Vibration analysis of composite circular and annular membranes

• Autorzy: Siedlecka U. , Zamorska I. , Kukla S.

Identyfikatory

DOI

10.17512/jamcm.2016.1.15

• Języki publikacji: EN

Abstrakty

EN

In this paper a solution to the free vibration problem of composite circular and annular membranes is presented. The vibrations of membranes whose material densities and/or thicknesses varied step-wise with the radial co-ordinate are considered. This approach is applied to approximate the solution to the vibration problem of a membrane with continuously varying density and/or thickness with the radial co-ordinate. The obtained analytical solutions are used in numerical investigations into the effect of parameters characterizing the composite membranes on their eigenfrequencies.

Słowa kluczowe

EN

composite membrane; free vibration; Green's functions

PL

membrana kompozytowa; wolne wibracje; funkcja Greena

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 1
• Strony: 149--159
• Opis fizyczny: Bibliogr. 11 poz., rys., tab.

Twórcy

autor

Siedlecka U.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Zamorska I.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Kukla S.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Laura P.A.A., Rossit C.A., La Malfa S., Transverse vibrations of composite, circular annular membranes: exact solution, Journal of Sound and Vibration 1998, 216(1), 190-193.
• [2] Gottlieb H.P.W., Exact solutions for vibrations of some annular membranes with inhomogeneous radial densities, Journal of Sound and Vibration 2000, 223(1), 165-170.
• [3] Jabareen M., Eisenberger M., Free vibrations of non-homogeneous circular and annular membranes, Journal of Sound and Vibration 2001, 240(3), 409-429.
• [4] Cap F.F., Eigenfrequencies of membranes of arbitrary boundary and with varying surface mass density, Applied Mathematics and Computation 2001, 124, 319-329.
• [5] Gutierrez A.A., Laura P.A.A., Bambill D.V., Jederlinic V.A., Hodges D.H., Axisymmetric vibrations of solid circular and annular membranes with continuously varying density, Journal of Sound and Vibration 1998, 212(4), 611-622.
• [6] Wei-Peng H., Zi-Chen D., Wen-Cheng L., Multi-symplectic methods for membrane free vibration equation, Applied Mathematics and Mechanics 2007, 28(9), 1181-1189.
• [7] Civalek Ö., Gürses M., Discrete singular convolution for free vibration analysis annular membranes, Mathematical and Computational Applications 2009, 14(2), 131-138.
• [8] Reutskiy S.Y., The methods of external and internal excitation for problems of free vibrations of non-homogeneous membranes, Engineering Analysis with Boundary Elements 2007, 31, 906-918.
• [9] Buchanan G.R., Vibration of circular membranes with linearly varying density along a diameter, Journal of Sound and Vibration 2005, 280, 407-414.
• [10] Zamorska I., Kukla S., Siedlecka U., Frequency analysis of composite annular membranes, Scientific Research of the Institute of Mathematics and Computer Science 2012, 11(1), 129-135.
• [11] Dahlquist G., Björck A., Numerical Methods in Scientific Computing, Society for Industrial and Applied Mathematics, Philadelphia 2008.

Uwagi

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