Δn alternates its sign across nodal points (zeros) when m ¼ 2 and 3. The average of
Δn over a cross section is zero. Therefore this buckling-induced Δn does not
contribute directly to the axial flow of electrons in a device operating with the
extensional deformation of the beam, but it does produce a lateral electric field
that acts on the electrons. The distribution of the normalized φ looks the same as Δn
and is not shown.
For beams with other end supports, the critical buckling loads can be determined
[5] using the concept of the effective length of a beam according to the mechanics of
materials [7]. Piezoelectric semiconductor beam devices often use beam arrays
between two films (see Fig. 4.13), which usually operate under a pressure. The
buckling load for a single beam in Eq. (4.91) can be used to determine the buckling
pressure of an array [5].
References
1. Z.L. Wang, Piezotronics and Piezo-Phototronics (Science Press, Beijing, 2012). in Chinese
2. C.L. Zhang, X.Y. Wang, W.Q. Chen, J.S. Yang, Bending of a cantilever piezoelectric semiconductor fiber under an end force, in Generalized Models and Non-Classical Approaches in
Complex Materials, ed. by H. Altenbach et al., (Springer, Cham, 2018), pp. 261–278
3. X.Y. Dai, F. Zhu, Z.H. Qian, J.S. Yang, Electric potential and carrier distribution in a piezoelectric semiconductor nanowire in time-harmonic bending vibration. Nano Energy 43, 22–28
(2018)
4. Y.X. Liang, Y.T. Hu, J.S. Yang, Transient bending vibration of a piezoelectric semiconductor
nanofiber under a suddenly applied shear force. Acta Mech. Solida Sin. 32, 688–697 (2019)
5. C. Liang, C.L. Zhang, W.Q. Chen, J.S. Yang, Static buckling of piezoelectric semiconductor
fibers. Mater. Res. Express 6, 125919 (2020)
6. J.S. Yang, Equations for the extension and flexure of a piezoelectric beam with rectangular cross
section and applications. Int. J. Appl. Electromagn. Mech. 9, 409–420 (1998)
7. J.M. Gere, S.P. Timoshenko, Mechanics of Materials, 2nd edn. (Wadsworth, Belmont, 1984)
Fig. 4.13 A beam array
under pressure
References
111
Δn over a cross section is zero. Therefore this buckling-induced Δn does not
contribute directly to the axial flow of electrons in a device operating with the
extensional deformation of the beam, but it does produce a lateral electric field
that acts on the electrons. The distribution of the normalized φ looks the same as Δn
and is not shown.
For beams with other end supports, the critical buckling loads can be determined
[5] using the concept of the effective length of a beam according to the mechanics of
materials [7]. Piezoelectric semiconductor beam devices often use beam arrays
between two films (see Fig. 4.13), which usually operate under a pressure. The
buckling load for a single beam in Eq. (4.91) can be used to determine the buckling
pressure of an array [5].
References
1. Z.L. Wang, Piezotronics and Piezo-Phototronics (Science Press, Beijing, 2012). in Chinese
2. C.L. Zhang, X.Y. Wang, W.Q. Chen, J.S. Yang, Bending of a cantilever piezoelectric semiconductor fiber under an end force, in Generalized Models and Non-Classical Approaches in
Complex Materials, ed. by H. Altenbach et al., (Springer, Cham, 2018), pp. 261–278
3. X.Y. Dai, F. Zhu, Z.H. Qian, J.S. Yang, Electric potential and carrier distribution in a piezoelectric semiconductor nanowire in time-harmonic bending vibration. Nano Energy 43, 22–28
(2018)
4. Y.X. Liang, Y.T. Hu, J.S. Yang, Transient bending vibration of a piezoelectric semiconductor
nanofiber under a suddenly applied shear force. Acta Mech. Solida Sin. 32, 688–697 (2019)
5. C. Liang, C.L. Zhang, W.Q. Chen, J.S. Yang, Static buckling of piezoelectric semiconductor
fibers. Mater. Res. Express 6, 125919 (2020)
6. J.S. Yang, Equations for the extension and flexure of a piezoelectric beam with rectangular cross
section and applications. Int. J. Appl. Electromagn. Mech. 9, 409–420 (1998)
7. J.M. Gere, S.P. Timoshenko, Mechanics of Materials, 2nd edn. (Wadsworth, Belmont, 1984)
Fig. 4.13 A beam array
under pressure
References
111