Conversion of Evanescent into Propagating Guided Waves in Plates

Current guided wave-based damage detection methods using advanced signal/image processing techniques can only process the damage information contained in the propagating guided waves since evanescent guided waves scattered from the damage decay exponentially away from it. The valuable subwavelength damage information concealed in the evanescent waves is therefore permanently lost in the damage image which may prevent the detection of the damage at the very early stage. Motivated by the possibility of achieving a 'super resolution' damage image by re-capturing subwavelength damage information contained in evanescent guided waves, this dissertation presents a feasibility study of converting evanescent into propagating guided waves in isotropic plates so that the far-field sensors can retrieve such valuable localized (subwavelength) damage information.;The properties of evanescent and propagating guided waves, i.e., Lamb waves and shear horizontal waves (SH waves), are first investigated by revisiting the formation of guided waves in isotropic plates and are characterized by the complex-valued dispersive curves. The important phase information and mode shapes for the propagating and evanescent guided waves are uncovered.;The differential and integral form complex reciprocity relations are derived for guided waves in isotropic plates as a theoretical base for solving waveguide mode analysis under either displacement or traction excitations in plates. Using the integral form reciprocity relations, the orthogonality relations for the guided wave modes are obtained and are discussed for propagating and evanescent modes, respectively. The power flow delivered to an elastic plate can be completely described by a complex power flow, with real part representing the radiative power and imaginary part describing the reactive power. This type of separation of complex power flow is then proved to be related to the usual separation made on the basis of propagating and evanescent guided waves as propagating guided waves carry pure real power flow and the power flow for evanescent waves turns out to be pure imaginary.;The conversion of evanescent into propagating Lamb waves is substantiated by prescribing Lamb evanescent time-harmonic displacements or tractions distributed through a narrow aperture at the edge of a semi-infinite plate. First, a purely Lamb evanescent field can be generated when Lamb evanescent displacements or tractions are incident upon the entire edge of the plate. The amplitude coefficient of the propagating Lamb waves being converted from evanescent is determined through a theoretical formulation based on the complex reciprocity theorem via the finite element analysis (FEA) and is verified through the validation of a complex power conservation relation. Power conversion efficiency analysis shows that the propagating power converted from evanescent excitation is strongly frequency dependent and can be significant.;The conversion of evanescent into propagating SH waves is demonstrated by prescribing SH evanescent time-harmonic displacement excitations through a narrow aperture at the edge of a semi-infinite plate. The formula derivation of the SH wave is much simpler than the Lamb wave counterpart. A purely SH evanescent field can be generated when SH evanescent displacement is incident. The conversion process is then demonstrated by solving the SH wave governing equation using a finite element method. A theoretical model based on the complex reciprocity theorem with the aid of FEA is proposed to quantify the amplitude coefficient of the converted propagating SH mode from evanescent and the amplitude coefficient is verified by proving a complex power conservation relation. Power conversion analysis shows that the conversion efficiency for propagating SH modes converted from evanescent varies dramatically as excitation frequency changes and can be significant.;The demonstration of converting evanescent into propagating guided waves in isotropic plates provides a theoretical foundation for subwavelength damage detection and imaging and may have potential application in structural health monitoring.