Free vibration analysis of variable thickness thin plates by two-dimensional differential transform method

This paper aims at extending the application of two-dimensional differential transform method (2D-DTM) to study the free vibration of thin plates with arbitrarily varying thickness. First, the differential equation of motion governing thin plates with varying thickness is derived using Hamilton's principle. Afterward, the 2D-DTM, a numerical method which is capable of reducing the size of computational work and can be applied to various types of differential equations, has been applied to derive the natural frequencies of variable thickness thin plates with different boundary conditions. Several numerical examples have been carried out to demonstrate the applicability and accuracy of the present method in free vibration analysis of both uniform plates and plates with variable thickness.