{"product_id":"vibrations-and-waves-in-continuous-9780470517383","title":"Vibrations and Waves in Continuous","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe subject of vibrations is of fundamental importance in engineering and technology. Discrete modelling is sufficient to understand the dynamics of many vibrating systems; however a large number of vibration phenomena are far more easily understood when modelled as continuous systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Vibrations of strings and bars 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Dynamics of strings and bars: the Newtonian formulation 1\u003c\/p\u003e \u003cp\u003e1.1.1 Transverse dynamics of strings 1\u003c\/p\u003e \u003cp\u003e1.1.2 Longitudinal dynamics of bars 6\u003c\/p\u003e \u003cp\u003e1.1.3 Torsional dynamics of bars 7\u003c\/p\u003e \u003cp\u003e1.2 Dynamics of strings and bars: the variational formulation 9\u003c\/p\u003e \u003cp\u003e1.2.1 Transverse dynamics of strings 10\u003c\/p\u003e \u003cp\u003e1.2.2 Longitudinal dynamics of bars 11\u003c\/p\u003e \u003cp\u003e1.2.3 Torsional dynamics of bars 13\u003c\/p\u003e \u003cp\u003e1.3 Free vibration problem: Bernoulli’s solution 14\u003c\/p\u003e \u003cp\u003e1.4 Modal analysis 18\u003c\/p\u003e \u003cp\u003e1.4.1 The eigenvalue problem 18\u003c\/p\u003e \u003cp\u003e1.4.2 Orthogonality of eigenfunctions 24\u003c\/p\u003e \u003cp\u003e1.4.3 The expansion theorem 25\u003c\/p\u003e \u003cp\u003e1.4.4 Systems with discrete elements 27\u003c\/p\u003e \u003cp\u003e1.5 The initial value problem: solution using Laplace transform 30\u003c\/p\u003e \u003cp\u003e1.6 Forced vibration analysis 31\u003c\/p\u003e \u003cp\u003e1.6.1 Harmonic forcing 32\u003c\/p\u003e \u003cp\u003e1.6.2 General forcing 36\u003c\/p\u003e \u003cp\u003e1.7 Approximate methods for continuous systems 40\u003c\/p\u003e \u003cp\u003e1.7.1 Rayleigh method 41\u003c\/p\u003e \u003cp\u003e1.7.2 Rayleigh–Ritz method 43\u003c\/p\u003e \u003cp\u003e1.7.3 Ritz method 44\u003c\/p\u003e \u003cp\u003e1.7.4 Galerkin method 47\u003c\/p\u003e \u003cp\u003e1.8 Continuous systems with damping 50\u003c\/p\u003e \u003cp\u003e1.8.1 Systems with distributed damping 50\u003c\/p\u003e \u003cp\u003e1.8.2 Systems with discrete damping 53\u003c\/p\u003e \u003cp\u003e1.9 Non-homogeneous boundary conditions 56\u003c\/p\u003e \u003cp\u003e1.10 Dynamics of axially translating strings 57\u003c\/p\u003e \u003cp\u003e1.10.1 Equation of motion 58\u003c\/p\u003e \u003cp\u003e1.10.2 Modal analysis and discretization 58\u003c\/p\u003e \u003cp\u003e1.10.3 Interaction with discrete elements 61\u003c\/p\u003e \u003cp\u003eExercises 62\u003c\/p\u003e \u003cp\u003eReferences 67\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 One-dimensional wave equation: d’Alembert’s solution 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 D’Alembert’s solution of the wave equation 69\u003c\/p\u003e \u003cp\u003e2.1.1 The initial value problem 72\u003c\/p\u003e \u003cp\u003e2.1.2 The initial value problem: solution using Fourier transform 76\u003c\/p\u003e \u003cp\u003e2.2 Harmonic waves and wave impedance 77\u003c\/p\u003e \u003cp\u003e2.3 Energetics of wave motion 79\u003c\/p\u003e \u003cp\u003e2.4 Scattering of waves 83\u003c\/p\u003e \u003cp\u003e2.4.1 Reflection at a boundary 83\u003c\/p\u003e \u003cp\u003e2.4.2 Scattering at a finite impedance 87\u003c\/p\u003e \u003cp\u003e2.5 Applications of the wave solution 93\u003c\/p\u003e \u003cp\u003e2.5.1 Impulsive start of a bar 93\u003c\/p\u003e \u003cp\u003e2.5.2 Step-forcing of a bar with boundary damping 95\u003c\/p\u003e \u003cp\u003e2.5.3 Axial collision of bars 99\u003c\/p\u003e \u003cp\u003e2.5.4 String on a compliant foundation 102\u003c\/p\u003e \u003cp\u003e2.5.5 Axially translating string 104\u003c\/p\u003e \u003cp\u003eExercises 107\u003c\/p\u003e \u003cp\u003eReferences 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Vibrations of beams 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Equation of motion 113\u003c\/p\u003e \u003cp\u003e3.1.1 The Newtonian formulation 113\u003c\/p\u003e \u003cp\u003e3.1.2 The variational formulation 116\u003c\/p\u003e \u003cp\u003e3.1.3 Various boundary conditions for a beam 118\u003c\/p\u003e \u003cp\u003e3.1.4 Taut string and tensioned beam 120\u003c\/p\u003e \u003cp\u003e3.2 Free vibration problem 121\u003c\/p\u003e \u003cp\u003e3.2.1 Modal analysis 121\u003c\/p\u003e \u003cp\u003e3.2.2 The initial value problem 132\u003c\/p\u003e \u003cp\u003e3.3 Forced vibration analysis 133\u003c\/p\u003e \u003cp\u003e3.3.1 Eigenfunction expansion method 134\u003c\/p\u003e \u003cp\u003e3.3.2 Approximate methods 135\u003c\/p\u003e \u003cp\u003e3.4 Non-homogeneous boundary conditions 137\u003c\/p\u003e \u003cp\u003e3.5 Dispersion relation and flexural waves in a uniform beam 138\u003c\/p\u003e \u003cp\u003e3.5.1 Energy transport 140\u003c\/p\u003e \u003cp\u003e3.5.2 Scattering of flexural waves 142\u003c\/p\u003e \u003cp\u003e3.6 The Timoshenko beam 144\u003c\/p\u003e \u003cp\u003e3.6.1 Equations of motion 144\u003c\/p\u003e \u003cp\u003e3.6.2 Harmonic waves and dispersion relation 147\u003c\/p\u003e \u003cp\u003e3.7 Damped vibration of beams 149\u003c\/p\u003e \u003cp\u003e3.8 Special problems in vibrations of beams 151\u003c\/p\u003e \u003cp\u003e3.8.1 Influence of axial force on dynamic stability 151\u003c\/p\u003e \u003cp\u003e3.8.2 Beam with eccentric mass distribution 155\u003c\/p\u003e \u003cp\u003e3.8.3 Problems involving the motion of material points of a vibrating beam 159\u003c\/p\u003e \u003cp\u003e3.8.4 Dynamics of rotating shafts 163\u003c\/p\u003e \u003cp\u003e3.8.5 Dynamics of axially translating beams 165\u003c\/p\u003e \u003cp\u003e3.8.6 Dynamics of fluid-conveying pipes 168\u003c\/p\u003e \u003cp\u003eExercises 171\u003c\/p\u003e \u003cp\u003eReferences 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Vibrations of membranes 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Dynamics of a membrane 179\u003c\/p\u003e \u003cp\u003e4.1.1 Newtonian formulation 179\u003c\/p\u003e \u003cp\u003e4.1.2 Variational formulation 182\u003c\/p\u003e \u003cp\u003e4.2 Modal analysis 185\u003c\/p\u003e \u003cp\u003e4.2.1 The rectangular membrane 185\u003c\/p\u003e \u003cp\u003e4.2.2 The circular membrane 190\u003c\/p\u003e \u003cp\u003e4.3 Forced vibration analysis 197\u003c\/p\u003e \u003cp\u003e4.4 Applications: kettledrum and condenser microphone 197\u003c\/p\u003e \u003cp\u003e4.4.1 Modal analysis 197\u003c\/p\u003e \u003cp\u003e4.4.2 Forced vibration analysis 201\u003c\/p\u003e \u003cp\u003e4.5 Waves in membranes 202\u003c\/p\u003e \u003cp\u003e4.5.1 Waves in Cartesian coordinates 202\u003c\/p\u003e \u003cp\u003e4.5.2 Waves in polar coordinates 204\u003c\/p\u003e \u003cp\u003e4.5.3 Energetics of membrane waves 207\u003c\/p\u003e \u003cp\u003e4.5.4 Initial value problem for infinite membranes 208\u003c\/p\u003e \u003cp\u003e4.5.5 Reflection of plane waves 209\u003c\/p\u003e \u003cp\u003eExercises 213\u003c\/p\u003e \u003cp\u003eReferences 214\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Vibrations of plates 217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Dynamics of plates 217\u003c\/p\u003e \u003cp\u003e5.1.1 Newtonian formulation 217\u003c\/p\u003e \u003cp\u003e5.2 Vibrations of rectangular plates 222\u003c\/p\u003e \u003cp\u003e5.2.1 Free vibrations 222\u003c\/p\u003e \u003cp\u003e5.2.2 Orthogonality of plate eigenfunctions 228\u003c\/p\u003e \u003cp\u003e5.2.3 Forced vibrations 229\u003c\/p\u003e \u003cp\u003e5.3 Vibrations of circular plates 231\u003c\/p\u003e \u003cp\u003e5.3.1 Free vibrations 231\u003c\/p\u003e \u003cp\u003e5.3.2 Forced vibrations 234\u003c\/p\u003e \u003cp\u003e5.4 Waves in plates 236\u003c\/p\u003e \u003cp\u003e5.5 Plates with varying thickness 238\u003c\/p\u003e \u003cp\u003eExercises 239\u003c\/p\u003e \u003cp\u003eReferences 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Boundary value and eigenvalue problems in vibrations 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Self-adjoint operators and eigenvalue problems for undamped free vibrations 243\u003c\/p\u003e \u003cp\u003e6.1.1 General properties and expansion theorem 243\u003c\/p\u003e \u003cp\u003e6.1.2 Green’s functions and integral formulation of eigenvalue problems 252\u003c\/p\u003e \u003cp\u003e6.1.3 Bounds for eigenvalues: Rayleigh’s quotient and other methods 255\u003c\/p\u003e \u003cp\u003e6.2 Forced vibrations 259\u003c\/p\u003e \u003cp\u003e6.2.1 Equations of motion 259\u003c\/p\u003e \u003cp\u003e6.2.2 Green’s function for inhomogeneous vibration problems 260\u003c\/p\u003e \u003cp\u003e6.3 Some discretization methods for free and forced vibrations 261\u003c\/p\u003e \u003cp\u003e6.3.1 Expansion in function series 261\u003c\/p\u003e \u003cp\u003e6.3.2 The collocation method 262\u003c\/p\u003e \u003cp\u003e6.3.3 The method of subdomains 266\u003c\/p\u003e \u003cp\u003e6.3.4 Galerkin’s method 267\u003c\/p\u003e \u003cp\u003e6.3.5 The Rayleigh–Ritz method 269\u003c\/p\u003e \u003cp\u003e6.3.6 The finite-element method 272\u003c\/p\u003e \u003cp\u003eReferences 288\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Waves in fluids 289\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Acoustic waves in fluids 289\u003c\/p\u003e \u003cp\u003e7.1.1 The acoustic wave equation 289\u003c\/p\u003e \u003cp\u003e7.1.2 Planar acoustic waves 294\u003c\/p\u003e \u003cp\u003e7.1.3 Energetics of planar acoustic waves 295\u003c\/p\u003e \u003cp\u003e7.1.4 Reflection and refraction of planar acoustic waves 297\u003c\/p\u003e \u003cp\u003e7.1.5 Spherical waves 300\u003c\/p\u003e \u003cp\u003e7.1.6 Cylindrical waves 305\u003c\/p\u003e \u003cp\u003e7.1.7 Acoustic radiation from membranes and plates 307\u003c\/p\u003e \u003cp\u003e7.1.8 Waves in wave guides 314\u003c\/p\u003e \u003cp\u003e7.1.9 Acoustic waves in a slightly viscous fluid 318\u003c\/p\u003e \u003cp\u003e7.2 Surface waves in incompressible liquids 320\u003c\/p\u003e \u003cp\u003e7.2.1 Dynamics of surface waves 320\u003c\/p\u003e \u003cp\u003e7.2.2 Sloshing of liquids in tanks 323\u003c\/p\u003e \u003cp\u003e7.2.3 Surface waves in a channel 330\u003c\/p\u003e \u003cp\u003eExercises 334\u003c\/p\u003e \u003cp\u003eReferences 337\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Waves in elastic continua 339\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Equations of motion 339\u003c\/p\u003e \u003cp\u003e8.2 Plane elastic waves in unbounded continua 344\u003c\/p\u003e \u003cp\u003e8.3 Energetics of elastic waves 346\u003c\/p\u003e \u003cp\u003e8.4 Reflection of elastic waves 348\u003c\/p\u003e \u003cp\u003e8.4.1 Reflection from a free boundary 349\u003c\/p\u003e \u003cp\u003e8.5 Rayleigh surface waves 353\u003c\/p\u003e \u003cp\u003e8.6 Reflection and refraction of planar acoustic waves 357\u003c\/p\u003e \u003cp\u003eExercises 359\u003c\/p\u003e \u003cp\u003eReferences 361\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA The variational formulation of dynamics 363\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 365\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Harmonic waves and dispersion relation 367\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Fourier representation and harmonic waves 367\u003c\/p\u003e \u003cp\u003eB.2 Phase velocity and group velocity 369\u003c\/p\u003e \u003cp\u003eReferences 372\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC Variational formulation for dynamics of plates 373\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 378\u003c\/p\u003e \u003cp\u003eIndex 379\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402351485271,"sku":"9780470517383","price":71.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470517383.jpg?v=1730480150","url":"https:\/\/bookcurl.com\/products\/vibrations-and-waves-in-continuous-9780470517383","provider":"Book Curl","version":"1.0","type":"link"}