Nonlinear thermal vibration of eccentrically stiffened Ceramic-FGM-Metal layer toroidal shell segments surrounded by elastic foundation

• The nonlinear vibration of eccentrically stiffened Ceramic-FGM-Metal layer convex and concave toroidal shell segments is investigated.
• The effects of characteristic of materials, geometrical ratios, layers and thermal environment are indicated.

The eccentrically stiffened Ceramic-FGM-Metal layer toroidal shell segments which applied for heat-resistant, lightweight structures in aerospace, mechanical, and medical industry and so forth are the new structures. Thus, the nonlinear vibration of eccentrically stiffened (ES) Ceramic-FGM-Metal (C-FGM-M) layer toroidal shell segments surrounded by an elastic medium in thermal environment is investigated in this paper. Based on the classical shell theory with the geometrical nonlinear in von Karman-Donnell sense, Stein and McElman assumption and the smeared stiffeners technique, the governing equations of motion of ES-C-FGM-M layer toroidal shell segments are derived. The dynamical characteristics of shells as natural frequencies, nonlinear frequency-amplitude relation, and nonlinear dynamic responses are considered. Furthermore, the effects of characteristics of geometrical ratios, ceramic layer, elastic foundation, pre-loaded axial compression and temperature on the dynamical behavior of shells are studied.