Juan Miguel Vivar-Perez

Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review

This paper reviews the state-of-the-art in numerical wave propagation analysis. The main focus in that regard is on guided wave-based structural health monitoring (SHM) applications. A brief introduction to SHM and SHM-related problems is given, and various numerical methods are then discussed and assessed with respect to their capability of simulating guided wave propagation phenomena. A detailed evaluation of the following methods is compiled: (i) analytical methods, (ii) semi-analytical methods, (iii) the local interaction simulation approach (LISA), (iv) finite element methods (FEMs), and (v) miscellaneous methods such as mass–spring lattice models (MSLMs), boundary element methods (BEMs), and fictitious domain methods. In the framework of the FEM, both time and frequency domain approaches are covered, and the advantages of using high order shape functions are also examined.

Homogenization of a micro-periodic helix

Equations of motion governing the dynamics of helix are studied in the situation when the microstructure is micro-periodic. Using the asymptotic homogenization method, we derive these equations in the case of waves much longer than the length scale of a periodic unit cell and for any finite number of phases in the cell. The procedure of constructing a formal asymptotic expansion solution is derived. Generally, the constitutive coefficients are harmonic averages, while the mass density and polar moment of inertia are arithmetic averages. These results are illustrated numerically on the case of a two-phase helix.

Homogenization of a Micro-Periodic Helix with Parabolic or Hyperbolic Heat Conduction

ABSTRACT Based on a recent model for vibration of an elastic helix [6], a thermoelastic heterogeneous helix is studied by the asymptotic homogenization method. The objective of the study is the determination of the averaged equation of motion and of the effective coefficients of a one-dimensional micro-periodic thermoelastic helix. The results are valid in the case of waves much longer than the length of the periodic unit cell, and for any finite number of phases for within that cell. Also perfect contact conditions between phases are considered. Generally, the constitutive coefficients are harmonic averages, while the mass density and polar moment of inertia are arithmetic averages.

Hybrid Simulation Methods: Combining Finite Element Methods and Analytical Solutions

In the context of wave propagation analysis the computational efficiency of numerical and semi-analytical methods is essential, as very fine spatial and temporal resolutions are required in order to describe all phenomena of interest, including scattering, reflection, mode conversion, and many more. These strict demands originate from the fact that high-frequency ultrasonic guided waves are investigated. In this chapter, our focus is on developing semi-analytical methods based on higher order basis functions and demonstrating their range of applicability. Thereby, we discuss the semi-analytical finite element method (SAFE) and a hybrid approach coupling spectral elements with analytical solutions in the frequency domain. The results illustrate that higher order methods are essential in order to decrease the numerical costs. Moreover, it is demonstrated that the proposed approaches are the methods of choice when we want to compute dispersion diagrams or if large parts of the structure are undisturbed and, therefore, can be described by analytical solutions. If, however, complex geometries are considered or the whole structure has to be investigated, only purely FE-based approaches seem to be a viable option.

The Effect of Imperfect Contact on the Homogenization of a Micro-periodic Helix

Under study are the equations governing the elastodynamics of a micro-periodic helix, i.e. a helix made of a sequence of unit cells, each containing a thin imperfect interphase embedded within a finite number of other phases. An averaged equation of motion, along with its effective constitutive coefficients, is determined via an asymptotic homogenization method. The results are valid in the case of wavelengths much longer than the length of the unit cell. Formulae for shorter wavelengths can be derived by admitting higher order terms in the expansion.