By J.H. Jeans, M.A., F.R.S
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279-283, ISSN 03015629 Chen, X. & Lal A. (2006). C. & Wu, S. (2002). A Design Approach of Tonpiltz Transducer, Jpn. J. Appl. , Vol. 6A, (June 2002), pp. ; Wu, S. C. (2004). 115, No. W. K. (2002). Smart Ultrasonic Transducer for Wire-Bonding Applications, Materials Chemistry and Physics, Vol. 95-100, ISSN 0254-0584 Feng, R. (1999). ; Minor, K. & Martin, S. (2004). Acoustic Streaming in Micro-Scale Cylindrical Channels, Applied Acoustics, Vol. W. (2001). Ultrasound-Enhanced Thrombolysis. Echocardiography, Vol.
2. Fig. 2. Shape of the mechanical subsystem The equation of free vibration of the mechanical subsystem was derived in agreement with d’Alembert’s principle. The external force F(t) was neglected. Taking into account equilibrium of forces and bending moments acting on the beam’s element, after transformations a well known equation was obtained: 2 y x, t t 2 a4 4y x,t x 4 , (7) where: a4 Eb J b . b Ab (8) Ab and Jb are the area and moment of inertia of the beam’s cross-section. In order to determine the solution of the differential equation of motion (7) Fourier method of separation of variables was used.
1, (2009), pp. , & Płaczek M. (2009c). , & Płaczek M. (2010a). Selection of Parameters of External Electric Circuit for Control of Dynamic Flexibility of a Mechatronic System. Solid State Phenomena, Vol. 164, (2010), pp. , & Płaczek M. (2010b). Development of Mathematical Model of a Mechatronic System. Solid State Phenomena, Vol. 164, (2010), pp. , & Płaczek M. (2010c). The analysis of vibrating systems based on the exact end approximate method. International Journal of Modern Manufacturing Technologies, Vol.