Constraint condition on transformation relation for generalized acoustics

For transformation acoustics (TA), the transformation relations for material and physical field are not unique when they are mapped from a virtual space to a physical space; the underlying mechanism is explored in this paper. We propose that the invariance of a physical process during a spatial mapping will impose the constraint condition for the transformation relation. This, together with the condition of energy conservation, provides a general method to derive the corresponding transformation relation for any physical process with the assumption of local affine transformation. When applied to TA, we show that the constraint conditions are not enough to determine the transformation relations completely, leaving a possibility to define them differently as found in the literature. New acoustic transformation relations with constant density or modulus are also proposed and validated numerically by constructing a two-dimensional acoustic cloak.

► We present a general framework for determining the transformation relations of physical quantities in generalized acoustics.
► Based on a physical view, we declare the PDE needs to retain its form in local Cartesian frames in order to maintain the same physical mechanism. In addition, every type of energy is separately conserved.
► These constraint conditions unify several different formulations of TA in the literature and enable also several new ones, and these constraint conditions lead to unique transformation relation for TO.
► The proposed theory implies that we have a convenient method to explore the transformation method in a vast range of potential dynamical systems.