This book is about recent mathematical, numerical and statistical approaches for elasticity imaging of inclusions and cracks with waves at zero, single or multiple non-zero frequencies. It considers important developments in asymptotic imaging, stochastic modeling, and analysis of both deterministic and stochastic elastic wave propagation phenomena and puts them together in a coherent way. It gives emphasis on deriving the best possible imaging functionals for small inclusions and cracks in the sense of stability and resolution. For imaging extended elastic inclusions, the book develops accurate optimal control methodologies and examines the effect of uncertainties of the geometric or physical parameters on their stability and resolution properties. It also presents an asymptotic framework for vibration testing and a method for identifying, locating, and estimating inclusions and cracks in elastic structures by measuring their modal characteristics.
Singular path-independent energy integrals for elastic bodies with thin elastic inclusions
