The BEM for dynamic analysis of plates with variable thickness J. T. Katsikadelis 1 , A. J. Yiotis 1 Summary A boundary-only method is presented for the dynamic analysis of plates with variable thickness based on the Analog Equation Method (AEM). The fourth order partial differential equation with variable coefficients describing the response of the plate is converted to an equivalent linear quasi-static problem for a plate with constant stiffness subjected to an “appropriate” fictitious load under the same boundary and initial conditions. The fictitious load is established using a technique based on the BEM. Numerical examples are presented to illustrate the efficiency and accuracy of the method. Introduction The vibration analysis of plates with variable thickness is pursued in various engineering disciplines, such as civil engineering, aerospace engineering and the design of machines. Information about the existing literature on this subject can be found in [1]. In [1] an effective BEM-based method for the static and dynamic analysis of plates with variable thickness has been developed using the concept of the analog equation [2]. In this paper the AEM is further developed to a boundary-only method by converting the domain integrals containing the fictitious load to boundary ones. This is achieved by approximating the fictitious load with a radial basis function series. The workout numerical examples validate the effectiveness of the proposed method. Governing equations and the AEM solution Consider a thin elastic plate of variable thickness, h h , occupying the two- dimensional multiply connected domain of the xy plane, bounded by the curves . If there is no abrupt variation in thickness, the equilibrium of a plate element subjected to a distributed transverse load , yields the following differential equation in terms of the deflection in Ω () = x , :{,} xy ∈Ω x Ω (,) t 1 K + 0 1 2 , , ,..., K Γ Γ Γ Γ g x 0 t ≥ (,) w t x (1) ( ) 4 2 2 2 2 2,( ), 2,( ), (1 ) , , 2, , , , , , (,) x x y y xx yy xy xy yy xx t tt D w D w D w D w D w D w D w cw hw g t ν ρ ∇ + ∇ + ∇ +∇ ∇ − − − + + + = x where is the variable flexural stiffness of the plate, c c the damping coefficient and the mass density. Moreover, the deflection w must satisfy the following boundary and initial conditions on the boundary and inside Ω 3 /12(1 ) D Eh ν = − ρ 2 β = () = x 0 i K i = = Γ = ∪ , β β on Γ (2a,b) * 1 2 () w V w α α α + = 3 * 1 2 , () n w M w + 3 1 National Technical University of Athens, Athens, Greece