Abstract
In this paper, considering the small scale effect, the linear free vibration in pre/post-buckled states and nonlinear dynamic stability of lipid tubules with in-plane movable ends are studied. The small scale effect is characterized by nonlocal elasticity theory. The vibration in pre/post-buckled regions is solved by the differential quadrature method (DQM), and the nonlinear dynamic stability is solved by incremental harmonic balance method (IHBM). In numerical results, the effects of small scale parameter, types of lipid tubule on vibration in pre/post-buckled states and nonlinear dynamic stability are discussed.
Similar content being viewed by others
References
Fang J (2007) Ordered arrays of self-assembled lipid tubules: fabrication and Applications. J Mater Chem 17:3479–3484
Meilander NJ, Pasumarthy MK, Kowalczyk TH, Cooper MJ, Bellamkonda RV (2003) Sustained release of plasmid DNA using lipid microtubules and agarose hydrogel. J Control Release 88:321–331
Meilander NJ, Yu X, Ziats NP, Bellamkonda RV (2001) Lipid-based microtubular drug delivery vehicles. J Control Release 71:141–152
Kameta N, Masuda M, Minamikawa H, Goutev NV, Rim JA, Jung JH, Shimizu T (2005) Selective construction of supramolecular nanotube hosts with cationic inner surfaces. Adv Mater 17:2732–2736
Kameta N, Masuda M, Mizuno G, Morii N, Shimizu T (2008) Supramolecular nanotube endo sensing for a guest protein. Small 4:561–565
Yamada K, Ihara H, Ide T, Fukumoto T, Hirayama C (1984) Formation of helical super structure from single-walled bilayers by amphiphiles with aligo-l-glutamic acid-head group. Chem Lett 13:1713–1716
Yager P, Schoen PE (1984) Formation of tubules by a polymerizable surfactant. Mol Cryst Liq Cryst 106:371–381
Fujima T, Frusawa H, Minamikawa H, Ito K, Shimizu T (2006) Elastic precursor of the transformation from glycolipid nanotube to vesicle. J Phys: Condens Matter 18:3089
Rosso R, Virga EG (1998) Exact statics and approximate dynamics of adhering lipid tubules. Contin Mech Thermodyn 10:107–119
Rosso R, Virga EG (1998) Adhesion by curvature of lipid tubules. Contin Mech Thermodyn 10:359–367
Stepanyants N, Jeffries GD, Orwar O, Jesorka A (2012) Radial sizing of lipid nanotubes using membrane displacement analysis. Nano Lett 12:1372–1378
Zhao Y, Mahajan N, Fang J (2006) Bending and radial deformation of lipid tubules on Self-Assembled Thiol Monolayers. J Phys Chem B 110:22060–22063
Zhao Y, Tamhane K, Zhang X, An L, Fang J (2008) Radial elasticity of self-assembled lipid tubules. ACS Nano 2:1466–1472
Zhao Y, An L, Fang J (2007) Buckling of lipid tubules in shrinking liquid droplets. Nano Lett 7:1360–1363
Zhao Y, An L, Fang J (2009) Buckling instability of lipid tubules with multibilayer walls under local radial indentation. Phys Rev E 80:021911
Zhao Y, Fang J (2008) Zigzag lipid tubules. J Phys Chem B 112:10964–10968
Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface Waves. J Appl Phys 54:4703–4710
Yang F, Chong A, Lam D, Tong P (2002) Couple stress based strain gradient theory for elasticity. Int J Solids Struct 39:2731–2743
Lam D, Yang F, Chong A, Wang J, Tong P (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51:1477–1508
Shen H-S (2011) Nonlinear analysis of lipid tubules by nonlocal beam model. J Theor Biol 276:50–56
Gao Y, Lei F-M (2009) Small scale effects on the mechanical behaviors of protein microtubules based on the nonlocal elasticity theory. Biochem Biophys Res Commun 387:467–471
Civalek Ö, Demir Ç (2011) Bending analysis of microtubules using nonlocal euler–bernoulli beam theory. Appl Math Model 35:2053–2067
Shen H-S (2013) A two-step perturbation method in nonlinear analysis of beams, plates and shells. Wiley, Singapore
Fu Y, Bi R, Zhang P (2009) Nonlinear dynamic instability of double-walled carbon nanotubes under periodic excitation. Acta Mech Solida Sin 22:206–212
Fu Y, Wang J, Mao Y (2012) Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment. Appl Math Model 36:4324–4340
Lau S, Cheung Y, Wu S (1982) A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems. J Appl Mech 49:849–853
Bert CW, Malik M (1996) Differential quadrature method in computational mechanics: a review. Appl Mech Rev 49:1–28
Shen H-S (2011) A novel technique for nonlinear analysis of beams on two-parameter elastic foundations. Int J Struct Stab Dyn 11:999–1014
Nayfeh AH, Emam SA (2008) Exact solution and stability of postbuckling configurations of beams. Nonlinear Dyn 54:395–408
Girish J, Ramachandra L (2005) Thermal postbuckled vibrations of symmetrically laminated composite plates with initial geometric imperfections. J Sound Vib 282:1137–1153
Bolotin VV (1964) The dynamic stability of elastic systems. Holden-Day, San Francisco
Wang CM, Zhang YY, He XQ (2007) Vibration of nonlocal Timoshenko beams. Nanotechnology 18(10):105401
Acknowledgments
This study is supported by the National Natural Science Foundation of China under Grant No. 11272117.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhong, J., Fu, Y. & Tao, C. Linear free vibration in pre/post-buckled states and nonlinear dynamic stability of lipid tubules based on nonlocal beam model. Meccanica 51, 1481–1489 (2016). https://doi.org/10.1007/s11012-015-0320-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-015-0320-z