**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31100

##### Parametric Vibrations of Periodic Shells

**Authors:**
B. Tomczyk,
R. Mania

**Abstract:**

**Keywords:**
Mathematical Modeling,
Micro-periodic shells,
length-scale effect,
parametric vibrations

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1061731

**References:**

[1] A. Bensoussan, J. L. Lions and G. Papanicolau, Asymptotic Analysis for Periodic Structures. Amsterdam, North-Holland, 1978.

[2] T. Lewiński and J. J. Telega, Plates, Laminates and Shells. Asymptotic Analysis and Homogenization. Singapore: World Scientific Publishing Company, 2000.

[3] J. Awrejcewicz, I. Andrianov and L. Manevitch, Asymptotical Mechanics of Thin-Walled Structures. Berlin: Springer, 2004.

[4] S. A. Ambartsumyan, Theory of Anisotropic Shells. Moscow: Nauka, 1974.

[5] B. Tomczyk, "On the modeling of thin uniperiodic cylindrical shells," J. Theor. Appl. Mech., vol. 41, pp. 755-774, 2003.

[6] B. Tomczyk, "On stability of thin periodically densely stiffened cylindrical shells," J. Theor. Appl. Mech., vol. 43, pp. 427-455, 2005.

[7] B. Tomczyk, "On dynamics and stability of thin periodic cylindrical shells," Diff. Eqs. Nonlin. Mech., ID 79853, pp. 1-23, 2006.

[8] B. Tomczyk, "A non-asymptotic model for the stability analysis of thin biperiodic cylindrical shells," Thin-Walled Struct., vol. 45, pp. 941-944, 2007.

[9] B. Tomczyk, "Vibrations of thin cylindrical shells with a periodic structure," PAMM, vol. 8, pp. 10349-10350, 2008.

[10] B. Tomczyk, B. "Dynamic stability of micro-periodic cylindrical shells," Mechanics and Mechanical Engineering., vol. 14, pp. 137-150, 2010.

[11] B. Tomczyk, "On the modeling of dynamic problems for biperiodically stiffened cylindrical shells," Civil and Environmental Engineering Reports, vol. 5, pp. 179-204, 2010.

[12] B. Tomczyk, "Thin cylindrical shells," in Thermomechanics of Microheterogeneous Solids and Structures. Tolerance Averaging Approach, Part II: Model Equations, C. Wo┼║niak, B. Michalak and J. J─Ödrysiak, Eds. Lodz: Lodz Technical University Press, 2008, pp. 165-175.

[13] B. Tomczyk, "Thin cylindrical shells," in Thermomechanics of Microheterogeneous Solids and Structures. Tolerance Averaging Approach, Part III: Selected Probmems, C. Wo┼║niak, B. Michalak and J. J─Ödrysiak, Eds. Lodz: Lodz Technical University Press, 2008, pp. 383- 411.

[14] B. Tomczyk, "On micro-dynamics of reinforced cylindrical shells," in Mathematical Modeling and Analysis in Continuum Mechanics of Microstructured Media, C. Wo┼║niak, et al., Eds. Gliwice: Silesian Technical University Press, 2010, pp. 121-135.

[15] B. Tomczyk, "Combined modeling of periodically stiffened cylindrical shells," in Selected Topics in Mechanics of the Inhomogeneous Media, C. Wo┼║niak, et al., Eds. Zielona Gora: Zielona Gora University Press, 2010, pp. 79-97.

[16] B. Tomczyk, "A combined model for problems of dynamics and stability of biperiodic cylindrical shells," in Mathematical Methods in Continuum Mechanics, K. Wilmański, B. Michalak and J. J─Ödrysiak, Eds. Lodz: Lodz Technical University Press, 2011, pp. 331-355.

[17] C. Wo┼║niak and E. Wierzbicki, Averaging Techniques in Thermomechanics of Composite Solids. Cz─Östochowa: Cz─Östochowa University Press, 2000.

[18] C. Wo┼║niak, B. Michalak and J. J─Ödrysiak, (Eds.), Thermomechanics of Microheterogeneous Solids and Structures. Tolerance Averaging Approach. Lodz: Lodz Technical University Press, 2008.

[19] C. Wo┼║niak, et al. (Eds.), Mathematical Modeling and Analysis in Continuum Mechanics of Microstructured Media. Gliwice: Silesian Technical University Press, 2010.

[20] C. Wo┼║niak, et al. (Eds.), Selected Topics in Mechanics of the Inhomogeneous Media. Zielona Gora: Zielona Gora University Press, 2010.

[21] S. Kaliski (Ed.), Vibrations. Warsaw-Amsterdam: PWN-Elsevier, 1992.