Nonlinear vibration analysis of fractional viscoelastic Euler–Bernoulli nanobeams based on the surface stress theory

作     者：M.Faraji Oskouie R.Ansari F.Sadeghi 

作者机构：Department of Mechanical EngineeringUniversity of Guilan 

出 版 物：《Acta Mechanica Solida Sinica》 (固体力学学报（英文版）)

年 卷 期：2017年第30卷第4期

页      面：416-424页

核心收录：

学科分类：08[工学] 0835[工学-软件工程] 0802[工学-机械工程] 080101[工学-一般力学与力学基础] 080201[工学-机械制造及其自动化] 0801[工学-力学（可授工学、理学学位）] 

主　　题：Fractional calculus Viscoelastic nanobeam Nonlinear vibrations 

摘      要：The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.