Tracking vibrational energy on curved shell structures in the mid-high frequency limit - a ray-tracing approach

Modelling the vibro-acoustic properties of mechanical built-up structures is a challenging task - especially in the mid to high frequency regime. Standard modelling tools such as finite and boundary element methods are robust only in the low frequency regime and are not scalable to higher frequencies due to the prohibitive increase in model size. We have recently developed a new method called Discrete Flow Mapping (DFM), which extends existing high frequency methods, such as the so-called Dynamical Energy Analysis (DEA), to work on meshed structures. DFM is based on local ray tracing approximations with ray trajectories moving along straight lines in each mesh segment. This describes the ray-dynamics well in homogenous, isotropic, flat plates or on curved shells at high frequencies in the geodesic ray limit. The situation changes if one considers curvatures being of the size of the wavelength leading to curved rays whose underlying equations of motion depends on the local radii of curvature (and the underlying shell model) in a non-trivial way. In this paper, we will consider ray-tracing approaches for energy transport in curved shells in the mid-to-high frequency limit. We will, in particular, analyse mid-frequency effects on the dispersion curves in curved plates and their effect on the ray dynamics and identify reflection/transmission behaviour due to these finite wavelength effects.