Propagator (monodromy matrix)

For more info about our services contact : help@bestpfe.com

Table of contents

1 Introduction 
2 Love waves in 1D PC 
2.1 Introduction
2.2 Background
2.2.1 Propagator (monodromy matrix)
2.2.2 Definition of conditional and modal SH impedances
2.2.3 Statement of the Love wave problem
2.3 Properties of the impedances
2.3.1 Layer impedance
2.3.2 Substrate impedances
2.4 Love wave spectrum
2.4.1 Overview of the spectrum
2.4.2 Number of Love waves per a stopband
2.4.3 Monotonicity of the Love wave branches
2.4.4 Lower bound of the Love wave spectrum
2.4.5 Fundamental branch
2.5 Numerical examples
2.6 Conclusion
3 Love waves in 2D PC 
3.1 Introduction
3.2 Problem statement
3.3 The resolvent
3.4 The spectral projector
3.4.1 The eigenspaces
3.4.2 The spectral projector definition via propagator eigenvalues
3.4.3 The alternative definition of the spectral projector via path integral
3.5 The dispersion equation
3.5.1 Love wave spectrum
3.5.2 Projection of the spectrum of the propagating waves
3.6 Numerical examples
3.7 Conclusion
4 Plate waves in 2D PC
4.1 Introduction
4.2 Problem statement
4.3 The dispersion equation in terms of the propagator
4.4 The dispersion equation in terms of the resolvent
4.5 The dispersion spectrum for mirror symmetric profiles
4.5.1 Problem decomposition for symmetric and antisymmetric waves
4.5.2 Dispersion equations in stable terms
4.6 Numerical examples
4.6.1 One array of inclusions
4.6.2 Two arrays of inclusions
4.7 The displacement and traction field
4.7.1 The wave field equation
4.7.2 Numerical examples
4.8 Conclusion
5 Guided waves in 2D PC 
5.1 Introduction
5.2 Problem statement
5.3 Dispersion equation with resolvent and projector
5.3.1 The localized waves spectrum
5.3.2 Projection of the spectrum of the propagating waves
5.4 The dispersion equation for the mirror-symmetric case
5.4.1 Problem decomposition for symmetric and antisymmetric waves
5.4.2 Dispersion equations in stable terms
5.5 Numerical examples
5.5.1 Square inclusions and 2D substrates
5.5.2 Circular inclusions and layered substrates
5.6 The displacement and traction field
5.6.1 The propagators for decreasing modes
5.6.2 The wave field equation
5.6.3 Numerical examples
5.7 Conclusion
6 Conclusions