TAILIEUCHUNG - Advances in Piezoelectric Transducers Part 5

Tham khảo tài liệu 'advances in piezoelectric transducers part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Modeling and Investigation of One-Dimensional Flexural Vibrating Mechatronic Systems with Piezoelectric Transducers 43 W1 hp - hp hk- yw IV. Eb 1 EpAp I hp yw 1 EbAw V hp hk - yw A I h - yw E_ q-----p Jw A. I h hk y . w p k Ư w 1 EpAp I hp yw - 1 l EbAw V hp hk yw J 48 49 To determine the value of shear stress on the plane of contact of the transducer and beam the following dependence was used x y . T - Sz y Jw b y 50 where SZ y is a static moment of cut off part of the composite beam s cross-section relative to the weighted neutral axis. Transverse force T x t can be calculated as a derivative of bending moment acting on the beam s cross-section T x S H W x t - W4 -Ạ t x õx 51 where W CiiEApWi yw hp Ì . hbEpJw Ệ hbWiCiiEApJw r -1 0 5hp yw. . r- 7 b b ------ Í -y A 1 ---- -yw hp hk 2 J hb yw -hp-hk hb yw -hp-hk L Jw 7 W4 CiiEAp W2 1 - yw hp Ì W 1 CiiEhbApJw r -1 Ệ 0 5hp -y 1 fl 7. TT- Aw f -yw hp hk . 2 J hb yw - hp- hk L J ỵ J Finally the discrete-continuous mathematical model of the system can be described as 52 53 Ổ2 y x t 4 ổ ổ4y x t Sz y ổ ổ2 .-1 2 -a I 1 T7 l 4 7 7 I 1 77 n r HW3 i x t -HW4 1 f F f ổt V St J 5x 2PiJwb at J3x 54 3Ur t . lbd31 lvb 33T . RZCP UC t -p-1 S1 x t p . 1 - k312 -UC t Z P 5t CV 7 Cr s11E 1V 7 Cphp 31 C Obtained system of equations is a mathematical model with assumptions of shear stress and eccentric tension of the glue layer. 44 Advances in Piezoelectric Transducers Discrete - continuous mathematical model taking into account a bending moment generated by the transducer and eccentric tension of a glue layer between the piezoelectric damper and beam s surface Taking into account parameters of the combined beam introduced in section the discrete-continuous mathematical model with influence of the glue layer on the dynamic characteristic of the system was developed. However in this model the impact of the piezoelectric transducer was described as a bending moment similarly as in the mathematical model with the assumption of .

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