Wyniki wyszukiwania - Biblioteka Nauki

1

Wave propagation in piezoelectric rings with rectangular cross-sections

100%

Zhang X. , Wang Y. , Chen H.

Journal of Theoretical and Applied Mechanics

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2015

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tom Vol. 53 nr 3

673--682

EN

The ring ultrasonic transducers are widely used in the ocean engineering and medical fields. This paper employs an extended orthogonal polynomial approach to solve the guided wave propagation in two-dimensional structures, i.e. piezoelectric rings with rectangular cross- -sections. The extended polynomial approach can overcome the drawbacks of the conven- tional orthogonal polynomial approach which can be used to solve wave propagation in one-dimensional structures. Through numerical comparison with the available results for a rectangular aluminum bar, the validity of the present approach is illustrated. The dispersion curves and displacement and electric potential distributions of various rectangular piezo- electric rings are calculated, and the effects of different radius to thickness ratios, width to height ratios and polarizing directions on the dispersion curves are illustrated.

2

Time-Domain Analysis of Echoes from Solid Spheres and Spherical Shells with Separated Transmit-Receive Configurations

100%

Wang Z. , Peng Z. , Zhou F. , Tang L.

Archives of Acoustics

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2024

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tom Vol. 49, nr 4

565--574

EN

The complexity of bistatic echo pulse sequences surpasses that of monostatic echo pulse sequences. Based on the scattering acoustic field of elastic spheres and spherical shells, a method is employed to calculate the time-domain echoes of solid spheres and spherical shells with transceiver separation under the condition of plane wave incidence. This is achieved by constructing the incident signal and performing a multiplication operation in the frequency domain with the target scattering acoustic field. Employing the contour integral method, we derive phase velocity and group velocity dispersion curves for circumferential waves propagating around these structures. Furthermore, under the assumption of plane wave incidence, we analyze the propagation paths of Rayleigh echoes for solid spheres and anti-symmetric Lamb waves for spherical shells. Estimation formulas for the arrival times of separated transmit-receive echoes are provided for both solid spheres and spherical shells. Our findings indicate that bistatic waves can be classified into clockwise and counterclockwise circulation patterns around the surfaces of these structures. Through a comparison with the time-angle spectrum of echoes, we demonstrate the accuracy of the proposed estimation formulas for echo arrival times. This study offers valuable insights for the identification of underwater targets.

3

Determination of dispersion curves for composite materials with the use of stiffness matrix method

88%

Barski M. , Pająk P.

Acta Mechanica et Automatica

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2017

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tom Vol. 11, no. 2

121--128

EN

Elastic waves used in Structural Health Monitoring systems have strongly dispersive character. Therefore it is necessary to determine the appropriate dispersion curves in order to proper interpretation of a received dynamic response of an analyzed structure. The shape of dispersion curves as well as number of wave modes depends on mechanical properties of layers and frequency of an excited signal. In the current work, the relatively new approach is utilized, namely stiffness matrix method. In contrast to transfer matrix method or global matrix method, this algorithm is considered as numerically unconditionally stable and as effective as transfer matrix approach. However, it will be demonstrated that in the case of hybrid composites, where mechanical properties of particular layers differ significantly, obtaining results could be difficult. The theoretical relationships are presented for the composite plate of arbitrary stacking sequence and arbitrary direction of elastic waves propagation. As a numerical example, the dispersion curves are estimated for the lamina, which is made of carbon fibers and epoxy resin. It is assumed that elastic waves travel in the parallel, perpendicular and arbitrary direction to the fibers in lamina. Next, the dispersion curves are determined for the following laminate [0°, 90°, 0°, 90°, 0°, 90°, 0°, 90°] and hybrid [Al, 90°, 0°, 90°, 0°, 90°, 0°], where Al is the aluminum alloy PA38 and the rest of layers are made of carbon fibers and epoxy resin.

4

An application of stiffness matrix method to determining of dispersion curves for arbitrary composite materials

88%

Barski M. , Pająk P.

Journal of KONES

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2016

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tom Vol. 23, No. 1

47--54

EN

Nowadays multi-layered composite material is very often applied in different kind of structures, like aircrafts, boats or vehicles. Parts of structures, which are made of these materials, are significantly lighter in comparison with traditional materials, like aluminum or steel alloys. On the other hand, the process of damage creation and evolution in the case of composites is much more complex. Moreover, the damages, which are characteristic for multi-layered materials (matrix cracking, fibre breakage, delaminations), are very difficult to detect at early stage of creation. Hence, there is a need to develop the advanced methods to detect them without destroying tested composite element. One of them is based on analysis of elastic wave propagation through the composite structure. Unfortunately, elastic waves possess strongly dispersive character. Thus, it is necessary to determine dispersion curves for investigated material before the tests in order to appropriate interpretation of received dynamic response of structure. In the case of arbitrary composite materials, it is rather challenging task. In the present article the relatively new, analytical method is applied, namely stiffness matrix method. The fundamental assumptions and the theoretical formulation of this method are discussed. Next numerical examples are presented, namely the dispersion curves are determined for the single orthotropic lamina and multi-layered 'quasi - isotropic' composite plate. The studied plates are made of glass fibres and epoxy resin. In the case of single lamina, the dispersion curves are determined in the parallel, perpendicular and arbitrary direction of waves propagation with respect to the fibre direction. In the case of multi-layered plates, the dispersion curves are computed for one arbitrary direction. Additionally, the phase and group velocities for fundamental modes and fixed excitation frequency are estimated in all directions of waves propagation.

5

Effects of initial stresses on guided waves in unidirectional plates

88%

Zhang X. M. , Yu J. G.

Archives of Mechanics

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2013

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tom Vol. 65, nr 1

3-26

EN

The guided wave propagation in unidirectional plates under gravity, homogeneous initial stress in the thickness direction and inhomogeneous initial stress in the wave propagating direction is investigated in this paper based on the theory of mechanics of incremental deformations. The Legendre orthogonal polynomial series expansion method is used to solve the coupled wave equation. Two different wave propagating directions, the fiber orientation and the vertical fiber orientation, are discussed respectively. The effects of the initial stresses on the Lamb-like wave and shear-horizontal (SH) wave are respectively investigated. The effects of the initial stresses on the dispersion curves and on the displacement and stress distributions are discussed.

6

Modeling the propagation of ultrasonic guided waves in a composite plate by a spectral approximation method

75%

Zitouni I. , Rhimini H. , Chouaf A.

Engineering Transactions

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2023

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tom Vol. 71, iss. 2

213--227

EN

Graphite-epoxy composites have been able to meet the multiple requirements of the space industry. However, the radiation from the spatial environment and non-perfect adhesion between the fibers and the matrix can lead to the appearance of imperfections. To handle this, we use non-destructive testing by ultrasonic guided waves known for its high accuracy in detecting defects. In this article, we study the propagation of ultrasonic guided waves in a graphite-epoxy composite plate by the spectral method. First, the mathematical formalism is explained for modeling guided waves in the composite material. Next, we plot the dispersion curves of the composite plate in different orientations of the fibers with a MATLAB program and the results are compared with those of the DISPERSE software. These give us information on the modes that propagate in the structure. We elaborate and explain a technique based on displacement symmetry to distinguish between the different modes. A discussion based on time-saving and accuracy is established to show the advantages of the method. The second part of our paper consists in giving a physical meaning to the spectral displacements normalized in amplitude. We propose to normalize the spectral eigenvectors by the acoustic power. We plot the displacement and stress profiles of the guided modes and we compare our results to the analytical ones. Perfect correspondence is found, indicating the accuracy of the approach developed. In addition, a study of the vibrational state in the composite plate is established for Lamb and horizontal shear modes at a specific frequency.

7

Wave propagation in functionally graded piezoelectric rods with rectangular cross-section

75%

Yu J. G. , Zhang B. , Lefebvre J. E. , Zhang C.

Archives of Mechanics

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2015

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tom Vol. 67, nr 3

213–-231

EN

For the purpose of design and optimization of functionally graded piezoelectric material (FGPM) transducers, wave propagation in FGPM structures has received much attention in the past twenty years. But research focused essentially on semi-infinite structures and one-dimensional structures, i.e., structures with a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. This paper proposes a double orthogonal polynomial series approach to solve the wave propagation problem in a two-dimensional (2D) FGPM structure, namely, an FGPM rod with a rectangular cross-section. The dispersion curves and electric potential distributions are illustrated.

8

Sequential stochastic identification of elastic constants using Lamb waves and particle filters

63%

Słoński M.

Computer Assisted Methods in Engineering and Science

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2014

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tom Vol. 21, no. 1

15--26

EN

Sequential stochastic identification of elastic parameters of thin aluminum plates using Lamb waves is proposed. The identification process is formulated as a Bayesian state estimation problem in which the elastic constants are the unknown state variables. The comparison of a sequence of numerical and pseudoexperimental fundamental dispersion curves is used for an inverse analysis based on particle filter to obtain sequentially the elastic constants. The proposed identification procedure is illustrated by numerical experiments in which the elastic parameters of an aluminum thin plate are estimated. The results show that the proposed approach is able to identify the unknown elastic constants sequentially and that this approach can be also useful for the quantification of uncertainty with respect to the identified parameters.

9

Numerical simulation of fundamental elastic wave modes coupling in composite plates

63%

Barski M. , Stawiarski A. , Chwał M. , Augustyn M.

Vibrations in Physical Systems

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2023

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tom Vol. 34, nr 1

art. no. 2023120

EN

In the case of the piezoelectric actuators of the cube-shaped installed symmetrically and perfectly bonded on both external surfaces of the plate-like structures, the symmetric and shear horizontal elastic wave modes are excited at the same time. The current work concerns the numerical simulation of the coupling of the above-mentioned elastic wave modes in a composite plate of angle ply configuration. In the first step, the dispersion curves for all studied composite configurations are estimated. Next, for the arbitrary chosen fixed frequency of the excitation, finite element simulations are performed. As a result of these simulations, the group velocities of the observed elastic modes are estimated. Next, the appropriate wave modes are identified by the comparison of the group velocities obtained from the analysis of the dispersion curves and from the simulations. In the cases for which the identification is possible, a good agreement between analytical and simulation results is observed.

10

The influence of the configuration of the fiber-metal laminates on the dispersion relations of the elastic wave modes

51%

Barski M. , Muc A. , Stawiarski A.

Vibrations in Physical Systems

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2020

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tom Vol. 31, nr 2

art. no. 2020202

EN

The current work is devoted to the determination of dispersion curves for elastic wave modes. The studied elastic waves propagate across metal-fiber hybrid composites. In order to solve the problem, special software has been developed with the use of C++. This software works with the MS Windows operating system and the proposed solution is based on the multi-threading mechanism. It makes possible to significantly speed up the calculations. The relatively new approach is used namely the stiffness matrix method. At the very beginning, the dispersion curves are determined for the traditional composite materials of cross-ply configuration, for which the layers are made of glass fiber/epoxy resin and carbon fiber/epoxy resin. The impact of the total number of layers on the dispersion curves is investigated. Next, the influence of the thickness of the layers, which are made of aluminum alloy, on the dispersion characteristic is studied. In the second case, it is assumed that the total thickness of the composite material wall for all cases is identical.

11

Stopband effect and sound transmission loss of periodic locally resonant structures

51%

Juros K. , Kras A. , Kamisiński T.

Vibrations in Physical Systems

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2021

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tom Vol. 32, nr 1

art. no. 2021105

EN

This paper investigates the theoretical aspects of sound attenuation of periodic structures with locally resonant elements. The stopband effect in frequency characteristics of infinite periodic structures created by the resonant elements is investigated. The dispersion curves calculation procedure is described in details with the influence of resonance frequency and mass of added locally resonant structure on width of the obtained stopband is investigated. The theoretical formulation for calculation of the sound transmission loss for periodic structure is derived. The performance of the structure with locally resonant elements is evaluated based on dispersion curves obtained for an infinite periodic structure and transmission loss calculated for finite structure is conducted.

12

Dispersion relations for composite structures. Pt. 2, Methods of determining dispersion curves

51%

Barski M. , Stawiarski A. , Chwał M.

Composites Theory and Practice

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2016

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tom R. 16, nr 3

147--153

EN

In the first part of the current review, the fundamental assumptions of the theoretical model of elastic waves propagation in multilayered composite material are presented. Next, the equations which describe elastic wave motion in the case of single orthotropic lamina are derived. In the second part of this work, the most commonly used method of determining dispersion curves for multilayered composite material are discussed, namely: the transfer matrix method (TMM), global matrix method (GMM), stiffness matrix method (SMM) and finally the semi-analytical finite element method (SAFE). The first three methods are based on the relationships which are derived in the first part of this review. Moreover, TMM and GMM should be considered numerically unstable in the case of a relatively large product value of wave frequency and the total thickness of the composite plate. However, SMM seems to be unconditionally stable. The last method is based on the finite element approach and it can be used in order to confirm the results obtained using the analytical method. Finally, exemplary dispersion curves are presented. The dispersion curves are determined for the 8-th layer of the composite material, which is made of carbon fiber and epoxy resin. It is assumed that the wave front travels in an arbitrary direction.

PL

W części pierwszej pracy omówiono założenia dotyczące teoretycznego modelu propagacji fal sprężystych w wielowarstwowych materiałach kompozytowych. Następnie wyprowadzono równania opisujące zjawisko propagacji fal sprężystych w pojedynczej warstwie o ortotropowych własnościach mechanicznych. W części drugiej przedstawiono podstawy najczęściej wykorzystywanych metod wyznaczania krzywych dyspersji dla ośrodków wielowarstwowych, a mianowicie: transfer matrix method (TMM), global matrix method (GMM), stiffness matrix method (SMM), a także semi-analytical finite element method (SAFE). Pierwsze trzy podejścia oparte są bezpośrednio na równaniach wyprowadzonych w części pierwszej. Metody TMM oraz GMM uważane są za numerycznie niestabilne w przypadku odpowiednio dużych wartości iloczynu częstotliwości i całkowitej grubości płyty kompozytowej. Natomiast wydaje się, że podejście SMM jest numerycznie bezwarunkowo stabilne. Ostatnia z wymienionych metod oparta jest na metodzie elementów skończonych i można ją efektywnie wykorzystać w celu potwierdzenia wyników otrzymanych przy użyciu poprzednio wymienionych algorytmów. Jako przykład pokazano krzywe dyspersji wyznaczone dla 8-warstwowego materiału kompozytowego wykonanego z włókna węglowego, przy czym założono, że czoło fali porusza się w dowolnie założonym kierunku.

13

Dispersion relations for composite structures. Pt. 1, Basic assumptions and relationships for monoclinic lamina

51%

Barski M. , Stawiarski A. , Chwał M.

Composites Theory and Practice

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2016

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tom R. 16, nr 3

125--131

EN

Nowadays, the propagation of elastic waves, particularly Lamb waves, is very often used in detecting damages in different kinds of composite materials. These systems are known as structural health monitoring (SHM). However, the phenomenon of Lamb wave propagation is very complex, especially in the case of thin-walled composite structures. Generally, three types of Lamb waves are observed, namely: longitudinal or pressure waves (L), shear vertical (SV) and shear horizontal (SH). The phase and group velocities of the mentioned waves depend on the thickness of the structure and the frequency of the excited signal. This fact makes proper interpretation of the received dynamic response of the structure difficult or even impossible. Therefore, determining the appropriate dispersion curves for different materials is a very important issue. In the present review, the most commonly used analytical approaches for determining dispersion curves in the case of multilayered composite plates are presented. At the very beginning of this work the solution for single isotropic plates is presented. Next, the fundamental assumptions of the theoretical model, which describe the elastic wave propagation phenomenon in multilayered materials, are discussed. In the first part, the relationships describing the elastic wave propagation for single orthotropic lamina are presented. There are two studied cases: namely when the wave front of the elastic wave travels along the principal directions of the material and when the wave front of the elastic wave travels in any arbitrary direction.

PL

Obecnie zjawisko propagacji fal sprężystszych, a w szczególności fal Lamba jest często wykorzystywane przy projektowaniu różnych systemów wykrywania uszkodzeń w wielowarstwowych materiałach kompozytowych. Systemy te są ogólnie znane pod skrótem SHM (Structural Health Monitoring). Jednakże, zjawisko propagacji fal Lamba w kompozytowych konstrukcjach cienkościennych posiada bardzo skomplikowany charakter. W ogólnym przypadku w zależności od płaszczyzny polaryzacji drgań cząstek rozróżniamy trzy rodzaje fal Lamba, a mianowicie: falę podłużną (L) oraz fale poprzeczne spolaryzowane w kierunku pionowym (SV) oraz poziomym (SH). Dodatkowo, każda z wymienionych fal w zależności od grubości materiału oraz częstotliwości generowanego sygnału posiada odpowiednie mody. Mody te propagują się z różną prędkością zarówno fazową, jak i grupową. Zjawisko to znacznie utrudnia interpretację zarejestrowanej dynamicznej odpowiedzi konstrukcji. W pracy szczegółowo opisano najczęściej wykorzystywane analityczne metody wyznaczania krzywych dyspersji. Na początku przedstawiono rozwiązanie dla jednowarstwowej płyty izotropowej. Następnie omówiono podstawowe założenia teoretycznego modelu propagacji fal sprężystych w materiałach wielowarstwowych. W części pierwszej zaprezentowano równania opisujące zjawisko propagacji fal sprężystych w jednowarstwowych płytach o własnościach ortotropowych. Rozważano dwa przypadki, a mianowicie kiedy czoło fal sprężystych porusza się wzdłuż osi głównych materiału oraz kiedy czoło fali porusza się w dowolnym kierunku.