Moderately large amplitude forced vibration of sandwich functionally graded auxetic beams: an analytical approach

Sandwich functionally graded (FG) auxetic beams are extensively utilized in aerospace, automotive, and biomedical industries due to their excellent strength-to-weight ratio, impact resistance, and tunable mechanical properties. The integration of FG materials with auxetic structures enhances their adaptability in advanced engineering applications. However, understanding their dynamic behavior under external excitations is essential for optimal design and structural reliability. Nonlinear interactions in such structures pose significant challenges in vibration analysis, necessitating robust analytical methods. This study presents a closed-form solution for the nonlinear forced vibration analysis of sandwich FG auxetic beams, offering an accurate and efficient method for predicting their dynamic response. The beam consists of two FG face sheets with material properties varying through the thickness and a re-entrant honeycomb auxetic core with an adjustable Poisson’s ratio. The governing nonlinear equations of motion are derived using the first-order shear deformation theory (FSDT), the modified Gibson model, and the von Kármán relations, formulated through Hamilton’s principle. A closed-form solution is obtained via the Galerkin method and multiple-scale technique. The results demonstrate that FG layers enable control of the overweight and dynamic response amplitude, with positive power law indexes reducing weight. Comparisons with finite element results confirm the accuracy of the proposed formulation.