Thermal Vibration of Thick FGM Circular Cylindrical Shells by Using TSDT

Abstract

The generalized differential quadrature (GDQ) method is used to study the thermal vibration of thick functionally graded material (FGM) circular cylindrical shells. The nonlinear coefficient effect of third-order shear deformation theory (TSDT) model of displacements on the thermal equations of motion is considered. The parametric effects of FGM power law index and environment temperature on the time responses of stresses and displacements are considered. The linear varied effect of shear correction coefficients on the calculation of stiffness integration is also considered. The simply homogeneous equation is used to find the values of vibration frequency, also the dynamic GDQ discrete equation in matrix form are used to find the values of time response and transient response for the thick FGM circular cylindrical shells.

Advanced Dynamic Thermal Vibration of Thick FGM Cylindrical Shells

“…The calculated values of frequency  of applied heat flux for the thermal loads can be obtained in the heat conduction equation and referred to [12] for more details. Also the calculated values of vibration frequency under free vibration ( ) can be obtained in the simply homogeneous equation and referred to [17] for more details.…”

“…In 2022, Hong [11] presented the dynamic advanced GDQ solutions of thick FGM plates under thermal vibration with the effects of TSDT and advanced shear factor that was in function of term of TSDT model, FGM power law index and environment temperature, but not in function of total thickness. Hong [12] in 2022 presented the GDQ solutions of thick FGM circular cylindrical shells under thermal vibration with the effects of TSDT and varied shear factor that was not in function of term of TSDT model. Hong [13] in 2022 studied the advanced GDQ results of thick FGM plates-cylindrical shells under thermal vibration with the effects of TSDT and advanced shear factor that was in function of term of TSDT model, FGM power law index and environment temperature, but not in function of total thickness of plates-cylindrical shells.…”

Thermal Vibration of Thick FGM Conical Shells by Using Third-Order Shear Deformation Theory

“…r is the minor middle-surface radius at x = 0, and R is the major middle-surface radius at x = L. β is the semi-vertex angle. The power-law function with power law index R n is used and expressed in material properties (E f gm , ν f gm ) by Hong [11], as follows.…”

“…2 are in constant value and can be applied by Hong [11] with the parameter R * instead of the R. Thus, dynamic differential equations with TSDT expressed in equilibrium matrix forms can be obtained for thick FGM conical shells under heating loads. Also, the varied values of shear correction coefficient k α are used for the integrals of shear stiffness Q i * j * in which subscripts i * , j * = 4, 5.…”

“…The displacements and thermal stresses of thick plates were also presented. Hong [11] presented the GDQ results of thick circular cylindrical shells by using the TSDT model. The von Karman type of strain-displacement equations and partial derivatives of displacements with respect to thickness direction are assumed.…”