Free Vibration Analysis of Cantilever Rectangular Plates with Variable Thickness

Abstract

A new method-mixed boundary grid method (FBGM) is proposed to analyze the free vibration of cantilever plates with variable thickness. The fundamental differential equations of the plate are established for the bending problem. By transforming these equations into integral equations in a small area and using the trapezoidal rule of the approximate numerical integration, the solution of these equations is obtained and chosen as Green function to obtain the characteristic equation of the free vibration. The accuracy of the numerical results for the natural frequency parameter calculated by the proposed method is investigated.

Natural vibration of tapered rectangular plate with exponential variation in non homogeneity

“…Huang et al [18] developed a discrete method to analyze the free vibration problem of orthotropic rectangular plates with variable thickness using Green function and obtained the effects of the aspect ratios, boundary conditions and the variation of the thickness on the frequencies. Huang et al [19] proposed new method (FBGM) to analyze the free vibration of cantilever plates with variable thickness and obtained the solution of characteristic equation of free vibration. Taher et al [20] evaluated first nine frequency parameters of circular and annular plates with variable thickness and combined boundary conditions, for different thickness to radius ratios by using three-dimensional elasticity theory.…”

Effect of linear variation in density and circular variation in Poisson’s ratio on time period of vibration of rectangular plate

“…The natural vibration of cantilever plates with variable thickness is analyzed by using mixed boundary grid method (FBGM) [1] and obtained characteristic equation and frequency parameters. A model [2] is presented to analyze the nonlinear vibrations of visco elastic thin rectangular plates by using von Kármán nonlinear strain-displacement relationships and obtained fundamental modes of a simply supported square plate with immovable edges.…”

Natural frequencies of an inhomogeneous square thin plate

“…При анализе изгибных колебаний прямоугольных пластин со средней, медленно меняющейся толщиной метод возмущений использовался в работе [8], где были получены в явном виде приближенные формулы для частот свободных колебаний при произвольных функциях толщины. В статье [9] предложен метод смешанной граничной сетки (FBGM) для анализа свободных колебаний консольных пластин переменной толщины. Авторами получены основные дифференциальные уравнения для изгиба пластины, преобразующиеся в интегральные уравнения, численное решение которых выбирается в качестве функции Грина для получения характеристического уравнения собственных частот.…”