@article{(Open Science Index):https://publications.waset.org/pdf/10006602,
	  title     = {A Refined Nonlocal Strain Gradient Theory for Assessing Scaling-Dependent Vibration Behavior of Microbeams},
	  author    = {Xiaobai Li and  Li Li and  Yujin Hu and  Weiming Deng and  Zhe Ding},
	  country	= {},
	  institution	= {},
	  abstract     = {A size-dependent Euler–Bernoulli beam model, which
accounts for nonlocal stress field, strain gradient field and higher
order inertia force field, is derived based on the nonlocal strain
gradient theory considering velocity gradient effect. The governing
equations and boundary conditions are derived both in dimensional
and dimensionless form by employed the Hamilton principle. The
analytical solutions based on different continuum theories are
compared. The effect of higher order inertia terms is extremely
significant in high frequency range. It is found that there exists
an asymptotic frequency for the proposed beam model, while for
the nonlocal strain gradient theory the solutions diverge. The effect
of strain gradient field in thickness direction is significant in low
frequencies domain and it cannot be neglected when the material
strain length scale parameter is considerable with beam thickness.
The influence of each of three size effect parameters on the natural
frequencies are investigated. The natural frequencies increase with
the increasing material strain gradient length scale parameter or
decreasing velocity gradient length scale parameter and nonlocal
parameter.},
	    journal   = {International Journal of Mechanical and Mechatronics Engineering},
	  volume    = {11},
	  number    = {3},
	  year      = {2017},
	  pages     = {551 - 561},
	  ee        = {https://publications.waset.org/pdf/10006602},
	  url   	= {https://publications.waset.org/vol/123},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 123, 2017},
	}