Axisymmetric thermal vibration analysis of graded porous circular plates based on physical neutral surface and Reddy’s third-order shear theory

Abstract

In this article, the free vibration of functionally graded porous (FGP) circular plate with various boundary conditions are investigated by means of the differential quadrature method (DQM) based on Reddy’s theory. Performance of the materials varies continuously in the whole thickness and two cosine forms of nonuniform porosity distribution along its thickness are considered. Hamilton’s principle is adopted to derive the governing equation of the system, which effectively considers the effects of thermal stress. It is worth noting that due to the introduction of physics neutral surface, reducing stretching-bending coupling effect, so the complex governing equations have been appropriately simplified. Then, using the DQ method, the natural frequencies of free vibration of FGP circular plates subjected to thermal environments with various boundary conditions were obtained. Convergence and comparative research are performed to prove the convergence, reliability, and accuracy of the DQ method. The effects of various factors such as porosity coefficient, porosity distribution pattern, temperature rise, thickness-diameter ratio, and boundary conditions on the natural frequencies are discussed in detail.

HIGHLIGHTS

• For the first time, the free vibration control equation of the graded porous circular plate in a thermal environment under the Reddy third-order shear theory is established.

• Introducing the concept of physics neutral surface, we simplify the very complex governing equations.

• The DQM is used to solve the controlling differential equation with the higher order vibration term caused by the higher order theory, and the vibration frequency of each order under three boundary conditions is given.

• The influence of porosity distribution on natural frequencies is highlighted.

• The effects of uniform and nonuniform heating on the dimensionless frequency are analyzed, and the effects of porosity coefficient, thickness-to-diameter ratio, and boundary conditions on frequency are discussed.

Keywords:

• Graded porous materials
• circular plate
• physics neutral surface
• free vibration
• frequency

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (grant number 12062010, 12362009) and the Key Project of Gansu Natural Science Foundation (23JRRA775). The authors would like to express their sincere appreciation.