The dispersion curves for guided waves have been of constant interest in the last decades, because they constitute the starting point for NDE ultrasonic applications. This paper presents an evolution of the semianalytical finite element method, and gives examples that illustrate new improvements and their importance for studying the propagation of waves along periodic structures of infinite width. Periodic boundary conditions are in fact used to model the infinite periodicity of the geometry in the direction normal to the direction of propagation. This method allows a complete investigation of the dispersion curves and of displacement/stress fields for guided modes in anisotropic and absorbing periodic structures. Among other examples, that of a grooved aluminum plate is theoretically and experimentally investigated, indicating the presence of specific and original guided modes.

ABSTRACT--An experimental method is developed to per-Z*(e0) form Hopkinson tests by means of viscoelastic bars by con-(~(o3) sidering the wave propagation attenuation and dispersion due s to the material rheological properties and the bar radial inertia ~l(t) (geometric effect). A propagation coefficient, representative of the wave dispersion and attenuation, is evaluated experi-mentally. Thus, the Pochhammer and Chree frequency equation is not necessary. Any bar cross-section shapes can be employed, and the knowledge of the bar mechanical properu ties is useless. The propagation coefficients for two PMMA v bars with different diameters and for an elastic aluminum alloy oJ bar are evaluated. These coefficients are used to determine P the normal forces at the free end of a bar and at the ends of cr two bars held in contact. As an application, the mechanical impedance of an accelerometer is evaluated.KEY WORDS--Hopkinson or Kolsky viscoelastic bars, geometric effects due to the radial inertia, wave attenuation, wave dispersion, accelerometer impedance = mechanical impedance = attenuation coefficient = longitudinal strain = longitudinal strain due to the incident wave = longitudinal strain due to the reflected wave = propagation coefficient = frequency = angular frequency = mass density of the bar = normal stress

Guided torsional waves in a bar with a noncircular cross section have been exploited by previous researchers to measure the density of fluids. However, due to the complexity of the wave behavior in the noncircular cross-sectional shape, the previous theory can only provide an approximate prediction; thus the accuracy of the measurement has been compromised. In this paper, a semianalytical finite element method is developed to model accurately the propagation velocity and leakage of guided waves along an immersed waveguide with arbitrary noncircular cross section. An accurate inverse model is then provided to measure the density of the fluid by measuring the change of the torsional wave speed. Experimental results obtained with a rectangular bar in a range of fluids show very good agreement with the theoretical predictions. Finally, the potentials to use the model for sensor optimization are discussed.

In this paper, constitutive relations are solved in the Fourier domain using a finite-element-based commercial software. The dynamic responses of viscoelastic bars or plates to either thermal or mechanical loads are predicted by considering complex moduli (Young, Poisson, stiffness moduli) as input data. These moduli are measured in the same frequency domain as that which is chosen for modeling the wave propagation. This approach is simpler since it suppresses the necessity of establishing a rheological model. Specific output processing then allows the numerical predictions to be compared to analytical solutions, in the absence of scatterers. The performances of this technique and its potential for simulating more complicated problems like diffraction of waves or for solving inverse problems are finally discussed.

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