Active vibration control of smart porous conical shell with elastic boundary under impact loadings using GDQM and IQM

Nonlinear Free Vibration Analysis of Functionally Graded Porous Conical Shells Reinforced with Graphene Nanoplatelets

“…It is assumed all the internal pores are tiny and the total volume fraction of the pores is small. Unlike other models for evaluating the material properties [30] and [39], in which Young's modulus, shear modulus, and mass density need to be assumed, the present model is based on the following assumption about the volume fraction V P (z) of the internal pores: here, e 0 denotes the porosity coefficient. Young's elastic modulus E(z) and mass density ρ(z) for various porosity distributions can be expressed as [39].…”

“…where E 1 and ρ 1 denote the maximum values of Young's modulus and mass density, and e m is the mass coefficients. Furthermore, the coefficients e 0 , e m and the Poisson ratio μ(z) are calculated as follows [39]: It is noted that the present model in Eqs.…”

“…(2) and (3), E 1 , ρ 1 , and μ 1 can be determined by using the Halpin-Tsai micromechanics model and the rule of the mixture as follows [39]:…”

“…Nevertheless, little work has been done for the porous truncated conical shells reinforced by nano filters [37]. Bahhadini et al [38] and Yan et al [39] studied the linear vibration of porous FG-GRC nanocomposite sandwich conical shells and found that the natural frequencies were increased with the rising material length-scale parameter and porosity coefficient. The vibration behaviour of porous sandwich truncated conical shells with FG face sheets and a saturated FGP core was studied by Rahmani et al [40] and Esfahani et al [41].…”

Analytical solution for free vibration analysis of GPL-RP beam integrated with piezoelectric layers

“…Nguyen et al [14] presented the geometrically nonlinear static and dynamic analyses of GPL-RP plates integrated with smart piezoelectric layers. Hao et al [15] studied the active vibration control of a porous truncated conical shell integrated with smart sensor and actuator layers under impact loadings.…”