On the computer simulation of the forced vibration characteristics of the microtubes using a couple of von-Kármán and modified couple stress theories

Abstract

The present article investigates the forced vibration behavior of axially functionally graded (AFG) tubes under external dynamic load using a pair of Euler-Bernoulli and von-Kármán equations in combination with the modified couple stress theory. The Hamilton principle is used to obtain the linear and nonlinear partial differential (PD) governing equations and the boundary conditions. Functionally graded materials (FGMs) are utilized to produce tube constructions that alter gradually throughout the length of the tube. The cross-section of the cylindrical tube was considered to be nonuniform throughout the tube length, and the porosity distribution in the radius direction was assumed to be nonuniform, resulting in the bi-directional material characteristics function. In order to solve the nonlinear motion equation, the generalized differential quadrature method (GDQM) was connected to the iteration technique. Following that, the computed linear and nonlinear results are thoroughly explained in order to explore the different effects on the resonance, natural frequency, and dynamic deflection.

Keywords:

• Nonlinear dynamic
• vibrational analysis
• axially functionally graded tube
• numerical procedure
• forced vibration