This study investigated FG carbon nanotubes filled composites, which are promising metamaterials that can be useful in the energy absorption field. This structure can absorb energy through elastic deformation. For this issue, absorbed energy and dynamic stability analysis of the FG-CNTRC curved panel surrounded by a non-polynomial viscoelastic substrate using three-dimensional poroelasticity theory is investigated. For stability of the structure after vibrating, the viscoelastic substrate as the non-polynomial viscoelastic model is presented. The curved panel comprises multilayer carbon nanotubes (CNT) which are uniformly distributed in all layers of facing sheets; however, the system’s weight fraction alters for each layer through the thickness orientation. The influences of several parameters, such as Winkler–Pasternak parameters, span angle CNTs’ volume fraction, length to radius ratio, compressibility coefficient, friction coefficient, torsional parameter, initial axial stress, and damping factor on the dynamic responses of the FG-CNTRC curved panel surrounded by a non-polynomial viscoelastic substrate are investigated. The golden result of this paper is that the effect of radial stress on the energy absorption is hardly dependent on the value of the foundation parameters. As an applicable outcome in pertained applications, by increasing the compressibility, and friction coefficients, the composite shell's energy absorption decreases.
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