Vibration of CFFF Functionally Graded Plates with an Attached Point Mass at an Arbitrary Point in Thermal Environment

Abstract

Purpose: In many cases, working on models such as carrying a point attached mass or distributed attached mass provides a more realistic depiction of the problem. The main reason for the vibration studies of the structural elements with coupled mass, which constitute the main purpose of this study, is to see the changes in the resonance frequency due to the attached mass and to reduce the resonance frequency to a desired value. Although the vibration problems of mass-loaded rectangular plates are a very common problem in engineering applications, no study on functionally graded plates has been found in the literature. In this study, the effect of the variation of temperature-dependent material properties along the thickness according to a simple power law on the vibration behavior of point mass carrying functionally graded plates is investigated for the cantilever (CFFF) boundary condition. Numerical studies are performed for different mass ratio (M), different location of point mass on the plate region and throughout the x axis, volume fractions with p and side-to-side ratio (a/b) at nonlinear temperature distribution. Methods: In this study, effect of the mass and temperature on free vibration of the functionally graded plate carrying a point mass at an arbitrary position is analysed with three-dimensional Ritz solution. Material properties of considered functionally graded plate are assumed to be temperature dependent and reinforcement in thickness direction according to a power law distribution and effective material properties are estimated using Mori-Tanaka homogenization method. Results: Free vibration frequencies decrease with increasing p index and increasing temperature difference. The frequencies obtained in the case of with point mass are always smaller than the frequency values obtained in the case of without point mass. When the point mass is located on a nodal line, the mass does not move during these and so frequency remains constant as independent of the presence of mass. If the mass is located on the nodal lines, at these frequencies it will resonate at the natural frequency of the unperturbed plate. Conclusion: The study shows that the effect of the presence of added mass, mass size and location on structures may not be negligible. © 2022, Krishtel eMaging Solutions Private Limited.