Acoustic signal analysis is commonly used for non-invasive pipeline condition assessment and diagnosis. Considering that pipeline systems are made of different materials ranging from steel to polymers, the analysis method is also contingent on the vibroacoustic properties of the pipe wall material. In this compilation, an adaptive, locally defined time marching technique is presented to analyze wave propagation models. The methodology is based on two time integration parameters, namely α and γ. Additionally, the authors present recent improvements in acoustic impedance methods to describe the transduction and propagation of guided elasticwaves in MEMS devices electrostatically actuated through thin air-gaps. The closing study focuses on the way in which the Lorentz force acting on a continuous medium from the side of the magnetic field has a significant effect on the behavior of magnetoacoustic waves.