This paper deals with the dynamic buckling of a sandwich truncated conical shell composed of polymer–carbon nanotubes–fiber multiphase nanocomposite layers. The structure is located in hygrothermal environments. The equivalent material properties of the multiphase nanocomposite layers are obtained using fiber micromechanics and Halpin–Tsai equations in hierarchy. According to Kelvin–Voigt theory, the realistic behavior of the structure is considered by considering the viscoelastic properties. The surrounding medium is simulated using visco-Pasternak model. The governing equations of the system are derived based on the classical theory by employing Hamilton’s principle. To obtain the dynamic instability region of the system, the differential quadrature method, and Bolotin’s method are utilized. The influences of various parameters such as structural damping, viscoelastic medium, number of layers, volume fraction of carbon nanotubes, temperature, and moisture changes on the analysis of the dynamic instability region of the structure are studied. The results reveal that by increasing the volume percent of carbon nanotubes, the dynamic instability region moves to higher frequencies.
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