Improvement in accuracy of finite modeling for ultrasonic transducers

Finite element modeling is a very powerful tool for designing transducers. However, obtaining high accuracy for displacement distribution becomes difficult if the mode of vibration is complicated. In this paper 1) a new method to partition triangular finite elements is proposed: a rectangular cell is divided into 8 triangular elements (for 3D, a cube is divided into 48 diamond-shaped elements). In comparison to 2 triangular elements, this partition is suitable to more complicated boundaries and the computed results are more accurate. In comparison to 4 triangular elements, computational speed is faster. 2) A new type of interpolation function is introduced in which not only displacements but also their derivatives are taken as variables. This approach assures that both displacements and their derivatives, therefore stresses, are continuous everywhere. The advantages of this method are: better accuracy for flexural mode transducers, for transducers incorporating soft materials, such as matching layers, backing layer and wrapping material, and for computation of stresses. 3) A description is given of how to use FEM to determine or refine properties of materials which are unknown or are imprecisely provided by the manufacturer. It is shown that maximum errors produced by this new method for a ceramic disk for different modes are 1% to 2% even for weak modes.