The present paper develops a new Bernoulli–Euler theory of microbeams for the consideration of small-scale effects and nonlinear terms, which are induced by the axial elongation of the beam and Kelvin–Voigt damping. The non-resonance and primary resonance of microbeams are researched through the application of Galerkin and multiple scale methods to the new model. The results suggest the following: (1) Nonlinear damping slightly affects the vibration amplitudes under the non-resonance condition; (2) nonlinear damping can significantly change the bifurcation points that induce a jump in the vibration amplitudes under the primary resonance condition. The current researches indicate that nonlinear damping is necessary for an accurate description of microbeam vibrations.

Enhancing the impact resistance performance of carbon fiber-reinforced polymer (CFRP) laminates stands as a prominent research focus among various nations. Existing studies have shown a tendency towards arbitrary selection of the inter-ply helix angle values in CFRP laminates, which is accompanied by a limited number of samples representing the chosen helix angles. However, existing studies have shown a relatively random selection of spiral angle values between CFRP laminates, and the sample size of selected spiral angles is limited, posing certain limitations. In order to tackle this problem, we have employed a systematic arrangement of combinations to select the optimal helix angle for CFRP laminates. Inspired by the biological structures of Bouligand, we have sequentially chosen 19 distinct sets of helix angles, aiming to overcome the inherent limitations and enhance the research outcomes in this field. In this study, we established 19 finite element models to investigate the behavior of Bouligand-inspired CFRP composite panels under high-velocity bullet impact. The models were created by selecting 19 sets of helix angles within the range of 0 to 90° with a 5° interval. The results show that the energy absorption of the Bouligand layer-stacking composite plate is better than that of the conventional plate. The optimal spiral angles of the CFRP laminate are 25° and 30°, and the energy absorption characteristics of the laminate are the best at these angles. The impact resistance is also the best at these angles. The energy absorption of the Bouligand layer-stacking composite plate is 396% higher in absorbed internal energy and 361% higher in absorbed kinetic energy compared to the conventional layer-stacking composite plate, significantly improving the ballistic performance of the CFRP bulletproof material and providing a reference for the design of individual protection equipment.