TAILIEUCHUNG - Ebook The physics of vibrations and waves (6th edition): Part 2

(BQ) Part 2 book "The physics of vibrations and waves" has contents: Waves in more than one dimension, fourier methods, waves in optical systems, interference and diffraction, wave mechanics, non linear oscillations and chaos, non linear waves, shocks and solitons. | 9 Waves in More than One Dimension Plane Wave Representation in Two and Three Dimensions Figure shows that in two dimensions waves of velocity c may be represented by lines of constant phase propagating in a direction k which is normal to each line, where the magnitude of k is the wave number k ¼ 2 = . The direction cosines of k are given by l¼ k1 ; k m¼ k2 k 2 2 where k 2 ¼ k 1 þ k 2 and any point rðx; yÞ on the line of constant phase satisfies the equation lx þ my ¼ p ¼ ct where p is the perpendicular distance from the line to the origin. The displacements at all points rðx; yÞ on a given line are in phase and the phase difference between the origin and a given line is ¼ 2 2 (path difference) ¼ p ¼ k Á r ¼ k 1x þ k 2y ¼ kp Hence, the bracket ð!t À Þ ¼ ð!t À kxÞ used in a one dimensional wave is replaced by ð!t À k Á rÞ in waves of more than one dimension, . we shall use the exponential expression e ið!tÀkÁrÞ In three dimensions all points rðx; y; zÞ in a given wavefront will lie on planes of constant phase satisfying the equation lx þ my þ nz ¼ p ¼ ct The Physics of Vibrations and Waves, 6th Edition H. J. Pain # 2005 John Wiley & Sons, Ltd 239 240 Waves in More than One Dimension k2 y l= k k1 m= k1 Crest Trough k k2 k lx + my = p = ct p λ 2 r(x ⋅y) k ⋅ r = k1x + k2y = kp x Figure Crests and troughs of a two-dimensional plane wave propagating in a general direction k (direction cosines l and m). The wave is specified by lx þ my ¼ p ¼ ct, where p is its perpendicular distance from the origin, travelled in a time t at a velocity c where the vector k which is normal to the plane and in the direction of propagation has direction cosines l¼ k1 ; k m¼ k2 ; k n¼ k3 k 2 2 2 (so that k 2 ¼ k 1 þ k 2 þ k 3 Þ and the perpendicular distance p is given by kp ¼ k Á r ¼ k 1 x þ k 2 y þ k 3 z Wave Equation in Two Dimensions We shall consider waves propagating on a stretched plane membrane of negligible thickness having a mass .

• Cơ khí - Chế tạo máy
• The physics of vibrations
• Waves in more than one dimension
• Fourier methods
• Waves in optical systems
• Interference and diffraction
• Wave mechanics
• Simple harmonic motion
• Damped simple harmonic motion
• The forced oscillator
• Transverse wave motion
• coupled oscillations
• Longitudinal waves
• Eddy current damper
• Suppression of vibrations
• Finite element analysis
• FEA Software package
• COMSOL multi physics
• Lecture General Physics II
• Bài giảng Vật lý đại cương 2
• Hooke’s law
• Mass system
• Elastic potential energy
• Energy transformations
• Vietnam Journal of Mechanics
• Wave energy converter using linear generator
• Wave energy convertor
• Linear electrical generator
• Permanent magnet generators
• Improved approximations for the rayleigh wave velocity in
• The rayleigh wave velocity in
• Maximum percentage errors
• Approximating the secular equation
• Can dislocations accelerate through the shear wave speed ”barrier”
• Dislocations accelerate through
• The velocity equals the shear wave speed
• The presence of acceleration
• Summary of mechanical engineering and engineering mechanics doctoral thesis
• The mechanical model and calculating design
• Electrical generator for sea wave energy
• The electrical generator
• Vietnams sea condition
• Introduction to quantum mechanics
• The basic theory
• The wave function
• Independent schrodinger equation
• Quantum mechanics in three dimensions
• Separation phenomenon in transonic flows produced
• Interaction between shock wave and boundary layer
• The physical nature
• Invicid transonic flows
• The full potential equation
• Simulation of transient ultrasonic wave propagation
• Fluid loaded heterogeneous cortical bone
• Functionally graded anisotropic material
• The ultrasound axial transmission technique
• The cortical layer
• Investigating corrugated laminated composite plates of wave form
• Investigating corrugated laminated composite plates
• Shallow cylindrical shells
• Empirical formulas and sufficiently
• Calculation of the wave parameters
• Sea dyke design and upgrading
• The sea dyke design
• The coastal line
• The project concerning the input data
• Two dimension numerical modeling
• Wave and wind induced currents
• Bed morphology evolution
• Phan Ri Binh Thuan coastal zone
• Experimental results on sand transport under waves
• Large scale wave flume
• Delta Flume of Delft Hydraulics
• Regular and irregular waves
• The basis of incorporating measurement
• Storm wave modeling
• Swan comparison of measurement data
• Modeling results for the storm muifa 11 2004
• The Red River Delta
• The SWAN model
• Wave Function
• Time Independent
• Schrödinger Equation
• Formalism
• Quantum Mechanics
• Three Dimensions
• Identical Particles
• Communications in Physics
• The modern induced matter approach
• General relativity for quantum mechanics
• Time space symmetry
• Microscopic cosmological model
• Wave like solution
• Klein Gordon Fock equation
• Decision making
• Information measure
• Statistical mechanics
• Enormously complex interact
• Lecture Physics A2
• Bài giảng Vật lý đại cương A2
• Vật lý đại cương A2
• Heisenberg’s uncertainty principle
• Matter wave
• De Broglie’s hypothesis
• Discrete atomic emission line
• Bài giảng Vật lý A2
• Diffraction of light
• Wave particle duality
• A method of skin frictional resistant reduction
• Creating small bubbles at bottom of ships
• Skin frictional resistant reduction
• Regular wave conditions
• Asymptotic in krylov bogoliubov mitropolsky sense solution
• Krylov bogoliubov mitropolsky
• Constructing approximate solut ions
• Klein Gordon IJretherton equations
• Lecture in Physicsplanetary atmospheres
• unbalanced flows
• fluid mechanics
• geophysical flows
• spontaneous wave