Thermal effects on the free vibration of joined FG-CNTRC conical-conical shells

Abstract

In this paper, the effects of temperature on free vibration of carbon nanotube reinforced composite (CNTRC) joined conical-conical shells are investigated. Carbon nanotubes (CNTs) are embedded across the thickness uniformly or functionally. Material properties of the shell are assumed to be functions of temperature. To study the free vibration of shells settled in thermal environments, it requires solving the static equations. Therefore, in order to derive these equations, first order shear deformation theory (FSDT) accompanied by von Kármán types of geometrical nonlinearity are employed in Hamilton's principle. Then, initial stress resultants due to equilibrium state, are extracted via linear membrane solution. Afterward, equations of motion are derived with regard to initial deformations and stresses. With considering the equations of motion for two cones together with boundary and continuity conditions, a set of governing equations is provided. To discretize the governing equations meridionally, generalized differential quadrature (GDQ) method is proposed. The results are primarily validated via comparing them with those of relevant researches in this field. Thereafter, some studies are carried out to exhibit the significant role of temperature variations, CNT distribution patterns, CNT volume fractions, cones' angles and boundary conditions on the free vibrational behaviors of joined conical shells. For the sake of preventing buckling occurrence during the present vibration analysis, critical buckling temperature Tcr is obtained by the procedure that the natural frequency takes zero value for the lowest temperature.