Effect of Exponential Temperature Variation on Frequencies of a Rectangular Plate of Non-linear Varying Thickness

Arun Kumar Gupta, Mamta .

Abstract


The differential equation governing the transverse motion of elastic rectangular plate of non-linear thickness variation with thermal gradient has been analyzed on the basis of classical plate theory. Following Levy 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. Effect of the thermal gradient together with taper constants on the natural frequencies of vibration is illustrated for the first three modes of vibration.


Keywords


Exponentially temperature, non-linear, thickness variation, vibration, rectangular plate

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