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Multi-point analysis of the virtual cell hinge element method

Zero, to make the equation (3) are non-zero solution of displacement,[link widoczny dla zalogowanych], you need to det a k 一一 0 (4) L / e ~ t42J free on board-style Lamb Lang layered transition equation of the general characteristics. Because G is a real matrix, so equation (4) is a nonlinear equation with real coefficients. If the medium parameters have been determined, using numerical methods, readily available from the characteristic equation of Lamb wave dispersion curves. Obtain the characteristic equation, the use of equation (3) board can be obtained in the displacement and stress distribution. 1.2 medium parameters on the impact of dispersion curves for the single-layer media,[link widoczny dla zalogowanych], the mass density of the Lamb transition did not affect the dispersion, if more in order, and h on the dimensionless dispersion curves (ie, c / Vs ~ h / a for the crossing length), only the orange parking ratio as an independent factor. Figure 2 Poisson's ratio to the different bending wave case (the first step mode) Lamb dispersion curves cross. It can be seen from the figure, with the Poisson ratio increases,[link widoczny dla zalogowanych], the velocity corresponding to the same frequency also slightly increased, but the impact of high frequency, a greater degree of u. Consider an extreme case, when the board is very thick or very high frequency, if a 0 to 0.5, the corresponding c / Vs range is from 0.87 to 0.96. In actual projects. According to state media, the selected material properties and Poisson's ratio difference between the actual situation is generally not more than 0.1, the resulting velocity error will be less than 5%. h, Figure 2, frequency of knocking Park juniper curve than on the ship of the plywood, the relative changes in mass density of each layer of the dispersion characteristics of Lamb crossing a slight impact. In general, the density difference between layers will slightly lower the phase velocity of Lamb waves, but the effect is small, the actual calculation is negligible. 2 double-layer plate for the Lamb wave dispersion characteristics of double-free board, Orange Park because of the mass density and dispersion curves than the effect of not, you can take layers of uniform Poisson's ratio of 0.25, the mass density the same. The following analyzes the transition layer Q ratio dispersion curves of Vibration Engineering 11 368 2.1 velocity ratio of volume Figure 3 (a), 3 (b) shear wave velocity is given six curved than the corresponding wave and longitudinal wave of the Lamb wave dispersion curves, layers of parameters shown in Figure, graph coordinates to plate thickness h and the dimensionless velocity V () curve crossing type C. b) a vertical cross-type mouth 0.25,[link widoczny dla zalogowanych], hI = h2, the white curve on the bottom s2/ysJ-1.0, 105,[link widoczny dla zalogowanych],1.2,1.5,25 t5 Figure 3 velocity ratio of the frequency curve of the King flexural wave type, and from Figure 3 (a) shows the same frequencies as the Lamb wave velocity increases; and in a frequency band in question, the dispersion curve with a peak velocity greater than the peak more apparent. As the frequency increases, wavelength decreases, when the wavelength is smaller than the thickness of the low velocity layer, the approximate dispersion curve is a straight line, and c = V for the asymptotic line for low-velocity layer of the half-space Rayleigh wave speed. For the longitudinal cross-type, two types of dispersion curves need to discuss the situation when V 2, that 2t <h.), the displacement plate mainly in the low-velocity layer, the distribution of forms and half-space similar to the situation in the Rayleigh transition. This high frequency dispersion curves trend. The same situation and the analysis of stress distribution can also be reached the same conclusion. Figure 4 (b) the dashed line (h/2t = 1.2) corresponding to Figure 3 (b) A point in the displacement and stress distribution, A crossing point in the longitudinal curve of the Seen by the displacement map, this time the share of high-speed layer higher percentage of energy, the spread of Lamb by crossing the upper and lower levels of the common constraints. As the frequency continues to increase, decreasing velocity, the energy distribution gradually moved to low-velocity layer. Based on the above analysis, the velocity ratio and thickness ratio of Lamb wave dispersion characteristics of the important factors, especially on the vertical transition

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