CE 5310 Lecture Notes - Lecture 5: Normal Mode, Wavenumber, Waveguide
Document Summary
The particle displacement from lamb waves actually represent a group of wave mode types. Harmonic wave propagation in along the plane direction is only possible for those combinations of frequency (f) and phase velocity (c) corresponding to standing waves in the thickness (perpendicular of wave propagation direction). These waves must obey the dispersion equation (lamb, 1917), from which dispersion curves can be calculated with for symmetric modes and (1) (cid:4666)(cid:3038)(cid:3118)(cid:2879)(cid:3081)(cid:3118)(cid:4667)(cid:3118)(cid:4675)(cid:2878)(cid:2869) (cid:3047)(cid:3028)(cid:3041)(cid:3080)(cid:3279)(cid:3118)(cid:3404)(cid:3398)(cid:4674) (cid:2872)(cid:3080)(cid:3081)(cid:3038)(cid:3118) (cid:3047)(cid:3028)(cid:3041)(cid:3081)(cid:3279)(cid:3118) (cid:4666)(cid:3038)(cid:3118)(cid:2879)(cid:3081)(cid:3118)(cid:4667)(cid:3118)(cid:4675)(cid:2879)(cid:2869) (2) (cid:2930)(cid:2911)(cid:2924)(cid:3080)(cid:3279)(cid:3118)(cid:3404)(cid:3398)(cid:4674) (cid:2872)(cid:3080)(cid:3081)(cid:3038)(cid:3118) (cid:2930)(cid:2911)(cid:2924)(cid:3081)(cid:3279)(cid:3118) for anti symmetric modes where (cid:573)(cid:2870)(cid:3404)(cid:3104)(cid:3118)(cid:3004)(cid:3291)(cid:3118)(cid:3398)(cid:1863)(cid:2870), (cid:574)(cid:2870)(cid:3404)(cid:3104)(cid:3118)(cid:3004)(cid:3294)(cid:3118)(cid:3398)(cid:1863)(cid:2870), =2 f, d =thickness, cp = longitudinal wave velocity, cs = shear wave velocity, k = wavenumber = (cid:3104)(cid:3004)(cid:3291)(cid:3283), (cid:1829)(cid:3043)(cid:3035)(cid:3404) (cid:1868)(cid:1860)(cid:1853)(cid:1871)(cid:1857) (cid:1874)(cid:1857)(cid:1864)(cid:1867)(cid:1855)(cid:1861)(cid:1872)(cid:1877). Now we consider the case of a plate having mixed boundary conditions with the rayleigh lamb equation for plates. In this section, we consider p and sv waves in the plate under conditions of plane strain.
