Studying harmonic resonances of axially moving FGM truncated conical shells on elastic foundation using a stress function method

Abstract

This paper investigates the nonlinear vibration behavior of axially moving porous functionally graded material (FGM) truncated conical shells supported by an elastic foundation using a stress function method. The governing equations of motion are derived from von Kármán nonlinear strain-displacement relations in conjunction with the Hamilton's principle. The equations are simplified using the Galerkin method and transformed into nonlinear ordinary differential equations, which are solved through the method of multiple scales (MMS). The frequency response is analyzed in the primary, subharmonic, and superharmonic resonance regions. The effects of porosity distribution patterns along the thickness, ceramic-to-metal volume fraction, axial velocity, semi-vertex angle of the conical shell, and geometric parameters are analyzed. Results indicate that increasing axial velocity amplifies hardening behavior and reduces fundamental natural frequency. The semi-vertex angle is found to significantly influence the hardening behavior, while the stiffness of Pasternak and Winkler elastic foundations effectively reduces the peak vibration amplitude. Moreover, Pasternak stiffness exhibits a more pronounced impact on the frequency response than Winkler stiffness. © 2025 Elsevier Ltd