Summary
The paper presents a theoretical formulation for spherical shells reinforced by meridional and circumferential stiffeners. Active damping of the shell is introduced through control action of piezoelectric coupled pairs bonded to the meridional stiffeners. The induced loads can include radial pressure and a thermal field that are independent of the circumferential coordinate. Neglecting local deformations between adjacent meridional stiffeners, the response of the shell will be axisymmetric. The analysis employs the Donnell-Mushtari-Vlasov version of Love's theory of shells together with a smeared stiffeners technique. The paper also considers a particular case of shell mounted piezoelectic coupled pairs without conventional stiffeners. A closed form solution is derived for spherical panels without conventional stiffeners within the range of the meridional coordinate between 75° and 90° using a version of the Geckeler approximation.
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References
Birman, V.: Active control of composite plates using piezoelectric stiffeners. Int. J. Mech. Sci.35, 387–396 (1993).
Birman, V.: Analytical models of sandwich plates with piezoelectric strip-stiffeners. Int. J. Mech. Sci.36, 567–578 (1994).
Knowles, G. J., Chang, V., Murray, J. J.: Suppression of acoustic noise transmission through piezo-coupled elastic plates. In: SPIE Proc. (The International Society for Optical Engineering), pp. 324–334, vol. 3041, Bellingham, Washington: SPIE 1997.
Murray, J. J., Knowles, G. J., Birman, V.: Composite shell piezoelectronic theory: application to spherical caps. In: Smart Materials and Structures (Tomlinson, G. R., Bullough, W. A., eds.), pp. 635–642, Proc. 4th European Conference on Smart Structures and Materials, Harrogate, UK 1998. Bristol Philadelphia: Institute of Physics Publishing 1998.
Simitses, G. J., Blackmon, C. M.: Snap-through buckling of eccentrically stiffened spherical caps. Int. J. Solids Struct.11, 1035–1049 (1975).
Love, A. E. H.: A treatise on the mathematical theory of elasticity, 4th ed., pp. 528–532. London: Cambridge University Press 1927.
Bert, C. W., Kim, C. D.: Analysis of buckling of hollow laminated composite drive shafts. Composite Science and Technology53, 343–351 (1995).
Soedel, W.: Vibration of shells and plates, pp. 57–58. New York: Marcel Dekker 1993.
Vlasov, V. Z.: Basic differential equations in the general theory of elastic shells, NASA TM 1241 (1951).
Birman, V., Adali, S.: Vibration damping using piezoelectric stiffener-actuators with application to orthotropic plates. Composite Struct.35, 251–261 (1995).
Skurlatov, E. D., Startzev, V. G., Suchova, L. N., Feldstein, V. A.: Nonlinear vibration and stability of shallow spherical panels subjected to impulsive loads. In: Problems of nonlinear vibrations of mechanical systems, p. 162, Kiv, Ukraine (1974). Reproduced in the book: Vol'mir, A. S.: Shells in the flow of fluid and gas, pp. 250–253. Moscow: Nauka 1976 (in Russian).
Kraus, H.: Thin elastic shells, pp. 261–271. New York: Wiley 1974.
Gould, P. L.: Analysis of shells and plates, pp. 418–423. New York: Springer 1988.
Gibson, R. F.: Principles of composite material mechanics, pp. 209–210. New York: McGraw-Hill 1994.
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Birman, V., Griffin, S. & Knowles, G. Axisymmetric dynamics of composite spherical shells with active piezoelectric/composite stiffeners. Acta Mechanica 141, 71–83 (2000). https://doi.org/10.1007/BF01176808
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DOI: https://doi.org/10.1007/BF01176808