Modeling approach for two-dimensional distributed transducers of arbitrary spatial distribution

Abstract

A new modeling method for two-dimensional distributed transducers with arbitrary spatial distribution is presented. The spatial weighting of a distributed transducer is defined using multidimensional distributions with composite functions as arguments. A differentiation theorem is derived for one-dimensional distributions of composite functions and is extended to multidimensions through the use of partial distributional derivatives and the product rule. The resulting theory is used to determine the differential operator describing the distributed transducer’s spatial dynamics. The methodology, which is valid for both uniaxial and biaxial transducers, is applied to several two-dimensional problems.