Impulse response backscattering measurements are presented and interpreted for the scattering of obliquely incident plane waves by air-filled finite cylindrical shells immersed in water. The measurements were carried out to determine the conditions for significant enhancements of the backscattering by thick shells at large tilt angles. The shells investigated are made of stainless steel and are slender and have thickness to radius ratios of 7.6% and 16.3%. A broadband PVDF ͑polyvinylidene fluoride͒ sheet source is used to obtain the backscattering spectral magnitude as a function of the tilt angle ͑measured from broadside incidence͒ of the cylinder. Results are plotted as a function of frequency and angle. These plots reveal large backscattering enhancements associated with elastic excitations at high tilt angles, which extend to end-on incidence in the coincidence frequency region. Similar features are present in approximate calculations for finite cylindrical shells based on full elasticity theory and the Kirchhoff diffraction integral. One feature is identified as resulting from the axial ͑meridional ray͒ propagation of the supersonic a 0 leaky Lamb wave. A simple approximation is used to describe circumferential coupling loci in frequency-angle space for several surface waves. The resulting loci are used to identify enhancements due to the helical propagation of the subsonic a 0Ϫ Lamb wave. © 1998 Acoustical Society of America. ͓S0001-4966͑98͒04302-1͔PACS numbers: 43.30.Gv, 43.20.Fn ͓DLB͔ INTRODUCTIONRecent high-frequency sonar images of truncated cylindrical shells indicate that the visibility of the ends of the shell can be improved by an elastic response of the shell.1 The enhancements are associated with a category of lth class of leaky ray shown in Fig. 1. The enhancement occurs when the tilt angle ␥ of the cylinder is close to the leaky wave coupling angle l ϭsin Ϫ1 (c/c l ), where c l is the phase velocity of the leaky wave and c is the speed of sound in the surrounding water. This ray is referred to as a meridional ray 2 since it is propagated along the meridian defined by the direction of the incident wave vector and the cylinder's axis. An analysis shows that the backscattering enhancement is associated with the vanishing of Gaussian curvature of the wavefront backscattered in the direction of the receiver. The enhancements reported 1 were for tilts in the vicinity of 18°and 35°corre-sponding to the excitation of symmetric and antisymmetric (s 0 and a 0 ͒ generalizations of leaky Lamb waves on the stainless steel cylinder used in those experiments. The purpose of the present paper is to document the existence of high-frequency backscattering enhancements for tilted cylindrical shells relevant to larger values of the tilt ␥ and in some cases, extending to ␥ϭ90°͑i.e., end-on incidence͒.The method of our investigation concerns the global response in the frequency-angle domain rather than the spatial responses emphasized in Ref.1. There are several reasons for identifying such high-frequency enhancement...

We have performed laser-Doppler vibrometry measurements of the vibration of a double-paddle oscillator. Seven modes with principally out-of-plane motion have been identified. Their resonance frequencies and mode shapes are in excellent agreement with three-dimensional finite element simulations. We have found that the second antisymmetric torsional mode has exceptionally good vibration isolation of its mode shape. This explains its extremely small low temperature internal friction below 10 K (2ϫ10 Ϫ8 3,4 Oscillators of similar design have been used in a variety of applications. 5,6 However, extending these designs to microelectromechanical systems ͑MEMS͒, a subject of recent interest, has not been as successful. The commonly achieved low Q in MEMS oscillators is a key obstacle limiting the applications of such technology, particularly in the area of rf electronics.7 In order to improve our understanding of the loss mechanisms that are at work in silicon based oscillators, and in particular to achieve higher Q versions of the DPOs and MEMS oscillators in general, we have investigated the dynamics and loss mechanisms of a DPO.In this letter we report laser Doppler vibrometry ͑LDV͒ measurements of the lowest seven out-of-plane modes of a DPO and the corresponding finite element modeling. Direct LDV measurements have enabled us to establish a detailed finite element method ͑FEM͒ 8 predictive capability for the frequencies and mode shapes of the DPO. A detailed prediction of the Q is not possible because of the coupling of the oscillator to its external environment. Nevertheless, an empirical relationship between the mode shapes and internal friction is found which provides insight into the damping mechanisms and may be a useful guide to the development of high Q oscillators using FEM tools.The silicon oscillator was made of a 300 m thick, floatzone refined, double-side polished, ͗100͘ oriented, and N-doped silicon substrate with ϳ2 k⍀ cm resistivity. Its long axis was along the ͗110͘ orientation. The oscillator was epoxied to an Invar block inside a vacuum chamber ͑1 mTorr͒. The oscillator was driven capacitively by an electrode mounted under one of the wings. A second identical electrode under the opposite wing was used as a detector to provide a continuous feedback signal for the drive electronics. This setup enabled stable operation of the oscillator at resonance. Capacitive coupling was achieved by depositing a 400 Å gold film onto the side of the DPO which faced the electrodes. The head and neck were not coated in order to minimize the energy loss caused by metal films 9 to the second antisymmetric torsion mode. For details of the oscillator setup, see Ref. 10.With the oscillator driven in a selected resonance its outof-plane surface velocity was measured with a LDV ( ϭ780 nm, 7 mW͒.11 Optical access for the laser was made through an optical window in the chamber. The sensitivity of the instrument for reflection from the polished bare silicon surface corresponds to a detection threshold of 0.1-1 Å over the freq...

Impulse backscattering measurements by a thick-walled finite cylindrical shell are examined in the time-frequency domain to identify and characterize individual ray contributions from generalized Lamb waves excited on the shell. Previous experiments and analysis in the frequency-aspect angle domain [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)] indicate that large backscattering enhancements occur in the midfrequency region for the shell tilted at large angles. Presently this experimental data is examined in the time-frequency domain for selected angles of incidence. Individual ray contributions are evident and their evolution over aspect angle is discussed. The most prominent contribution is due to the meridional ray of the a0 leaky Lamb wave. This feature distinctly highlights the truncation of the shell and is found over a range of aspect angles spanning 200 degrees for the frequencies examined. Also observed are periodic features corresponding to end-reflected helical waves of the a0-. These scattering features are significantly different from those reported for thin-walled finite cylinders at low frequencies. The present results may be useful for target identification and localization and as a comparison tool for high-frequency computational scattering models.

The method of modulated ultrasonic radiation pressure, previously used to drive the capillary modes of drops and bubbles, is used to excite the capillary modes of a cylindrical oil bridge in a Plateau tank. Specific modes may be selected by adjusting the modulation frequency and the location or orientation of the bridge in the ultrasonic field. Mode frequencies were measured as a function of the slenderness for the lowest two axisymmetric modes and two nonaxisymmetric modes. The frequencies of the lowest modes agree with an approximate theory which neglects viscous corrections where the interfacial tension is a fitted parameter.

High-frequency scattering enhancements from a submerged infinite cylindrical shell are studied by means of partial wave series (PWS) calculations and a ray approximation. For certain oblique angles of incidence it is possible to launch a generalized leaky Lamb wave which propagates strictly in the axial direction on the shell. This meridional leaky wave radiates with a locally flat wavefront curvature and produces large far-field amplitudes over a range of tilt angles. When combined with a reflection from a discontinuity in the shell, this process can give rise to large backscattering enhancements at large tilt angles for thick finite cylindrical shells [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785–794 (1998)] and is present in sonar images. A convolution formulation ray theory for the far-field meridional ray amplitude is compared with the exact PWS solution in the region where enhancements are observed for both the a0 and s0 Lamb waves. The ray theory correctly predicts both the peak enhancement amplitude and the general shape of the enhancement curve.