**Journal of Theoretical**

and Applied Mechanics

and Applied Mechanics

**52**, 1, pp. 15-24, Warsaw 2014

### Exponential temperature effect on frequencies of a rectangular plate of non-linear varying thickness: a quintic spline technique

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.

*Keywords*: exponentially temperature, non-linear; thickness variation; vibration; rectangular plate