Active structural acoustic illusions

We present active manipulation of the structural vibrations of an elastic body to generate an acoustic illusion. The resultant illusion misrepresents the nature, size and number of objects in the exterior acoustic domain. We demonstrate our technique, herein termed active structural acoustic illusion, using an elastic cylindrical shell. The radial motion of the shell at its cavity resonance frequencies is actively modified using localised mechanical forces. Acoustic illusions are generated to resemble the scattered acoustic field by one or more rigid cylinders of different size and location.


Vibro-acoustic response of an elastic cylindrical shell
We herein present an analytical formulation to describe the vibro-acoustic response of a thin elastic cylindrical shell excited by an incident plane wave, a monopole source or a structural point force.
The shell is of radius a (measured to the mid-plane thickness) and thickness h . The shell model adopted here is based on Donnell-Mushtari theory with a modifying operator by Flügge-Byrne-Lur'ye in which the longitudinal displacement of the cylinder is assumed to be constant [1]. Both the exterior and interior fluid media are assumed to be inviscid with density f ρ and speed of sound f c .
where i 1 = − , ( )′ is the derivative with respect to the argument, k is the acoustic wavenumber, and n J , n H are Bessel and Hankel functions of the first kind of order n , respectively. The first term on the right hand side of Eq. (3) denotes the incident field due to a plane wave, where the coefficient for a plane wave is given by i ( ) n n n a J ka ′ = [2]. The second term on the right hand side of Eq. (3) represents the combined scattered and radiated field, where n b is an unknown coefficient of order n .
For monopole excitation, the exterior pressure becomes where R is the distance between the monopole source and the field point ( , ) r θ . Using Graf's addition theorem, the first term on the right hand side of Eq. (4) corresponding to the incident field arising from a monopole source is expressed in terms of the cylinder's local coordinates as follows where b , α denote the distance and angle between the monopole source and the elastic cylindrical shell, as shown in Fig. 1. The coefficient related to the incident field now becomes For point force excitation, the exterior pressure field corresponds to the structure-borne sound and is given by For plane wave, monopole or point force excitation of the cylindrical shell, the interior acoustic pressure can be expressed as where n c is the coefficient for the interior field. The shell radial and tangential displacements are given as follows [1] i ( ) where n w and n v are the radial and tangential displacement Fourier coefficients of order n , respectively. The shell radial displacement is coupled to the interior and exterior acoustic pressure fields by the following kinematic conditions

Acoustic scattering by two rigid cylinders
A brief overview of the analytical framework for acoustic scattering by two rigid cylinders arising from incident plane wave excitation is herein described. Figure 2 shows two rigid cylinders of radii 1 a and 2 a , an incident plane wave propagating left to right and the coordinate system used to determine the acoustic pressure at a field point. In the vicinity of the first cylinder of radius 1 a , the total pressure field is given by [2] ( ) expressed in terms of the local coordinate system of the first cylinder. Using Graf's addition theorem, the scattered field arising from the second cylinder can be expressed in terms of 1 It is now possible to apply the boundary condition given by Eq.
The same procedure can be used for the second cylinder of radius 2 a , resulting in