Vibration model modification of fluted sandwich cylindrical shells

Abstract

Focusing on the current state of research on the rough theoretical modelling of fluted cylindrical shell structures that can be used as lightweight engineering components, the present study aims to overcome the unreasonable geometric feature characterization, inaccurate equivalent density, and crude equivalent modulus approximation of the cylindrical fluted core in existing models by employing rigorous theoretical derivations. For the first time, a revised vibration model is proposed in the present work to achieve higher precision prediction outcomes for the natural frequency and impulse response of fluted sandwich cylindrical shells. In addition, the constraint forms of boundary conditions are enriched via the virtual spring skill, and specific constraint conditions are relaxed to a continuous elastic constraint state to facilitate the various boundary simulations. The theoretical framework is constructed, the standardized characterizations of the geometrical features of the cylindrical fluted core are regulated, and the exact equivalent density calculation formulas are determined, with the elastic moduli being improved and corrected. Relying on the first-order shear deformation theory and the generalized Hooke's law, the displacement fields and constitutive relations of fluted sandwich cylindrical shells are established, and the dynamic equations are derived through the Rayleigh-Ritz method, with the eigenvalues and eigenfunctions solved therein to obtain the natural frequencies and mode shapes. The transient responses under the triangular, rectangular, exponential, and half-sine impulse excitations are formulated by the Newmark-Beta numerical path. The desired model parameters and their selection criteria are extracted from conducting the convergence analysis, and the numerical validations are then carried out by comparing the calculation results of the proposed model with full-size finite element simulations, and the errors of the uncorrected model results and the numerical advantages of the corrected model are quantified. The influencing laws of key configuration changes on the frequency and response manifestations of such structures are revealed, which can contribute to citation benchmarks and design references for subsequent research.