EXPONENTIAL TEMPERATURE EFFECT ON FREQUENCIES OF A RECTANGULAR PLATE OF NON-LINEAR VARYING THICKNESS: A QUINTIC SPLINE TECHNIQUE
EXPONENTIAL TEMPERATURE EFFECT ON FREQUENCIES OF A RECTANGULAR PLATE OF NON-LINEAR VARYING THICKNESS: A QUINTIC SPLINE TECHNIQUE
复制标题
非线性变厚矩形板频率的指数温度效应：五次样条技术
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Jain Mamta
中科院分区：
文献类型：
--
作者：
Arun Gupta;Jain Mamta
基于经典板理论，分析了厚度随温度梯度非线性变化的弹性矩形板横向运动微分方程。本文采用Levy的方法，即两平行边简支的方法，用五次样条插值技术，求解了温度呈指数分布的单向非线性变厚度板运动的四阶微分方程。对于等间隔的情况，给出了计算该微分方程解的算法。对于前三种振动模式，说明了热梯度和锥度常数对振动固有频率的影响。
The differential equation governing the transverse motion of an elastic rectangular plate of non-linear thickness variation with thermal gradient has been analyzed on the basis of classical plate theory. Following Levy's approach, i.e. the two parallel edges are simply supported, the fourth-order differential equation governing the motion of such plates of non-linear varying thickness in one direction with exponentially temperature distribution has been solved by using the quintic splines interpolation technique for two different combinations of clamped and simply supported boundary conditions at the other two edges. An algorithm for computing the solution of this differential equation is presented for the case of equal intervals. The effect of thermal gradient together with taper constants on the natural frequencies of vibration is illustrated for the first three modes of vibration.