Nonlinear combined vibration modeling and analysis of honeycomb-filled corrugated core cylindrical shells considering thermal effects

The present study develops an analytical model to obtain the static mechanical properties and nonlinear vibration behaviors of an emerging composite core cylindrical shell with promising application prospects in engineering components, where the object is constituted by a honeycomb-filled corrugated core and gradient-distributed composite supporting and covering skins. Explicit calculation expressions of the equivalent macro-mechanical properties of the core and skin are first achieved by employing the modified Halpin-Tsai approach and macroscopic and microscopic strain energy density invariance criterion, and energy computation formulas for the overall structure are derived based on the first-order shear deformation theory and energy methods, which take the von Kármán nonlinear terms into account, with Rayleigh dissipation function, thermal strain energy and the external work generated by the multi-harmonic external loads being characterized. The nonlinear dynamic equations of the system are determined by the Euler-Lagrange routine, while the Galerkin discretization and static condensation techniques are used to reconstruct the mechanics equation for the reduction of the degrees of freedom. The solution procedures regarding the linear and nonlinear vibration behaviors are proposed by eigen-parameters and the multiscale approach, which incorporate the intrinsic frequency, mode shapes, history responses, amplitude-frequency relation, and phase characteristics. The model outcomes are validated by comparison analyses, which in turn elucidate the external manifestations and internal mechanisms of the time-domain course response, amplitude-frequency curves, and phase trajectories triggered by several combined resonance occasions, with the discrepancies in these standards being revealed. The influencing rules and underlying physical causes of critical conformation variables on the multi-harmonic combination resonance behaviors are disclosed, and some proposals conducive to enhancing the structural dynamics capabilities are reported.