振动与冲击
振動與遲擊
진동여충격
JOURNAL OF VIBRATION AND SHOCK
2015年
9期
210-217
,共8页
FGM圆环板%初始热应力%面内自由振动%无量纲频率%Hamilton 原理%微分求积法
FGM圓環闆%初始熱應力%麵內自由振動%無量綱頻率%Hamilton 原理%微分求積法
FGM원배판%초시열응력%면내자유진동%무량강빈솔%Hamilton 원리%미분구적법
FGM (Functionally Graded Material)annular plates%initial thermal stress%in-plane free vibration%dimensionless frequency%Hamilton's principle%DQM
基于二维弹性理论和Hamilton原理，假设材料物理性质随温度变化且沿圆环板径向按照幂律梯度分布，导出了温度影响下 FGM薄圆环板面内自由振动的运动微分方程。用微分求积法（DQM）计算了温度影响下 FGM圆环板面内自由振动的无量纲频率，并与各向同性材料圆环板面内自由振动的无量纲频率进行了比较，说明该分析方法的有效性。同时考虑了沿圆环板径向均匀升温和非均匀升温两种情况下，几何参数、材料性质和温度变化对面内自由振动频率的影响。
基于二維彈性理論和Hamilton原理，假設材料物理性質隨溫度變化且沿圓環闆徑嚮按照冪律梯度分佈，導齣瞭溫度影響下 FGM薄圓環闆麵內自由振動的運動微分方程。用微分求積法（DQM）計算瞭溫度影響下 FGM圓環闆麵內自由振動的無量綱頻率，併與各嚮同性材料圓環闆麵內自由振動的無量綱頻率進行瞭比較，說明該分析方法的有效性。同時攷慮瞭沿圓環闆徑嚮均勻升溫和非均勻升溫兩種情況下，幾何參數、材料性質和溫度變化對麵內自由振動頻率的影響。
기우이유탄성이론화Hamilton원리，가설재료물이성질수온도변화차연원배판경향안조멱률제도분포，도출료온도영향하 FGM박원배판면내자유진동적운동미분방정。용미분구적법（DQM）계산료온도영향하 FGM원배판면내자유진동적무량강빈솔，병여각향동성재료원배판면내자유진동적무량강빈솔진행료비교，설명해분석방법적유효성。동시고필료연원배판경향균균승온화비균균승온량충정황하，궤하삼수、재료성질화온도변화대면내자유진동빈솔적영향。
Based on the two-dimensional elastic theory and the Hamilton's principle,the differential motion equations for in-plane free vibration of the functionally graded material thin annular plate in thermal environment were derived.In the equations,the material properties were assumed to be temperature-dependent and graded in the radial direction of annular plates according to power law distributions.By using differential quadrature method (DQM),the dimensionless frequency parameters of in-plane free vibration of FGM annular plates under thermal environment were obtained.The formulations were validated by comparing the results with those available in literatures.Considering the cases of uniform and variable temperature rise distribution in the radial direction of annular plate respectively,the effects of geometrical parameters,material graded index and temperature rise on the natural frequencies of in-plane free vibration of annular plates were investigated.
