of a quantum Penning nanotrap under the action of a perturbing inhomogeneous Ioffe magnetic field and also the role of frequency resonance modes. We present a general scheme for constructing the asymptotic behavior of the eigenstates by the generalized geometric quantization method and obtain the reproducing measure in the integral representation of eigenfunctions.     

An Adaptive Hybrid Spectral Method for Stochastic Helmholtz Problems

The implementation of an adaptive hybrid spectral method for Helmholtz equations with random parameters is addressed in this work. New error indicators for generalized polynomial chaos for stochastic approximations and spectral element methods for physical approximations are developed, and systematic adaptive strategies are proposed associated with these error indicators. Numerical results show that these error indicators provide effective estimates for the approximation errors, and the overall adaptive procedure results in efficient approximation method for the stochastic Helmholtz equations.     

On the categorization of demand patterns

The categorization of alternative demand patterns facilitates the selection of a forecasting method and it is an essential element of many inventory control software packages. The common practice in the inventory control software industry is to arbitrarily categorize those demand patterns and then proceed to select an estimation procedure and optimize the forecast parameters. Alternatively, forecasting methods can be directly compared, based on some theoretically quantified error measure, for the purpose of establishing regions of superior performance and then define the demand patterns based on the results. It is this approach that is discussed in this paper and its application is demonstrated by considering EWMA, Croston's method and an alternative to Croston's estimator developed by the first two authors of this paper. Comparison results are based on a theoretical analysis of the mean square error due to its mathematically tractable nature. The categorization rules proposed are expressed in terms of the average inter-demand interval and the squared coefficient of variation of demand sizes. The validity of the results is tested on 3000 real-intermittent demand data series coming from the automotive industry.     

Estimating parameters of polynomial models with errors in variables and no additional information

The problem of estimating a polynomial model with a classical error in the input factor is under consideration in the functional case. The nonparametric method recently introduced for estimating structural dependences does not use any additional information, but it is very effortconsuming computationally and needs samples of large size.We propose some easier methods. The first approach is based on a preliminary estimation of the Berkson error variance under assumption of its normal distribution by the maximum likelihood method for a piecewise linearmodel. This estimate of variance is used for recovering the parameters of a polynomial by the methods of general and adjusted least squares. In case the error variance deviates from normal distribution, an adaptive method is developed that is based on the generalized lambda distribution. These approaches were applied for solving the problem of knowledge level evaluation.     

An inference-finite element model for field problems

A semi-stochastic model for field problems is presented. The model uses a correlative scheme for the estimation of physical parameters and an uncertainty finite element analysis to estimate the statistical properties of the solution process. A comparison is made with a regression-finite element model which indicates the superiority of the introduced correlative-finite element uncertainty analysis.