Scattering of mechanical waves from the perspective of open systems

In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why spectrum undergoes peaks and dips (resonances) at specific locations how these connect vibrational properties scatterer. resonance are connected eigenvalues dimensional effective operator, H e f , corresponding developments presented perspective open systems, which seeks convert (scatterer+environment) involving only This achieved through projection operator formalism allows us formally calculate . An interesting corollary our analysis deep connection between in eigenfrequencies scatterer under Neumann boundary condition. We bring out point further by considering 3D elastic shell, connecting results classical acousto-elastic theory. • Mechanical considered systems. Effective Hamiltonian computed Connection Hamiltonian, Green’s function, clarified Ideas applied continuum scattering.