Semi-analytical method and vibration isolation analysis of dynamic response of multi-layer gradient BCC lattice structures

• Inspired by the density gradient in pomelo peel, two types of multilayer gradient lattice structures were developed based on the conventional BCC lattice. • Equivalent constitutive parameters were derived using the strain energy method, and the Young’s modulus of unit cells was spatially characterized via crystallography theory. • A semi-analytical dynamics model was established for the multilayer lattice using improved Fourier series and 3D elasticity theory. • Vibration level difference was applied to assess isolation performance across gradient strategies, leading to an optimal layout proposal. Drawing inspiration from the density variation between layers in pomelo peel to achieve vibration damping, this study proposes two types of multilayer gradient BCC lightweight lattice structures with gradient interlayer relative densities by modifying unit cell height and strut radius based on the traditional BCC lightweight lattice structure. Firstly, the equivalent constitutive matrix of the multilayer gradient BCC lattice structure is first derived using an equivalent strain energy approach. Within the framework of three-dimensional linear elasticity, the governing equations for vibration are subsequently formulated by incorporating the pseudo-excitation method. The displacement field across the entire structure is represented through an improved Fourier series formulation, which combines a standard Fourier cosine expansion with auxiliary closed-form functions constructed to satisfy essential boundary conditions. The Ritz method is then employed to determine the vibration characteristics of the multilayer gradient lattice system. The proposed approach is validated through comprehensive numerical examples, confirming its accuracy and reliability. Furthermore, the influence of unit cell parameters and gradient configurations on dynamic response is systematically analyzed. Results indicate that the strut radius exerts a substantial effect on the vibrational behavior of both gradient designs A and B, whereas the unit cell height predominantly influences only the response of gradient structure A. Comparative analysis reveals optimal vibration isolation performance in irregular gradient Structure A and positive gradient Structure B. The irregular configuration shows enhanced impedance mismatch effects, offering distinct advantages for low-frequency vibration control. The research results can provide references for vibration reduction and noise suppression technologies in aerospace and marine applications.