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

• Autorzy: Barski M. , Stawiarski A. , Chwał M.

Warianty tytułu

PL

Równania dyspersji dla struktur kompozytowych. Cz. 2, Metody wyznaczania krzywych dyspersji

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Lamb waves; composite materials; anisotropic layer; dispersion curves; phase velocity; group velocity

PL

fale Lamba; materiały kompozytowe; warstwa anizotropowa; prędkość fazowa; prędkość grupowa

• Wydawca: Polskie Towarzystwo Materiałów Kompozytowych
• Czasopismo: Composites Theory and Practice
• Rocznik: 2016
• Tom: R. 16, nr 3
• Strony: 147--153
• Opis fizyczny: Bibliogr. 39 poz., rys.

Twórcy

autor

Barski M.

• Cracow University of Technology, Institute of Machine Design, al. Jana Pawła II 37, 31-864 Krakow, Poland

autor

Stawiarski A.

• Cracow University of Technology, Institute of Machine Design, al. Jana Pawła II 37, 31-864 Krakow, Poland

autor

Chwał M.

• Cracow University of Technology, Institute of Machine Design, al. Jana Pawła II 37, 31-864 Krakow, Poland

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.