@article{c3f9ed90ceed4f538731e63a6890a83b, title = "On a consistent dynamic finite-strain shell theory and its linearization", abstract = "In this paper, a dynamic finite-strain shell theory is derived, which is consistent with the three-dimensional (3-D) Hamilton{\textquoteright}s principle with a fourth-order error under general loadings. A series expansion of the position vector about the bottom surface is adopted. By using the bottom traction condition and the 3-D field equations, the recursive relations for the expansion coefficients are successfully obtained. As a result, the top traction condition leads to a vector shell equation for the first coefficient vector, which represents the local momentum-balance of a shell element. Associated weak formulations, in connection with various boundary conditions, are also established. Furthermore, the derived equations are linearized to obtain a novel shell theory for orthotropic materials. The special case of isotropic materials is considered and comparison with the Donnellâ€“Mushtari (D-M) shell theory is made. It can be shown that, to the leading order, the present shell theory agrees with the D-M theory for statics. Thus, the present shell theory actually provides a consistent derivation for the former one without any ad hoc assumptions. To test the validity of the present dynamic shell theory, the free vibration of a circular cylindrical shell is studied. The results for frequencies are compared with those of the 3-D theory and excellent agreements are found. In addition, it turns out that the present shell theory gives better results than the Fl{\"u}gge shell theory (which is known to provide the best frequency results among the first-approximation shell theories).", keywords = "asymptotic analysis, Donell theory, dynamics, finite and linearized elasticity, Shell theory", author = "Zilong Song and Jiong Wang and Hui-Hui Dai", year = "2019", month = aug, doi = "10.1177/1081286517754245", language = "English", volume = "24", pages = "2335â€“2360", journal = "Mathematics and Mechanics of Solids", issn = "1081-2865", publisher = "Sage Publications Ltd.", number = "8", }