Frequency multiplication resonances of spatial four-direction braided composite sandwich cylindrical shells with three-dimensional lattice pyramid cores exposed to harmonic loads and thermal environments

In response to the current status of unfulfilled nonlinear dynamics prediction and evaluation tools for novel lightweight spacecraft components, the matched theoretical model and solution procedures for spatial four-direction braided composite sandwich cylindrical shells with three-dimensional lattice pyramid cores are proposed. This will reveal their nonlinear free vibration characteristics and frequency multiplication resonant behaviors. In particular, the nonlinear thermal strains and energy exerted by the thermal expansions are considered by the Green-Lagrange function. The constructed theoretical formulation achieves the equivalent mechanical performance characterization of the three-dimensional lattice pyramid core and spatial four-way braided composites. Based on these explicit expressions, the nonlinear dynamical equations of such a structure subjected to the uniformly distributed harmonic load and thermal environment are derived by employing the first-order shear deformation theory, allowing for the von Kármán geometrical large deformation assumption and the Euler-Lagrange equation. The Green's thermal strain addition terms are introduced. The nonlinear frequencies with initial magnitudes, the amplitude-frequency attributes, and phase trajectories of the primary, super-frequency, and sub-frequency resonances are analytically derived using the multiscale approach. Also, comparison studies are conducted to verify the correctness of the modelling techniques and output data. The manifestations and mechanisms in different nonlinear vibration behaviors are disclosed. Finally, the impact of configuration adjustments and environmental factors on the anti-vibration capability of the structure is characterized via prime dynamic indicators. Some adjustment strategies are reported for pursuing low resonant amplitudes and narrow resonant regions.