Free Vibration Analysis of Laminated Composite Plates with General Boundary Elastic Supports Under Initial Thermal Load

Mohammed B Hammed,Widad I Majeed

doi:10.22153/kej.2019.09.004

Abstract

Free vibration behavior was developed under the ratio of critical buckling temperature of laminated composite thin plates with the general elastic boundary condition. The equations of motion were found based on classical laminated plate theory (CLPT) while the solution functions consists of trigonometric function and a continuous function that is added to guarantee the sufficient smoother of the so-named remaining displacement function at the boundaries, in this research, a modified Fourier series were used, a generalized procedure solution was developed using Ritz method combined with the imaginary spring technique. The influences of many design parameters such as angles of layers, aspect ratio, thickness ratio, and ratio of initial in- plane thermal load in addition to different boundary conditions on the natural frequencies of laminated plate is analyzed. In general, the changes of fundamental natural frequency is inversely proportional with the ratio of thermal buckling load, also most parameters aspect ratio effect on the natural frequency about 35 – 40%. The present results were compared with those obtained by other researchers, and show good agreement.

Highlights

Composite materials are widely employed in many engineering disciplines applications in mechanical and civil engineering
Random free vibrations under the thermal loading of laminated composite plates with all boundary conditions was studied at [1], the randomness in lamina coefficients of thermal expansion and material properties are taking into consideration
Fundamental natural frequency of square plates with various boundary conditions under different thermal buckling load ratio (d), is calculated and listed in Tables 3 and 4 for symmetric cross laminated plates and anti-symmetric angle ply which give small error when compared with results obtained by numerical program ANSYS

Summary

Introduction

Composite materials are widely employed in many engineering disciplines applications in mechanical and civil engineering. Random free vibrations under the thermal loading of laminated composite plates with all boundary conditions was studied at [1], the randomness in lamina coefficients of thermal expansion and material properties are taking into consideration. [5] Presented the influence of hydrothermal conditions such as moisture and temperature on buckling load and free vibration frequency of laminated composite plates. The present work investigates the free vibration analysis under effect of critical buckling temperature of laminated composite thin plate with general boundary condition, based on classical laminated plate theory and using Rayleigh–Ritz method, the displacement function as Fourier cosine series, plus, an arbitrary continuous function proposed by [15] for first time, so the effect of angle-ply orientation, boundary conditions, aspect ratio, and different composite materials properties are examined. Uniform temperature distribution is taken into consideration

Total Mechanical Energy

Boundary Conditions

Admissible Functions

Determination of the Natural Frequency Under in-Plane Thermal Buckling Load

Numerical Result

Conclusion