Nonlinear free vibration analysis of prestressed circular cylindrical shells on the Winkler/Pasternak foundation

• Published in: Thin-walled structures Vol. 53; pp. 26 - 39
• Main Authors: Bakhtiari-Nejad, Firooz, Mousavi Bideleh, Seyed Milad
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.04.2012; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Hydrostatic pressure; Nonlinear free vibration; Perturbation; Physics; Prestress; Rayleigh–Ritz; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Thin cylindrical shells; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Winkler/Pasternak foundation; Thin cylindrical shells; Winkler/Pasternak foundation; Prestress; Hydrostatic pressure; Rayleigh–Ritz; Perturbation; Nonlinear free vibration; High strain; Thin shell; Displacement(deformation); Perturbation method; Elastic foundations; Uniaxial tension stress; Free vibration; Revolution shell; Experimental study; Natural frequency; Rayleigh-Ritz; Rayleigh Ritz method; Equations of state; Circular cylinder; Ritz method; Cylindrical shell; Non linear effect; Structural analysis; Pasternak foundation; Internal pressure; Prestress Hydrostatic pressure
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2011.12.015

Nonlinear free vibration analysis of prestressed circular cylindrical shells placed on Winkler/Pasternak foundation is investigated in the present paper. The nonlinearity is considered due to large deflections. Simultaneous effects of prestressed condition and elastic foundation on natural frequencies of the shells under various boundary conditions are examined extensively in this study. The nonlinear Sanders–Koiter shell theory is employed in order to derive strain–displacement relationships. The nonlinear classical Love's thin shell theory is also applied in some specific cases due to contrast the results. Beam modal functions are used to approximate spatial displacement field. The governing equations in linear state are solved by the Rayleigh–Ritz procedure. Perturbation methods are used to find the relationship between vibration amplitude and frequency in nonlinear state. Prestress state includes the effects of internal hydrostatic pressure and initial uniaxial tension. Results are compared with published theoretical and experimental data for some specific cases. ► Nonlinear vibration of prestressed shells on Winkler/Pasternak foundation. ► Nonlinearities are considered due to the large amplitude vibrations. ► Concurrent effects of prestress and elastic foundation are studied for shell vibrations. ► The nonlinear Love and Sanders' thin shell theories are employed and compared. ► Perturbation method used to find amplitude/frequency relation in nonlinear state.