Tolerance Models of Dynamic Problems for Microheterogeneous Cylindrical Shells
Barbara Tomczyk · Journal of Applied Nonlinear Dynamics · 2014
Thin linearly elastic Kirchhoff-Love-type circular cylindrical shells with a periodically micro - inhomogeneous structure in circumferential direction (uniperiodic shells) are investigated. At the same time, these shells have constant structure in axial direction. The aim of this contribution is to formulate some new mathematical non-asymptotic averaged models for the analysis of selected dynamic problems for the shells under consideration. These, so-called, tolerance models are derived by means of a certain extended version of the known tolerance (non-asymptotic) modelling of micro-heterogeneous media presented in [Tomczyk, B. and Woźniak, C. (2012), Tolerance models in elastodynamics of certain reinforced thin-walled structures. In: Kolakowski, Z. & Kowal-Michalska, K. (eds.), Statics, Dynamics and Stability of Structures, vol.2, Technical University of Lodz Press, Lodz, 123-153]. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, the tolerance model equations proposed here have constant coefficients depending also on a cell size. Hence, these models make it possible to investigate the effect of a length scale on the global shell dynamics. Moreover, a certain homogenized (asymptotic) model, being independent of a microstructure size, is also derived applying the extended tolerance averaging technique proposed in the above mentioned monograph.