Free vibration of functionally graded composite doubly‐curved shells with embedded polymeric viscoelastic core

Abstract Functionally graded composite doubly‐curved shells with embedded polymeric viscoelastic core possess significant potential for application across various fields, including spacecraft engineering, automotive chassis design, and the structural components of medical equipment. In this paper, based on complex modulus theory and Rayleigh‐Ritz method, the governing differential equations of this structure are established and solved by an efficient method. The results are compared with those of published literature, and the validity of the theoretical model is verified. The dynamic characteristics of functional gradient composite spherical shell, hyperbolic shell and elliptical shell with damping membrane embedded are analyzed by using the verified theoretical model. The research conclusion furnishes theoretical underpinning for the design and application of the structure. Highlights An analytical model was developed for predicting dynamic characteristics; The validity of the model was confirmed; Effects of structural parameters on dynamic characteristics were conducted.