Renato Forcinetti

Numerical Simulation of Wave Propagation

Wave equations are hyperbolic partial differential equations (PDEs) which describe the propagation of various types of waves, such as acoustic, elastic, and electromagnetic waves. In order to solve PDEs, the finite element method (FEM) can be used. After a brief introduction to the mathematical method used by FEM to evaluate the solution in nodes, where the polynomial curve that interpolates the differential equation has to be solved, we will describe the methodology used to solve the wave propagation problem described by the Helmholtz’s equation. The wave propagation problem is analyzed by following specific steps: construction of the geometry to study, application of the boundary conditions, and meshing of the domain to be solved. The same procedure is used to simulate the behavior of piezoelectric transducers and the problem of wave propagation in medium with defects. Finally, the procedure followed for the simulation of acoustic problems using a specific software, i.e., COMSOL Multiphysics, is illustrated.

Ultrasonics for the Diagnosis of a Trachite Stone Wall

The aim of this chapter is to show the potentiality of a novel approach to ultrasonic investigation of masonry structures. In order to obtain useful, rapid and relatively low cost informations, the ultrasonic “Direct Transmission Technique” is applied on the structure under exam. This technique uses a beam of ultrasonic waves emitted by a transducer and received by another one placed on the opposite surface of the structure. The waves pass through the (ample under test) and are reflected and refracted by incidental discontinuities encountered along the path. The characteristics of the ultrasonic vibration are then investigated in order to obtain interesting information on the conditions of the materials. In particular, the attention has been focused on the correlation between the average density of the ray paths and the characteristics of acquired signals. This feature has been extracted from signals obtained by direct measurements on a real stone masonry with a known internal cavity. Then measurements have been related to the known geometry to verify the actual correlation with the characteristics of the traversed paths.