What is the effect of harmonic temperature variation on the vibration of rectangular plate with linear thickness in x direction and parabolic thickness variationin y direction?
I would think that in order to solve this problem you will need to use a variational method and/or an energy method to couple the physics therefore you require additional information for the boundary conditions of the plate like type of vibration (free, forced or resonant), what loading type, damping, etc.
I would not expect much effect, unless the Young modulus is significantly altered! Metals would not be measurably influenced, carbon composites would only show marginal effect, only glass-reinforced composites and rubber blades would significantly alter their vibration response if the temperature variations affect the vitreous transition of the material ! (hence the maximum gradient of the young modulus variation v/s temperature).
The result would reveal a shift of natural frequencies and an alteration of the mode shapes...
Can this help?
Bernard
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