振动与冲击
振動與遲擊
진동여충격
Journal of Vibration and Shock
2015年
20期
74-79
,共6页
Winkler-Pasternak 弹性地基%FGM梁%自由振动%无量纲频率%微分求积法
Winkler-Pasternak 彈性地基%FGM樑%自由振動%無量綱頻率%微分求積法
Winkler-Pasternak 탄성지기%FGM량%자유진동%무량강빈솔%미분구적법
Winkler-Pasternak elastic foundation%functionally graded material beam%free vibration%dimensionless frequency%differential quadrature method
基于二维线弹性理论，建立 Winkler-Pasternak 弹性地基上功能梯度（Functionally Graded Material，FGM）梁自由振动控制微分方程。假设材料物性沿梁厚度方向按幂律分布，采用微分求积法（Differential Quadrature Method，DQM）数值求解4种不同边界 FGM梁自由振动无量纲频率特性。将计算结果与 Winkler-Pasternak 弹性地基梁对比表明，该分析方法对弹性地基梁自由振动研究行之有效，并考虑边界条件、梯度指数、跨厚比、地基系数对 FGM梁自振频率影响。
基于二維線彈性理論，建立 Winkler-Pasternak 彈性地基上功能梯度（Functionally Graded Material，FGM）樑自由振動控製微分方程。假設材料物性沿樑厚度方嚮按冪律分佈，採用微分求積法（Differential Quadrature Method，DQM）數值求解4種不同邊界 FGM樑自由振動無量綱頻率特性。將計算結果與 Winkler-Pasternak 彈性地基樑對比錶明，該分析方法對彈性地基樑自由振動研究行之有效，併攷慮邊界條件、梯度指數、跨厚比、地基繫數對 FGM樑自振頻率影響。
기우이유선탄성이론，건립 Winkler-Pasternak 탄성지기상공능제도（Functionally Graded Material，FGM）량자유진동공제미분방정。가설재료물성연량후도방향안멱률분포，채용미분구적법（Differential Quadrature Method，DQM）수치구해4충불동변계 FGM량자유진동무량강빈솔특성。장계산결과여 Winkler-Pasternak 탄성지기량대비표명，해분석방법대탄성지기량자유진동연구행지유효，병고필변계조건、제도지수、과후비、지기계수대 FGM량자진빈솔영향。
Based on the two-dimension theory of linear elasticity,the free vibration differential equations for FGM beams resting on Winkler-Pasternak elastic foundations were derived.The material properties were supposed to change continuously along the thickness of the beam according to the power law distribution.Using the differential quadrature method (DQM),the dimensionless natural frequencies of FGM beams under four different boundary conditions were investigated.The formulations were validated by comparing the results obtained with those available in the literature for homogeneous beams on Winkler-Pasternak elastic foundations.The influences of the boundary conditions,material graded index,length-to-thickness ratio and elastic coefficients of foundations on the non-dimensional frequency parameters of FGMbeams were discussed.
