### ENERGY ANALYSIS OF FREE TRANSVERSE VIBRATIONS OF THE VISCO-ELASTICALLY CONNECTED DOUBLE-MEMBRANE SYSTEM

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#### Abstract

The presented paper deals with the analysis of energy transfer in the visco-elastically connected circular double-membrane system for free transverse vibration of the membranes. The system motion is described by a set of two coupled non-homogeneous partial differential equations. The solutions are obtained by using the method of separation of variables. Once the problem is solved, natural frequencies and mode shape functions are found, and then the form of solution for small transverse deflections of membranes is derived. Using the obtained solutions, forms of reduced kinetic, potential and total energies, as functions of dissipation of the whole system and subsystems, are determined. The numerical examples are given as an illustration of the presented theoretical analysis as well as the possibilities to investigate the influence of different parameters and different initial conditions on the energies transfer in the system.

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Postlethwaite, J., Lamping, S.R., Leach, G.C, Hurwitz, M.F., Lye, G.J., 2004, Flux and transmission characteristics of a vibrating microfiltration system operated at high biomass loading, Journal of Membrane Science 228, pp. 89–101.

Jaffrin, M.Y., 2008, Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems, Journal of Membrane Science 321 , pp. 7–25.

Vassilopoulou, I., Gantes, C. J., 2010, Vibration modes and natural frequencies of saddle form cable nets, Computers & structures, 88(1), pp. 105-119.

Bao, Z., Mukherjee, S., Roman, M., Aubry, N., 2004, Nonlinear vibrations of beams, strings, plates, and membranes without initial tension, Journal of Applied Mechanics, 71(4), pp. 551-559.

Oniszczuk, Z., 1998, Vibrations of elastically connected circular double-membrane compound system, Scientiific Works of Rzeszow University of Technology, Civil Engineering 132, pp. 61-81.

Oniszczuk, Z., 1999, Transverse vibrations of elastically connected rectangular double- membrane compound system, Journal of Sound and Vibration 221(2), pp. 235-250.

Noga, S., 2010, Free transverse vibration analysis of an elastically connected annular and circular double-membrane compound system, Journal of Sound and Vibration 329, pp. 1507–1522.

Noga, S., 2008, Numerical analysis of a free transverse vibration of an elastically connected annular double-membrane compound system, Acta Mechanica Slovaca 3-A , pp. 307–312.

Karliĉić, D., 2012, Free transversal vibrations of a double-membrane system, Scientific Technical Review 62, pp. 77–83.

Simonović, J., 2008, Dynamics of Mechanical Systems of Complex Structure, Magister thesis, Faculty of Mechanical Engineering, University of Niš , in Serbian, pp. 249.

Hedrih, K. S., 2006, Transversal vibrations of double plate systems, Acta Mechanica Sinica, 22, pp. 487-501.

Hedrih, K. S., Simonović, J., 2007, Transversal vibrations of a non-conservative double circular plate system, Facta Universitatis, Series Mechanics, Automatic Control and Robotics 6(1), pp. 19-64.

Hedrih, K. S., Simonović, J. D., 2010, Non-linear dynamics of the sandwich double circular plate system, International Journal of Non-Linear Mechanics 45(9), pp. 902-918.

Kelly, S. Graham, 2007, Advanced Vibration Analysis, Boca Raton, FL: CRC/Taylor & Francis, p. 1-637.

Hedrih, K. S., Simonović, J. D., 2012, Energies of the Dynamics in a Double Plate Nonlinear System, International Journal of Bifurcation and Chaos 21(10), pp. 2993-3011.

Hedrih, K. S., 2009, Energy transfer in the hybrid system dynamics (energy transfer in the axially moving double belt system), Archive of Applied Mechanics 79, pp. 529-540.

Karliĉić, D., Cajić, M., 2012, Energy Transfer Analysis of an Elastically Connected Circular Double-Membrane Compound System, Book of abstracts, 8th European Solid Mechanics Conference, Graz (2012).

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