Exact solution to the structural instability of a parallel array of mutually attracting identical simply-supported plates

• Autorzy: Wang X. , Liu L.
• Języki publikacji: EN

Abstrakty

EN

By means of the theory of elasticity, we investigate the structural instability of a parallel array of identical simply-supported plates. One plate interacts with the neighboring plates through surface attractive forces. The proposed method is based on the 2 × 2 transfer matrix for a plate and on the solution of the generalized eigenvalue problem for the plate array. Analytical expressions of the critical interaction coefficients for two, three and four interacting plates are obtained when the end-effect of the plates at the ends of the parallel array and the surface energy of the plates are ignored. The influence of the end-effect and surface energy on the critical interaction coefficient is also numerically studied. Our solution is valid whether the plates are thin or extremely thick.

Słowa kluczowe

EN

structural instability; surface force; critical interaction coefficient; transfer matrix; generalized eigenvalue problem; exact solution

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2017
• Tom: Vol. 69, nr 3
• Strony: 243--256
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Wang X.

• School of Mechanical and Power Engineering East China University of Science and Technology 130 Meilong Road Shanghai 200237, China

autor

Liu L.

• School of Mechanical and Power Engineering East China University of Science and Technology 130 Meilong Road Shanghai 200237, China

Bibliografia

• 1. J. Zhu, C.Q. Ru, A. Mioduchowski, Structural instability of a parallel array of mutually attracting identical microbeams, J. Micromech. Microeng., 16, 2220–2229, 2006.
• 2. J. Zhu, C.Q. Ru, A. Mioduchowski, Surface-forces-driven instability of comb-drive microcantilevers in MEMS, J. Adhesion Sci. Tech., 20, 1125–1146, 2006.
• 3. J. Zhu, C.Q. Ru, A. Mioduchowski, Instability of a large coupled microbeam array initialized at its two ends, J. Adhesion, 83, 195–221, 2007.
• 4. J. Zhu, Pull-in instability of two opposing microcantilever arrays with different bending rigidities, Int. J. Mech. Sci., 50, 55–68, 2008.
• 5. A. Ramezani, A. Alasty, Instability of nanocantilever arrays in electrostatic and van der Waals interactions, J. Phys. D: Appl. Phys., 42, 225506, 2009.
• 6. A. Ramezani, A. Alasty, Combined action of Casimir and electrostatic forces on nanocantilever arrays, Acta Mech., 212, 305–317, 2010.
• 7. L.H. He, J. Jiang, Transient mechanical response of laminated elastic strips with viscous interfaces in cylindrical bending, Compos. Sci. Tech., 63, 821–828, 2003.
• 8. X. Wang, R. Jing, Surface instability of an imperfectly bonded thin elastic film under surface van der Waals forces, Z. Angew. Math. Phys., 68, (1), 1–20, 2017.