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Mechanics of Solids Volume IV: Waves in Elastic and Viscoelastic Solids (Theory and Experiment)

126,99 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.06.1984

Herausgeber

C. Truesdell

Verlag

Springer Berlin

Seitenzahl

334

Maße (L/B/H)

24,4/17/2 cm

Gewicht

608 g

Auflage

Softcover reprint of the original 1st edition 1974

Sprache

Englisch

ISBN

978-3-540-13163-2

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.06.1984

Herausgeber

C. Truesdell

Verlag

Springer Berlin

Seitenzahl

334

Maße (L/B/H)

24,4/17/2 cm

Gewicht

608 g

Auflage

Softcover reprint of the original 1st edition 1974

Sprache

Englisch

ISBN

978-3-540-13163-2

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: GPSR Kontakt

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  • Produktbild: Mechanics of Solids
  • Produktbild: Mechanics of Solids
  • Wave Propagation in Nonlinear Viscoelastic Solids..- I. Introduction.- 1. Background. Scope of this article.- 2. Plan of this article. Notation.- II. Experimental methods in one-dimensional wave propagation.- 3. Introductory remarks.- 4. Planar impact loading configuration.- 5. Measurement of the transmitted wave profiles.- ?) The displacement interferometer.- ?) The velocity interferometer.- ?) Diffuse surface interferometry.- ?) In-material interferometry.- 6. Determination of wave front velocities.- III. One-dimensional motions in materials with memory.- 7. Kinematics and balance laws.- 8. Classification of waves.- 9. Simple materials with fading memory.- IV. Propagation of acoustic waves.- 10. Infinitesimal sinusoidal progressive waves.- 11. Determination of the stress relaxation function from acoustic wave experiments.- V. Propagation of one-dimensional steady waves.- 12. The existence of steady waves.- 13. Experimental observation of steady shock waves.- 14. Finite linear viscoelasticity and the evaluation of material response functions.- 15. Steady shock wave solutions.- VI. Growth and decay of one-dimensional shock waves.- 16. The shock amplitude equation.- 17. The critical acceleration.- 18. Shock pulse attenuation.- 19. Some remarks on the evolution of steady shock waves.- VII. Growth and decay of one-dimensional acceleration waves.- 20. The amplitude of waves in homogeneously deformed regions.- 21. Expansive waves in precompressed regions.- ?) Acceleration wave.- ?) Expansive wave decay.- 22. Compressive wave growth in undeformed regions at rest.- 23. Toward a three-dimensional characterization of nonlinear viscoelastic solids.- ?) Dilatational response of isotropic finite linear viscoelastic solids.- ?) The velocity of acceleration waves in isotropic solids subject to hydrostatic pressure.- ?) Experimental determination of the instantaneous and equilibrium pressure-density curves.- VIII. Thermodynamic influences on viscoelastic wave propagation.- 24. Thermodynamics of materials with memory.- ?) Constitutive assumption with temperature as the independent thermodynamic variable.- ?) Constitutive assumption with entropy as the independent thermodynamic; variable.- 25. Propagation of steady shock waves.- ?) Steady waves in thermoviscoelastic solids.- ?) A specific thermoviscoelastic constitutive assumption and the evaluation of material response functions.- ?) Steady shock wave solutions.- 26. The growth and decay of shock waves.- ?) General properties of shock transition.- ?) The shock amplitude equation.- ?) Shock wave behavior in a particular thermoviscoelastic solid.- 27. The growth and decay of acceleration waves.- 28. Stress-energy response.- References.- Waves in Solids..- A. Introduction.- 1. Scope.- 2. Notation.- B. Foundations.- 3. Motion and deformation.- 3.1. Geometry of deformation. Strain.- 3.2. Derivatives with respect to time.- 3.3. Useful identities involving J.- 3.4. Transport theorem.- 3.5. More identities.- 4. Stress.- 5. Energy flux and distributed sources.- 6. Equations of balance.- 6.1. Mass balance.- 6.2. A useful formula.- 6.3. Equation of motion.- 6.4. Energy balance.- C. Equilibrium states.- 7. Motivation. Mutative and nonmutative processes.- 8. Thermostatic assumptions. Basis of classical thermostatics.- 9. Tensor and abbreviated notation.- 10. Thermostatic relations and coefficients.- 10.1. Thermodynamic potentials.- 10.2. Specific heats.- Table 10.1. Thermodynamic potentials and their derivatives.- 10.3. Maxwell coefficients.- 10.4. The differences.- 10.5. The difference Cr — Cv and the ratio.- 10.6. Strain dependence of the specific heats and expansion coefficients.- 10.7. Internal energy as a function of other variables.- 10.8. Internal energy as an independent variable.- Table 10.2. Internal energy as a function of (V?, T), (??, T), (??, S).- Table 10.3. S, T, ?? as functions of (V?,U).- Table 10.4. S, T, V? as functions of (??, U).- 10.9. Grüneisen numbers.- 11. Thermostatics under hydrostatic pressure.- 11.1. Thermodynamic potentials.- Table 11.1. Thermodynamic potentials and their derivatives under spherical stress.- 11.2. Compressiblity, bulk modulus, volumetric expansion coefficient.- 11.3. Specific heats at constant volume and constant pressure.- 11.4. Arbitrariness of reference pressure.- 11.5. Maxwell coefficients.- 11.6. BS/B=Cp/CJ.- 11.7. Grüneisen number ?.- 11.8. Pressure derivatives of the specific heats and expansion coefficient.- 11.9. Internal energy as a function of other variables.- 11.10. Internal energy as an independent variable.- Table 11.2. Internal energy as a function of (J, T), (p, T), (p, S).- Table 11.3. S, T, p as functions of (J, U).- Table 11.4. S, T, J as functions of (p, U.- 11.11. Other derivatives with respect to pressure.- Table 11.5. Expressions for pressure derivatives evaluated at zero pressure.- 11.12. Derivatives with respect to temperature.- 11.13. Thermal expansion at constant pressure.- D. Electromechanical interactions.- 12. Basic equations of electromagnetic theory in a material representation.- 12.1. Maxwell’s field equations.- 12.2. Units.- 12.3. Effect of particle velocity.- 12.4. Material representations of fields and their properties.- 12.5. Material representation of the field equations.- 12.6. Integral forms of the equations.- 12.7. Electrodynamic potentials.- 12.8. Poynting’s theorem in spatial and material representations.- 13. Results based on the electrodynamical theory of Tiersten and Tsai.- 13.1. Introduction.- 13.2. The theory of Tiersten and Tsai.- 13.3. The total stored energy.- 13.4. Thermostatics.- 13.5. Equation of motion.- 14. Extension of thermostatics to include electromechanical interactions.- 14.1. Material coefficients.- Table 14.1. Derivatives of U(D, B, S, Vij).- Table 14.2. Thermodynamic potentials including electrical variables (after Mason, 1966).- Table 14.3. Connections among the various coefficients.- Table 14.4. Replacements for obtaining pyroelectric relations from thermoelastic relations.- 14.2. Linear piezoelectric equations.- E. Material symmetry.- 15. Isotropy groups, Laue groups, and crystal point groups.- Table 15-1- Laue groups, generators of associated rotation groups, and point groups included in each Laue group.- Table 15.2. The thirty-two crystal point groups.- Table 15.3. Order of the point groups and number of symmetry operations of each kind.- Table 15.4. Essential symmetry of the crystal systems.- 16. Effect of symmetry on material coefficients.- Table 16.1. Forms of a first-rank polar tensor referred to the conventional cartesian system.- Table 16.2. Second-rank polar tensors.- Table 16.3. Third-rank polar tensors.- Table 16.4. Fourth-rank polar tensors.- Table 16.5. Fifth-rank polar tensors.- Table 16.6. Third-order elastic constants for the eleven Laue groups and for isotropic media.- F. Exponentially damped plane waves.- 17. Complex representation of waves.- 17.1. Waves sinusoidal in time, attenuated in space.- 17.2. Waves sinusoidal in space decaying in time.- 17.3. Inhomogeneous plane waves.- 18. Stress and deformation in exponentially damped plane sinusoidal waves.- G. Linear viscoelastic interactions.- 19. The linear viscoelastic model.- 20. One-dimensional linear viscoelastic models.- 20.1. Introduction.- 20.2. Sinusoidal time variations.- 20.3. Decaying time variations.- Table 20.1. Functions associated with five special models of viscoelasticity.- 20.4. Special cases of linear viscoelasticity.- 21. A difficulty: Thermal effects.- H. Thermoviscoelastic media.- 22. General relations.- 23. A special model for thermoviscoelasticity.- 24. Linearized steady-state response.- I. Small-amplitude waves that are sinusoidal in time.- 25. Thermoviscoelastic medium.- 26. Elastic medium with Newtonian viscosity and heat conduction according to Fourier’s law.- 27. Idealized thermoelastic medium. Elastic medium.- 28. Initially stressed elastic medium.- 28.1. Introduction.- Table 28.1. Description of reference and present states.- 28.2. Linearization of the equation of motion.- 28.3. Solutions for small-amplitude waves.- 28.4. Propagation direction and velocity.- J. Ultrasonic measurements as a function of static initial stress.- 29. Determination of third-order elastic coefficients.- 29.1. Introduction.- 29.2. Initial derivative of QN W2 in terms of material properties.- 30. Effective elastic coefficients.- 30.1. Introduction.- 30.2. Lack of uniqueness of coefficients in equation of motion.- 30.3. Symmetry.- 30.4. Essential difference between wave propagation in unstressed and anisotropically stressed media.- 30.5. Effective elastic coefficients under hydrostatic pressure.- 30.6. Interpretation of the effective elastic coefficients ? ijkm as coefficients in a linearized stress-deformation relation.- 30.7. Relations of effective elastic coefficients to the bulk modulus and compressibility.- 30.8. Measurement of effective elastic coefficients.- 31. Pressure derivatives of elastic coefficients.- 31.1. Introduction.- 31.2. Pressure derivatives of thermodynamic coefficients.- 31.3. Pressure derivatives of effective coefficients.- 31.4. Relation between effective and thermodynamic elastic coefficients.- 31.5. Relation between pressure derivatives of effective and thermodynamic coefficients.- Table 31.1. ??v under hydrostatic pressure (monoclinic and triclinic classes excluded).- Table 31.2. Difference of pressure derivatives of effective and thermodynamic elastic coefficients, (monoclinic and triclinic classes excluded).- Table 31.3. Pressure derivatives of effective and thermodynamic elastic coefficients.- K. Analysis of ultrasonic measurements as a function of temperature.- 32. Elastic coefficients as a function of temperature.- 33. Derivatives with respect to temperature.- L. Examples.- 34. Elastic waves in crystals.- 34.1. Introduction.- 34.2. Special forms of the coefficients for cubic crystals.- 34.3. Conditions for a positive definite strain energy in cubic crystals.- 34.4. Acoustical tensor for arbitrary propagation directions in a cubic crystal.- 34.5. Directions for purely longitudinal and transverse waves in cubic crystals.- Table 34.1. Pure modes in cubic crystals.- 34.6. Determination of elastic constants.- 35. Thermoviscoelastic waves in cubic crystals.- 36. Piezoelectrically excited vibrations.- 36.1. Thickness-shear vibrations of an infinite plate.- 36.2. Electromechanical coupling coefficient.- 36.3. Electrical impedance of a vibrating piezoelectric plate.- 36.4. Equivalent circuit of a piezoelectric transducer.- 36.5. Thickness-longitudinal vibrations of an infinite piezoelectric plate.- 37. Radial motion of thin circular piezoelectric ceramic disks.- 38. Waves of finite amplitude in elastic media.- 38.1. Equation of motion.- 38.2. Characteristics of the equation of one-dimensional longitudinal motion.- 38.3. Simple-wave solution.- 38.4. The discontinuity distance.- 38.5. Particle velocity in the oscillating simple wave.- 38.6. Solution for the displacement.- 38.7. Relation of harmonic growth to higher-order elastic coefficients.- 38.8. Hypothetical linear medium for one-dimensional longitudinal motion.- 38.9. One-dimensional longitudinal stress-extension relation.- 39. Longitudinal shock waves in elastic solids.- 39.1. Relations that apply across a shock propagating into a medium at rest in its reference configuration.- 39.2. The connection of the stress-extension relation to the curve of shock velocity versus particle velocity.- 39.3. Thermodynamic considerations.- 40. Reflection of longitudinal waves at normal incidence.- 40.1. Reflection of a continuous disturbance.- 40.2. Reflection of a shock wave.- 41. Longitudinal motion of a piezoelectric material.- 41.1. Series expansions of the stress and electric field.- 41.2. Entropy jump across a shock in a piezoelectric material.- 41.3. Approximate solution for the passage of a shock wave through a shortcircuited piezoelectric slab.- “Uncoupled” approximation.- “Coupled approximation”.- 41.4. Determination of coefficients.- References.- Namenverzeichnis. — Author Index.- Sachverzeichnis (Deutsch-Englisch).- Subject Index (English-German).