LEADER 04336nam  22006975  450 
001 9910337872303321
005 20240312201740.0
010   $a3-030-14927-7
024 7 $a10.1007/978-3-030-14927-7
035   $a(CKB)4100000007938170
035   $a(MiAaPQ)EBC5754969
035   $a(DE-He213)978-3-030-14927-7
035   $a(PPN)235671460
035   $a(EXLCZ)994100000007938170
100   $a20190415d2019      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aWaves with Power-Law Attenuation$b[electronic resource] /$fby Sverre Holm
205   $a1st ed. 2019.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019.
215   $a1 online resource (336 pages)
311 0 $a3-030-14926-9 
327   $aPreface -- Acknowledgements -- About the Author -- List of Symbols -- List of Figures -- List of Tables -- 1 Introduction -- Part I Acoustics and Linear Viscoelasticity -- 2 Classical Wave Equations -- 3 Models of Linear Viscoelasticity -- 4 Absorption Mechanisms and Physical Constraints -- Part II Modeling of Power-Law Media -- 5 Power-Law Wave Equations from Constitutive Equations -- 6 Phenomenological Power-Law Wave Equations -- 7 Justification for Power Laws and Fractional Models -- 8 Power Laws and Porous Media -- 9 Power Laws and Fractal Scattering Media -- Appendix A Mathematical Background -- Appendix B Wave and Heat Equations -- Index.
330   $aThis book integrates concepts from physical acoustics with those from linear viscoelasticity and fractional linear viscoelasticity. Compressional waves and shear waves in applications such as medical ultrasound, elastography, and sediment acoustics often follow power law attenuation and dispersion laws that cannot be described with classical viscous and relaxation models. This is accompanied by temporal power laws rather than the temporal exponential responses of classical models. The book starts by reformulating the classical models of acoustics in terms of standard models from linear elasticity. Then, non-classical loss models that follow power laws and which are expressed via convolution models and fractional derivatives are covered in depth. In addition, parallels are drawn to electromagnetic waves in complex dielectric media. The book also contains historical vignettes and important side notes about the validity of central questions. While addressed primarily to physicists and engineers working in the field of acoustics, this expert monograph will also be of interest to mathematicians, mathematical physicists, and geophysicists. Couples fractional derivatives and power laws and gives their multiple relaxation process interpretation Investigates causes of power law attenuation and dispersion such as interaction with hierarchical models of polymer chains and non-Newtonian viscosity Shows how fractional and multiple relaxation models are inherent in the grain shearing and extended Biot descriptions of sediment acoustics Contains historical vignettes and side notes about the formulation of some of the concepts discussed.
606   $aSound
606   $aMultibody systems
606   $aVibration
606   $aMechanics, Applied
606   $aMathematical physics
606   $aUltrasonics
606   $aAcoustical engineering
606   $aGeophysics
606   $aAcoustics
606   $aMultibody Systems and Mechanical Vibrations
606   $aMathematical Physics
606   $aUltrasonics
606   $aEngineering Acoustics
606   $aGeophysics
615  0$aSound.
615  0$aMultibody systems.
615  0$aVibration.
615  0$aMechanics, Applied.
615  0$aMathematical physics.
615  0$aUltrasonics.
615  0$aAcoustical engineering.
615  0$aGeophysics.
615 14$aAcoustics.
615 24$aMultibody Systems and Mechanical Vibrations.
615 24$aMathematical Physics.
615 24$aUltrasonics.
615 24$aEngineering Acoustics.
615 24$aGeophysics.
676   $a534
700   $aHolm$b Sverre$4aut$4http://id.loc.gov/vocabulary/relators/aut$0838667
906   $aBOOK
912   $a9910337872303321
996   $aWaves with Power-Law Attenuation$91873206
997   $aUNINA