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Acoustic scattering from functionally graded cylindrical shells

Jamali J., Naei M. H., Honarvar F., Rajabi M.

Archives of Mechanics

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2011

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Vol. 63, nr 1

25-25

EN

In this paper, the method of wave function expansion is adopted to study the scattering of a plane harmonic acoustic wave incident upon an arbitrarily thick-walled, functionally graded cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach, are employed to present an analytical solution based on the three-dimensional exact equations of elasticity. Three models, representing the elastic properties of FGM interlayer are considered. In all models, the mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the shell. In the first two models, the rule of mixture governs. The main difference between them is the set of elastic constants (e.g., Lamé’s constants in model I and Young’s modulus and Poisson’s ratio in Model II) which are governed by the rule of mixtures. In the third model, an elegant self-consistent micromechanical model which assumes an interconnected skeletal microstructure in the graded region is employed. Particular attention is paid to backscattered acoustic response of these models in a wide range of frequency and for different shell wall-thicknesses. The results reveal a technical comparison between these models. In addition, by examining various cases (i.e., different shell wall-thicknesses, various profiles of variations and different volume concentration of constituents), the impact of the overall volume concentration of constituents and also the profile of variations, on the resonant response of the graded shell is investigated. Limiting cases are considered and good agreement with the solutions available in the literature is obtained.

2

Pasywne sterowanie drgań układu dyskretno-ciągłego

Holka H., Nowicki K.

Zeszyty Naukowe. Mechanika / Akademia Techniczno-Rolnicza w Bydgoszczy

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2000

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Z. 47 (228)

129-138

PL

W pracy przedstawiono metodę sterowania poziomem drgań układu dyskretno-ciągłego przy zastosowaniu strukturalnej syntezy podatności. Metoda może być również stosowana do aktywnego sterowania drgań za pomocą równań stanu, które wyznaczono na podstawie otrzymanej macierzy podatności. Pracę zakończono przykładem.

EN

The paper presents a method of passive control of discrete flexible system vibration with the receptance synthesis which can be applied also to the active method of vibration control by a formulation of space equations from the receptance matrix. The study includes the results of numerical investigations.

3

Wybór zmiennych stanu układów dyskretno-ciągłych na podstawie syntezy podatności

Holka H.

Zeszyty Naukowe. Mechanika / Akademia Techniczno-Rolnicza w Bydgoszczy

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1999

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Z. 44 (221)

39-47

PL

W pracy przedstawiono syntezę podatności metodą strukturalną. Metoda posiada szereg zalet. Każdy z podukładów pojawia się w strukturze samodzielnie i jeżeli podukład jest trudny do opisu analitycznego można go wyznaczyć doświadczalnie. Metoda może być również zastosowana do aktywnych układów kontroli drgań ponieważ na podstawie znajomości macierzy można wyznaczyć równania stanu układu. W celu przedstawienia proponowanej metody proces zakończono przykładem.

EN

The paper presents the synthesis of the receptance by using the block diagrams. This methos has same advantages. Each sub-system is described by its receptance and occour in the formulas separately and the second, if the sub-system is so complicated its receptance can be obtained by experiments. It can be applied also to the active method of vibration control by formulation the state space equations from the receptance matrix. In oder to illustrate the connection of the receptance and transformation to the state-space equations the example was presented.