B. Loh and P. I. Ro, an object transport system using flexural ultrasonic progressive waves generated by two-mode excitation, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol.47, issue.4, pp.994-999, 2000.

X. Li, oscillation propagating in non-contact linear piezoelectric ultrasonic levitation transporting system?From solid state to fluid media, Proc. IEEE Micro Electro Mechanical Systems, pp.951-956, 1991.

. Wang and J. Hata, Theoretical and experimental investigation of traveling wave propagation on a several-millimeter-long cylindrical pipe driven by piezoelectric ceramic tubes, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol.57, issue.7, pp.1600-1611, 2010.

M. Kuribayashi, Excitation conditions of flexural traveling waves for a reversible ultrasonic linear motor, The Journal of the Acoustical Society of America, vol.77, issue.4, pp.1431-1435, 1985.
DOI : 10.1121/1.392037

Y. Tanaka and . Kikushima, Active Wave Control of a Flexible Beam. Proposition of the Active Sink Method., JSME international journal. Ser. 3, Vibration, control engineering, engineering for industry, vol.34, issue.2, pp.159-167, 1991.
DOI : 10.1299/jsmec1988.34.159

I. Gabai and . Bucher, Spatial and Temporal Excitation to Generate Traveling Waves in Structures, Journal of Applied Mechanics, vol.77, issue.2
DOI : 10.1115/1.3176999

B. Vloebergh, F. Gabay, J. Bucher, and M. Feldman, study and optimization of traveling wave generation in finite-length beams on the sensing and tuning of progressive structural vibration waves, Math. Comput. Simul. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol.81, issue.52 9, pp.290-301, 2005.

I. Gabai and . Bucher, Excitation and sensing of multiple vibrating traveling waves in one-dimensional structures, Journal of Sound and Vibration, vol.319, issue.1-2, pp.406-425, 2009.
DOI : 10.1016/j.jsv.2008.06.013

B. Nogarède, analytical modelling of travelling-wave piezomotor stators using a variational approach, Eur. Phys. J. AP, vol.6, issue.1, pp.71-79, 1999.

F. Giraud and B. , A torque estimator for a traveling wave ultrasonic motor - application to an active claw, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.53, issue.8, pp.1468-1477, 2006.
DOI : 10.1109/TUFFC.2006.1665104

URL : https://hal.archives-ouvertes.fr/hal-01110739

I. Bucher, Estimating the ratio between travelling and standing vibration waves under non-stationary conditions, Journal of Sound and Vibration, vol.270, issue.1-2, pp.341-359, 2004.
DOI : 10.1016/S0022-460X(03)00539-X

M. S. Riaz and B. F. Feeny, Proper Orthogonal Modes of a Beam Sensed with Strain Gages, Journal of Vibration and Acoustics, vol.125, issue.1, pp.129-131, 2003.
DOI : 10.1115/1.1521950