Modelling of Mechanical Systems
The modelling of mechanical systems provides engineers and students with the methods to model and understand mechanical systems by using both mathematical and computer-based tools. Written by an eminent authority in the field, this is the second of four volumes which provide engineers with a compreh...
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| Main Authors | , |
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| Format | eBook |
| Language | English |
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Chantilly
Elsevier Science & Technology
2005
Butterworth-Heinemann Elsevier Butterworth-Heinemann |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 0750668466 9780750668460 0750668474 9780750668477 |
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| Abstract | The modelling of mechanical systems provides engineers and students with the methods to model and understand mechanical systems by using both mathematical and computer-based tools. Written by an eminent authority in the field, this is the second of four volumes which provide engineers with a comprehensive resource on this cornerstone mechanical engineering subject. Dealing with continuous systems, this book covers solid mechanics, beams, plates and shells. In a clear style and with a practical rather than theoretical approach, it shows how to model continuous systems in order to study vibration modes, motion and forces. Appendices give useful primers on aspects of the mathematics introduced in the book. Other volumes in the series cover discrete systems, fluid-structure interaction and flow-induced vibration.
* Axisa is a world authority in the modelling of systems* Comprehensive coverage of mathematical techniques used to perform computer-based analytical studies and numerical simulations* A key reference for mechanical engineers, researchers and graduate students in this cornerstone subject |
|---|---|
| AbstractList | The modelling of mechanical systems provides engineers and students with the methods to model and understand mechanical systems by using both mathematical and computer-based tools. Written by an eminent authority in the field, this is the second of four volumes which provide engineers with a comprehensive resource on this cornerstone mechanical engineering subject. Dealing with continuous systems, this book covers solid mechanics, beams, plates and shells. In a clear style and with a practical rather than theoretical approach, it shows how to model continuous systems in order to study vibration modes, motion and forces. Appendices give useful primers on aspects of the mathematics introduced in the book. Other volumes in the series cover discrete systems, fluid-structure interaction and flow-induced vibration.
* Axisa is a world authority in the modelling of systems* Comprehensive coverage of mathematical techniques used to perform computer-based analytical studies and numerical simulations* A key reference for mechanical engineers, researchers and graduate students in this cornerstone subject Written by an eminent authority in the field, Modelling of Mechanical Systems: Fluid-Structure Interaction is the third in a series of four self-contained volumes suitable for practitioners, academics and students alike in engineering, physical sciences and applied mechanics. The series skilfully weaves a theoretical and pragmatic approach to modelling mechanical systems and to analysing the responses of these systems. The study of fluid-structure interactions in this third volume covers the coupled dynamics of solids and fluids, restricted to the case of oscillatory motions about a state of static equilibrium. Physical and mathematical aspects of modelling these mechanisms are described in depth and illustrated by numerous worked out exercises. · Written by a world authority in the field in a clear, concise and accessible style · Comprehensive coverage of mathematical techniques used to perform computer-based analytical studies and numerical simulations · A key reference for mechanical engineers, researchers and graduate students |
| Author | Trompette, Philippe Axisa, François |
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| Discipline | Engineering Mathematics |
| DocumentTitleAlternate | Modélisation des systèmes mécaniques. English Structural elements |
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| Notes | Available also in a print ed. First published in France 2001 by Hermes Science, entitled Modélisation des systèmes mécaniques continus, Tome 2. Mode of access: Internet via World Wide Web. Title from title screen. |
| OCLC | 476003120 437178427 |
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| Publisher | Elsevier Science & Technology Butterworth-Heinemann Elsevier Butterworth-Heinemann |
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| Snippet | The modelling of mechanical systems provides engineers and students with the methods to model and understand mechanical systems by using both mathematical and... Written by an eminent authority in the field, Modelling of Mechanical Systems: Fluid-Structure Interaction is the third in a series of four self-contained... |
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| SubjectTerms | Mechanics, Applied System analysis |
| SubjectTermsDisplay | Electronic books. Mechanics, Applied. System analysis. |
| TableOfContents | 2.2.3.5. Concentrated loads. -- 2.2.3.6. Intermediate supports -- 2.2.3.7. Torsion with warping:Saint Venant 's theory -- 2.2.4. Pure bending mode of deformation -- 2.2.4.1. Simplifying hypotheses of the Bernoulli -Euler model -- 2.2.4.2. Local equilibrium -- 2.2.4.3. Elastic boundary conditions -- 2.2.4.4. Intermediate supports -- 2.2.4.5. Concentrated loads -- 2.2.4.6. General solution of the static and homogeneous equation -- 2.2.4.7. Application to some problems of practical interest -- 2.2.5. Formulation of the boundary conditions -- 2.2.5.1. Elastic impedances. -- 2.2.5.2. Generalized mechanical impedances -- 2.2.5.3. Homogeneous and inhomogeneous conditions -- 2.2.6. More about transverse shear stresses and straight beam models -- 2.2.6.1. Asymmetrical cross-sections and shear (or twist) centre -- 2.2.6.2. Slenderness ratio and lateral deflection -- 2.3. Thermoelastic behaviour of a straight beam -- 2.3.1. 3D law of thermal expansion -- 2.3.2. Thermoelastic axial response -- 2.3.3. Thermoelastic bending of a beam -- 2.4. Elastic-plastic beam -- 2.4.1. Elastic-plastic behaviour under uniform traction -- 2.4.2. Elastic-plastic behaviour under bending -- 2.4.2.1. Skin stress -- 2.4.2.2. Moment-curvature law and failure load -- 2.4.2.3. Elastic-plastic bending:global constitutive law -- 2.4.2.4. Superposition of several modes of deformation -- Chapter 3. Straight beam models:Hamilton 's principle -- 3.1. Introduction -- 3.2. Variational formulation of the straight beam equations -- 3.2.1. Longitudinal motion -- 3.2.1.1. Model neglecting the Poisson effect -- 3.2.1.2. Model including the Poisson effect (Love -Rayleigh model) -- 3.2.2. Bending and transverse shear motion -- 3.2.2.1. Bending without shear:Bernoulli -Euler model -- 3.2.2.2. Bending including transverse shear:the Timoshenko model in statics 4.2.2.4. Bending coupled with shear modes -- 4.2.3. Rayleigh 's quotient -- 4.2.3.1. Bending of a beam with an attached concentrated mass. -- 4.2.3.2. Beam on elastic foundation -- 4.2.4. Finite element approximation. -- 4.2.4.1. Longitudinal modes. -- 4.2.4.2. Bending modes. -- 4.2.5. Bending modes of an axially preloaded beam -- 4.2.5.1. Natural modes of vibration -- 4.2.5.2. Static buckling analysis. -- 4.3. Modal projection methods -- 4.3.1. Equations of motion projected onto a modal basis -- 4.3.2. Deterministic excitations. -- 4.3.2.1. Separable space and time excitation -- 4.3.2.2. Non-separable space and time excitation -- 4.3.3. Truncation of the modal basis -- 4.3.3.1. Criterion based on the mode shapes -- 4.3.3.2. Spectral criterion -- 4.3.4. Stresses and convergence rate of modal series -- 4.4. Substructuring method -- 4.4.1. Additional stiffnesses -- 4.4.1.1. Beam in traction-compression with an end spring -- 4.4.1.2. Truncation stiffness for a free-free modal basis -- 4.4.1.3. Bending modes of an axially prestressed beam -- 4.4.2. Additional inertia -- 4.4.3. Substructures by using modal projection. -- 4.4.3.1. Basic ideas of the method -- 4.4.3.2. Vibration modes of an assembly of two beams linked by a spring -- 4.4.3.3. Multispan beams -- 4.4.4. Nonlinear connecting elements -- 4.4.4.1. Axial impact of a beam on a rigid wall -- 4.4.4.2. Beam motion initiated by a local impulse followed by an impact on a rigid wall -- 4.4.4.3. Elastic collision between two beams -- Chapter 5. Plates:in-plane motion -- 5.1. Introduction -- 5.1.1. Plate geometry -- 5.1.2. Incidence of plate geometry on the mechanical response -- 5.2. Kirchhoff -Love model -- 5.2.1. Love simplifications. -- 5.2.2. Degrees of freedom and global displacements -- 5.2.3. Membrane displacements,strains and stresses. -- 5.2.3.1. Global and local displacements Intro -- MODELLING OF MECHANICAL SYSTEMS VOLUME 2 -- Contents -- Preface -- Introduction -- Chapter 1. Solid mechanics -- 1.1.Introduction -- 1.2. Equilibrium equations of a continuum -- 1.2.1. Displacements and strains -- 1.2.2. Indicial and symbolic notations -- 1.2.3. Stresses -- 1.2.4. Equations of dynamical equilibrium -- 1.2.5. Stress-strain relationships for an isotropic elastic material -- 1.2.6. Equations of elastic vibrations (Navier 's equations) -- 1.3. Hamilton's principle -- 1.3.1. General presentation of the formalism -- 1.3.2. Application to a three-dimensional solid -- 1.3.2.1. Hamilton 's principle -- 1.3.2.2. Hilbert functional vector space. -- 1.3.2.3. Variation of the kinetic energy -- 1.3.2.4. Variation of the strain energy. -- 1.3.2.5. Variation of the external load work -- 1.3.2.6. Equilibrium equations and boundary conditions -- 1.3.2.7. Stress tensor and Lagrange 's multipliers -- 1.3.2.8. Variation of the elastic strain energy -- 1.3.2.9. Equation of elastic vibrations -- 1.3.2.10. Conservation of mechanical energy -- 1.3.2.11. Uniqueness of solution of motion equations -- 1.4. Elastic waves in three-dimensional media -- 1.4.1. Material oscillations in a continuous medium interpreted as waves -- 1.4.2. Harmonic solutions of Navier 's equations -- 1.4.3. Dilatation and shear elastic waves -- 1.4.3.1. Irrotational,or potential motion -- 1.4.3.2. Equivoluminal,or shear motion. -- 1.4.3.3. Irrotational harmonic waves (dilatation or pressure waves) -- 1.4.3.4. Shear waves (equivoluminal or rotational waves) -- 1.4.4. Phase and group velocities . -- 1.4.5. Wave reflection at the boundary of a semi-infinite medium -- 1.4.5.1. Complex amplitude of harmonic and plane waves at oblique incidence -- 1.4.5.2. Reflection of (SH)waves on a free boundary -- 1.4.5.3. Reflection of (P)waves on a free boundary -- 1.4.6. Guided waves. 1.4.6.1. Guided (SH)waves in a plane layer -- 1.4.6.2. Physical interpretation -- 1.4.6.3. Waves in an infinite elastic rod of circular cross-section -- 1.4.7. Standing waves and natural modes of vibration -- 1.4.7.1. Dilatation plane modes of vibration -- 1.4.7.2. Dilatation modes of vibration in three dimensions -- 1.4.7.3. Shear plane modes of vibration -- 1.5. From solids to structural elements -- 1.5.1. Saint-Venant 's principle -- 1.5.2. Shape criterion to reduce the dimension of a problem -- 1.5.2.1. Compression of a solid body shaped as a slender parallelepiped -- 1.5.2.2. Shearing of a slender parallelepiped -- 1.5.2.3. Validity of the simplification for a dynamic loading -- 1.5.2.4. Structural elements in engineering -- Chapter 2. Straight beam models:Newtonian approach -- 2.1. Simplified representation of a 3D continuous medium by an equivalent 1D model -- 2.1.1. Beam geometry -- 2.1.2. Global and local displacements -- 2.1.3. Local and global strains -- 2.1.4. Local and global stresses -- 2.1.5. Elastic stresses -- 2.1.6. Equilibrium in terms of generalized stresses -- 2.1.6.1. Equilibrium of forces -- 2.1.6.2. Equilibrium of the moments. -- 2.2. Small elastic motion -- 2.2.1. Longitudinal mode of deformation -- 2.2.1.1. Local equilibrium -- 2.2.1.2. General solution of the static equilibrium without external loading -- 2.2.1.3. Elastic boundary conditions -- 2.2.1.4. Concentrated loads. -- 2.2.1.5. Intermediate supports -- 2.2.2. Shear mode of deformation -- 2.2.2.1. Local equilibrium -- 2.2.2.2. General solution without external loading -- 2.2.2.3. Elastic boundary conditions -- 2.2.2.4. Concentrated loads. -- 2.2.2.5. Intermediate supports -- 2.2.3. Torsion mode of deformation -- 2.2.3.1. Torsion without warping -- 2.2.3.2. Local equilibrium -- 2.2.3.3. General solution without loading -- 2.2.3.4. Elastic boundary conditions 3.2.2.3. The Rayleigh -Timoshenko dynamic model -- 3.2.3. Bending of a beam prestressed by an axial force -- 3.2.3.1. Strain energy and Lagrangian -- 3.2.3.2. Vibration equation and boundary conditions -- 3.2.3.3. Static response to a transverse force and buckling instability -- 3.2.3.4. Follower loads -- 3.3. Weighted integral formulations -- 3.3.1. Introduction -- 3.3.2. Weighted equations of motion -- 3.3.3. Concentrated loads expressed in terms of distributions -- 3.3.3.1. External loads -- 3.3.3.2. Intermediate supports -- 3.3.3.3. A comment on the use of distributions in mechanics -- 3.3.4. Adjoint and self-adjoint operators -- 3.3.5. Generic properties of conservative operators -- 3.4. Finite element discretization -- 3.4.1. Introduction -- 3.4.2. Beam in traction-compression -- 3.4.2.1. Mesh. -- 3.4.2.2. Shape functions -- 3.4.2.3. Element mass and stiffness matrices -- 3.4.2.4. Equivalent nodal external loading -- 3.4.2.5. Assembling the finite element model -- 3.4.2.6. Boundary conditions -- 3.4.2.7. Elastic supports and penalty method -- 3.4.3. Assembling non-coaxial beams -- 3.4.3.1. The stiffness and mass matrices of a beam element for bending -- 3.4.3.2. Stiffness matrix combining bending and axial modes of deformation. -- 3.4.3.3. Assembling the finite element model of the whole structure -- 3.4.3.4. Transverse load resisted by string and bending stresses in a roof truss. -- 3.4.4. Saving DOF when modelling deformable solids -- Chapter 4. Vibration modes of straight beams and modal analysis methods -- 4.1. Introduction -- 4.2. Natural modes of vibration of straight beams -- 4.2.1. Travelling waves of simplified models -- 4.2.1.1. Longitudinal waves -- 4.2.1.2. Flexure waves -- 4.2.2. Standing waves,or natural modes of vibration -- 4.2.2.1. Longitudinal modes. -- 4.2.2.2. Torsion modes. -- 4.2.2.3. Flexure (or bending)modes 5.2.3.2. Global and local strains A4.7. Hankel functions -- A4.8. Asymptotic forms for large values of the argument -- A4.9. Modified Bessel functions of the first and second kinds -- Appendix A5. Spherical functions -- A5.1. Legendre functions and polynomials -- A5.2. Recurrence and orthogonality relations for Legendre polynomials -- A5.3. Spherical Bessel functions -- A5.4. Recurrence relations for spherical Bessel functions -- A5.5. Spherical Hankel functions -- Appendix A6. Specific impedances of several substances -- References -- IDXIndex -- Colour plates Cover -- TOCContents -- Preface -- Introduction -- CHChapter 1. Introduction to fluid-structure coupling -- 1.1. A short outline of fluid-structure coupled systems -- 1.2. Dynamic equations of fluid-structure coupled systems -- 1.3. Linear approximation of the fluid equations -- CHChapter 2. Inertial coupling -- 2.1. Introduction -- 2.2. Discrete systems -- 2.3. Continuous systems -- CHChapter 3. Surface waves -- 3.1. Introduction -- 3.2. Gravity waves -- 3.3. Surface tension -- 3.4. Sloshing modes -- 3.5. Fluid-structure interaction -- CHChapter 4. Plane acoustical waves in pipe systems -- 4.1. Introduction -- 4.2. Free sound waves in pipe systems: plane and harmonic waves -- 4.3. Forced waves -- 4.4. Speed of sound -- CHChapter 5. 3D Sound waves -- 5.1. 3D Standing sound waves (acoustic modes) -- 5.2. Guided wave modes and plane wave approximation -- 5.3. Forced waves -- CHChapter 6. Vibroacoustic coupling -- 6.1. Local equilibrium equations -- 6.2. Piston-fluid column system -- 6.3. Vibroacoustic coupling in tube and ducts circuits -- 6.4. Application to a few problems -- 6.5. Finite element method -- CHChapter 7. Energy dissipation by the fluid -- 7.1. Preliminary survey on linear modelisation of dissipation -- 7.2. Radiation damping -- 7.3. Dissipation induced by viscosity of the fluid -- 7.4. Dissipation in acoustic waves -- Appendix A1. A few elements of thermodynamics -- A1. Thermodynamic refresher -- Appendix A2. Mechanical properties of common materials -- A2.1. Phase diagram -- A2.2. Gas properties -- A2.3. Liquid properties -- A2.4. Solid properties -- Appendix A3. The Green identity -- Appendix A4. Bessel functions -- A4.1. Definition -- A4.2. Bessel functions of the first kind -- A4.3. Bessel functions of the second kind -- A4.4. Recurrence relations -- A4.5. Remarkable integrals -- A4.6. Lommel integrals |
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