A New Beam Element for Static, Free and Forced Vibration Responses of Microbeams Resting on Viscoelastic Foundation Base
- PDF / 2,600,520 Bytes
- 17 Pages / 595.276 x 790.866 pts Page_size
- 19 Downloads / 176 Views
RESEARCH PAPER
A New Beam Element for Static, Free and Forced Vibration Responses of Microbeams Resting on Viscoelastic Foundation Based on Modified Couple Stress and Third‑Order Beam Theories Reza Damghanian1 · Kamran Asemi1 · Masoud Babaei2 Received: 27 April 2020 / Accepted: 27 October 2020 © Shiraz University 2020
Abstract In this paper, a new beam element based on third-order Reddy beam theory and modified couple stress theory is introduced for static and dynamic analyses of microbeams. The beam is resting on Kelvin–Voigt-type viscoelastic foundation. Equilibrium equations are derived by using Hamilton’s principle. Galerkin finite element method is applied to the governing equations, and shape functions of the new beam element have been derived. As a result, applying only six elements are suitable for assessing beam behavior precisely, and it is beneficial due to the reduction in computation time. The proposed element is a two-node element with 4 degrees of freedom at each node. The effect of different stiffness and damping of viscoelastic foundation, boundary condition and length parameters on natural frequency and transient response of the microbeam is investigated. Keywords Microbeam · Reddy beam theory · Modified couple stress theory · Galerkin finite element method · Viscoelastic foundation · Dynamic analyses
1 Introduction Owing to wide application of micro- and nanoscale devices in micro-electro-mechanical systems (MEMS), nano-electro-mechanical systems (NEMS) and atomic force microscopes (AFMs), many investigations of their behavior have been conducted by researchers. In the mentioned technologies, the elements are being engendered applying the microfabrication techniques. Micro-sensors and micro-actuators are among the most beneficial and pragmatic elements of MEMS. As the structure is scaled down, the size effect phenomena influence the dynamic responses directly. It is experimentally illustrated that the size dependency of microstructures could not be captured by the classical elasticity theory, consequently non-classical elasticity theories emerge.
* Kamran Asemi k.asemi@iau‑tnb.ac.ir 1
Department of Mechanical Engineering, North Tehran Branch, Islamic Azad University, P.O.B. 1651153311, Tehran, Iran
Department of Mechanical Engineering, University of Eyvanekey, Eyvanekey, Semnan, Iran
2
In the investigation of nanoscale devices, it is well known that the scale effect is a significant parameter, and classical continuum theories are unable to capture the size dependency observed in these nanostructures (Fleck et al. 1994; Lam et al. 2003; Stölken and Evans 1998). Thus, some advanced theories were employed to investigate the behavior of nanostructures such as couple stress theory (Zhou and Li 2001), strain gradient theory (Fleck and Hutchinson 1997), modified couple stress theory (Yang et al. 2002) and nonlocal elasticity theory (Eringen 1983). Among them, the couple stress theory has been conducted by Koiter, Ejike, Mindlin and Tiersten (Koiter 1964; Mindlin and Tiersten 1962; Ejike
Data Loading...
