Modeling of transient bending wave in an infinite plate and its coupling to arbitrary shaped piezoelements

Estimating the location and energy of impacts is of primary importance for assessing the condition of structures. Particularly, such estimation can be easily obtained from the energy flow in the structures, which is usually derived from the Poynting vector. In order to measure the Poynting vector in a thin plate using piezoelements bonded on the plate, an analytical formulation of the impulse response in thin infinite plates is presented. The knowledge of the impulse response of any linear time invariant (LTI) system is precious information for the determination of its behavior under arbitrary inputs. When dealing with propagation, and especially mechanical wave propagation, a common approach consists in using numerical methods that are often time-consuming, especially for multi-coupled systems. This paper proposes a new approach for modeling the impulse response of an infinite plate with surface-bonded piezoelectric elements. The proposed analytical formulation allows bypassing numerical analysis drawbacks, in particular instabilities occurring at high frequencies, case-dependent systems and computational requirements, while giving the response for any time and space domain values using a simple convolution. The proposed model relies on flexural wave decomposition over the spatial frequency domain and corresponds to a time generalization of the angular spectrum theory, thus introducing flexural wave propagation as a time-varying spatial filter. Once the impulse is know in the spatial frequency domain, the inverse Fourier transform is applied and leads to the impulse response in the physical domain. From this model, an analytical expression of the impulse voltage response of the piezoelectric transducers and the Poynting vector can be derived quite easily. The predicted impulse response is then compared to FEM simulation results and experimental measurements in order to assess the model.     

A unified approach for the analysis of bridges,plates and axisymmetric shells using the linear mindlin strip element

In this paper a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross section in an easily and unified manner is presented. The formulation is based on Mindlin's shell plate theory. One dimensional finite elements are used to discretize the transverse section and Fourier expansions are used to define the longitudinal/circumferential behavior of the structure. The element used is the simple two noded strip element with just one single integrating point. This allows to obtain all the element matrices in an explicit and economical form. Numerical examples for a variety of straight and curve bridges, axisymmetric shells and plate structures which show the efficiency of the formulation and accuracy of the linear strip element are given.     

A stabilized MITC element for accurate wave response in Reissner–Mindlin plates

Residual based finite element methods are developed for accurate time-harmonic wave response of the Reissner–Mindlin plate model. The methods are obtained by appending a generalized least-squares term to the mixed variational form for the finite element approximation. Through judicious selection of the design parameters inherent in the least-squares modification, this formulation provides a consistent and general framework for enhancing the wave accuracy of mixed plate elements. In this paper, the mixed interpolation technique of the well-established MITC4 element is used to develop a new mixed least-squares (MLS4) four-node quadrilateral plate element with improved wave accuracy. Complex wave number dispersion analysis is used to design optimal mesh parameters, which for a given wave angle, match both propagating and evanescent analytical wave numbers for Reissner–Mindlin plates. Numerical results demonstrates the significantly improved accuracy of the new MLS4 plate element compared to the underlying MITC4 element.     

Dynamic response of frameworks by fast fourier transform

A general numerical method for determining the dynamic response of linear elastic plane frameworks to dynamic shocks, wind forces or earthquake excitations is presented. The method consists of formulating and solving the dynamic problem in the frequency domain by the finite element method and of obtaining the response by a numerical inversion of the transformed solution with the aid of the fast Fourier transform algorithm. The formulation is based on the exact solution of the transformed governing equation of motion of a beam element and it consequently leads to the exact solution of the problem. Flexural, and axial motion of the framework members are considered. The effects of damping (external viscous or internal viscoelastic), axial forces on bending, rotatory inertia and shear deformation on the dynamic response are also taken into account. Numerical examples to illustrate the method and demonstrate its advantages over other methods are presented.     

Frequency domain structural synthesis for quasi-static crack propagation: Global–local analysis

Computational efficiencies of a general formulation for frequency domain structural synthesis are exploited in its development as a flexible framework for global–local static and dynamic analysis. Functioning either as a substructure coupling or structural modification procedure, a quasi-static crack propagation analysis is performed demonstrating both computational efficiency and ease in coupling a local analysis to a global finite element analysis. The two alternative algorithms, based on substructure coupling and structural modification, are compared, and are also compared to a traditional finite element solution, and experimental data. The synthesis-based algorithms are shown to significantly outperform the traditional finite element solution.     

Linear free flexural vibration of cracked functionally graded plates in thermal environment

In this paper, the linear free flexural vibrations of functionally graded material plates with a through center crack is studied using an 8-noded shear flexible element. The material properties are assumed to be temperature dependent and graded in the thickness direction. The effective material properties are estimated using the Mori–Tanaka homogenization scheme. The formulation is developed based on first-order shear deformation theory. The shear correction factors are evaluated employing the energy equivalence principle. The variation of the plates natural frequency is studied considering various parameters such as the crack length, plate aspect ratio, skew angle, temperature, thickness and boundary conditions. The results obtained here reveal that the natural frequency of the plate decreases with increase in temperature gradient, crack length and gradient index.     

An 8-node assumed stress hybrid element for analysis of shells

In this paper an 8-node quadrilateral assumed-stress hybrid shell element is presented. The formulation is based on Hellinger–Reissner variational principle. The element is developed by flat shell approach by combining a membrane element with a Mindlin plate element. The proposed element has six degrees of freedom per node and permits an easy connection to other types of finite elements. Numerical examples are presented to show that the validity and efficiency of the present element for static and free vibration analysis.     

A robust adaptive feedforward method for the compensation of harmonic disturbances

Most of disk drives suffer from various disturbances that degrade read–write performances. As the track density rapidly increases, basic drive functions may fail even with a small scale disturbance in a normal operating environment. For the reason, an accurate identification of the repeatable runout (RRO) of a hard disk drive has been one of the most important tasks for the successful servo designs in modern hard disk drive integration. Extensive research efforts have been dedicated for the compensation of the runouts and produced many successful strategies to minimize the influences to the critical basic drive functions. Primarily for the simple implementation and the cost reduction in the actual drive development and manufacturing, most of the developed methods being used in the actual drive integration are preferred to be formulated on time domain or frequency domain with very basic limited functions. The primitive frequency domain approaches usually require extensive calculations and large physical memories. In the present work, a RRO compensation method that combines advantages of the transient Fourier coefficients (TFC) and the least mean square (LMS) update is introduced. Combining the two methods in a proper fashion, the present work provides many benefits for the drive design and outperforms the previous compensation methods. The proposed method requires significantly less amount of computational work and physical memories compared to the conventional runout compensation methods. And it also provides effective frequency component selectivity so that the compensation resources are to be concentrated to a specific problem reason. Comprehensive frequency domain formulation of the method followed by a series of experimental test results is provided in the present article.     

An electronic learning environment for the study of seismic wave propagation

An electronic learning environment is developed for the simulation and processing of seismic wave propagation in layered media and implemented as an Elastodynamics Toolbox in Matlab. The calculation of harmonic and transient wave propagation is based on a direct stiffness formulation that is introduced in a computer program Spectral and integrated as an external function in the Elastodynamics Toolbox. The learning environment contains pre- and postprocessing modules, an on-line user's manual and a set of documented examples where various aspects of seismic wave propagation are described and illustrated. The primary motivation for this work is to support a course on seismic wave propagation in layered media. The toolbox has also potential to be used in a research environment to compute the Green's functions of multilayered elastic media, which are needed in boundary element formulations to solve dynamic soil–structure interaction problems.     

Non-linear finite element analysis of composite beams with interlayer slips

This article presents a new non-linear finite element formulation for the analysis of two-layer composite plane beams with interlayer slips. The element is based on the corotational method. The main interest of this approach is that different linear elements can be automatically transformed to non-linear ones. To avoid curvature locking that may occur for low order element(s), a local linear formulation based on the exact stiffness matrix is used. Five numerical applications are presented in order to assess the performance of the formulation.     

Boundary element formulation for two-dimensional creep problems using isoparametric quadratic elements

A boundary element formulation for creep and time-dependent material behaviour problems based on an initial strain approach is presented. The details of numerical algorithm are shown where isoparametric quadratic elements are used both for the boundary elements and the quadrilateral domain cells. The Euler method with automatic time-step control scheme is implemented for time integration. Two creep power laws, time-hardening and strain-hardening, are employed to analyse a number of problems, including a square plate, a plate with a circular hole and a plate with a semi-circular notch subjected to a uniaxial load. The results are compared with analytical solutions where available and the corresponding finite element solutions.     

Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study

In this study, the effect of the centrifugal forces on the eigenvalue solution obtained using two different nonlinear finite element formulations is examined. Both formulations can correctly describe arbitrary rigid body displacements and can be used in the large deformation analysis. The first formulation is based on the geometrically exact beam theory, which assumes that the cross section does not deform in its own plane and remains plane after deformation. The second formulation, the absolute nodal coordinate formulation (ANCF), relaxes this assumption and introduces modes that couple the deformation of the cross section and the axial and bending deformations. In the absolute nodal coordinate formulation, four different models are developed; a beam model based on a general continuum mechanics approach, a beam model based on an elastic line approach, a beam model based on an elastic line approach combined with the Hellinger–Reissner principle, and a plate model based on a general continuum mechanics approach. The use of the general continuum mechanics approach leads to a model that includes the ANCF coupled deformation modes. Because of these modes, the continuum mechanics model differs from the models based on the elastic line approach. In both the geometrically exact beam and the absolute nodal coordinate formulations, the centrifugal forces are formulated in terms of the element nodal coordinates. The effect of the centrifugal forces on the flap and lag modes of the rotating beam is examined, and the results obtained using the two formulations are compared for different values of the beam angular velocity. The numerical comparative study presented in this investigation shows that when the effect of some ANCF coupled deformation modes is neglected, the eigenvalue solutions obtained using the geometrically exact beam and the absolute nodal coordinate formulations are in a good agreement. The results also show that as the effect of the centrifugal forces, which tend to increase the beam stiffness, increases, the effect of the ANCF coupled deformation modes on the computed eigenvalues becomes less significant. It is shown in this paper that when the effect of the Poisson ration is neglected, the eigenvalue solution obtained using the absolute nodal coordinate formulation based on a general continuum mechanics approach is in a good agreement with the solution obtained using the geometrically exact beam model.     

The speaker identification by using genetic wavelet adaptive network based fuzzy inference system

In this paper, an intelligent speaker identification system is presented for speaker identification by using speech/voice signal. This study includes both combination of the adaptive feature extraction and classification by using optimum wavelet entropy parameter values. These optimum wavelet entropy values are obtained from measured Turkish speech/voice signal waveforms using speech experimental set. It is developed a genetic wavelet adaptive network based on fuzzy inference system (GWANFIS) model in this study. This model consists of three layers which are genetic algorithm, wavelet and adaptive network based on fuzzy inference system (ANFIS). The genetic algorithm layer is used for selecting of the feature extraction method and obtaining the optimum wavelet entropy parameter values. In this study, one of the eight different feature extraction methods is selected by using genetic algorithm. Alternative feature extraction methods are wavelet decomposition, wavelet decomposition – short time Fourier transform, wavelet decomposition – Born–Jordan time–frequency representation, wavelet decomposition – Choi–Williams time–frequency representation, wavelet decomposition – Margenau–Hill time–frequency representation, wavelet decomposition – Wigner–Ville time–frequency representation, wavelet decomposition – Page time–frequency representation, wavelet decomposition – Zhao–Atlas–Marks time–frequency representation. The wavelet layer is used for optimum feature extraction in the time–frequency domain and is composed of wavelet decomposition and wavelet entropies. The ANFIS approach is used for evaluating to fitness function of the genetic algorithm and for classification speakers. It has been evaluated the performance of the developed system by using noisy Turkish speech/voice signals. The test results showed that this system is effective in detecting real speech signals. The correct classification rate is about 91% for speaker classification.     

Large‐signal distributed millimeter‐wave multifinger pHEMT modeling using time‐domain technique

The finite‐difference time‐domain (FDTD) method is used for the large‐signal modeling of a multifinger pHEMT, which is considered as five nonlinear coupled distributed transmission lines. The developed model, which is based on the exact physical layout of multifinger pHEMT, not only accurately describes the propagation effects along the electrodes at higher frequencies but it also includes major nonlinearities of the I–V and Q–V characteristics. Using the transmission line theory, a proper nonlinear equivalent lumped circuit model is allocated for the differential length of the quintuple‐line transistor and the nonlinear active multiconductor transmission line (NAMCTL) equations are derived. These nonlinear, coupled differential equations are numerically solved using the FDTD method. The proposed model is applied to a 100 nm GaAs pHEMT and the simulation results are compared with the results of conventional sliced model in Keysight ADS simulator. The developed transient nonlinear model accurately predicts both the S‐parameters (1–150 GHz) and large‐signal power performances especially at millimeter wave frequency range. The proposed model can be useful in design and analysis of various types of high‐frequency nonlinear integrated circuits.     

A boundary element method for steady convective heat diffusion in three-dimensions

A higher-order boundary element method recently developed by the current authors [Numer. Heat Trans. Part B: Fundamentals 45 (2004) 109] for two-dimensional steady convective heat diffusion is generalized to three-dimensions. In order to facilitate an accurate and efficient boundary element formulation, we introduce an influence domain due to these convective kernels and then localize the surface integrations only within the domain of influence. The localization of the kernels becomes more prominent as the Peclet number of the flow increases. This, in turn, leads to increasing sparsity and improved conditioning of the global matrix. Consequently, iterative solvers for sparse matrices become the primary choice. In this paper, we consider an example problem with an exact solution and investigate the accuracy and efficiency of the boundary element formulation for Peclet numbers in the range from 10 to 1000. The bi-quartic boundary elements included in this study are shown to provide acceptable levels of resolution.     

Damping optimization of viscoelastic laminated sandwich composite structures

Recent developments on the optimization of passive damping for vibration reduction in sandwich structures are presented in this paper, showing the importance of appropriate finite element models associated with gradient based optimizers for computationally efficient damping maximization programs. A new finite element model for anisotropic laminated plate structures with viscoelastic core and laminated anisotropic face layers has been formulated, using a mixed layerwise approach. The complex modulus approach is used for the viscoelastic material behavior, and the dynamic problem is solved in the frequency domain. Constrained optimization is conducted for the maximization of modal loss factors, using gradient based optimization associated with the developed model, and single and multiobjective optimization based on genetic algorithms using an alternative ABAQUS finite element model. The model has been applied successfully and comparative optimal design applications in sandwich structures are presented and discussed.     

Triangular thick plate elements based on a hybrid-Trefftz approach

The paper presents a family of triangular, thick plate elements derived using the hybrid-Trefftz approach. Exact solutions of the governing thick plate equations are used as interpolations for the internal element displacements. An immediate benefit of this approach is that the locking problem is avoided a priori. Independent interpolations are used to describe the displacement and rotations on the element boundaries. The element formulation is based on a modified hybrid-stress principle, leading to a standard stiffness formulation. This enables the elements to be readily implemented into existing finite element schemes. A number of examples are considered to demonstrate the accuracy achieved by the elements.