Open AccessVibration of functionally graded Mindlin plate based on a modified strain gradient elasticity theory
Author(s) -
Jintao Jiang,
Lifeng Wang
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/531/1/012023
Subject(s) - plate theory , vibration , boundary value problem , dimensionless quantity , elasticity (physics) , bending of plates , mathematical analysis , normal mode , materials science , mathematics , mechanics , physics , composite material , acoustics , bending
Vibrational behavior of functionally graded (FG) microplates is investigated by a new modified strain gradient Mindlin plate (MSGMP) model. With the help of Hamilton’s principle, the dynamic equation is easily obtained. Furthermore, the general forms of boundary conditions are gotten by using coordinate transformation. The MSGMP model can be degenerated to a couple stress elastic Mindlin plate model or the classical Mindlin plate (CMP) model. Analytical solutions of vibrational problem of a rectangular microplate with four simply supported edges are gotten. Numerical results reveal significant effects of the dimensionless nonlocal parameters, the power law index and vibration mode on the free vibration behavior of FG plate.