Natural vibrations of micro beams with nonrigid supports

Abstract

The present study aims to provide some new information for the design of micro systems. It deals with free vibrations of Bernoulli–Euler micro beams with nonrigid supports. The study is based on the formulation of the modified couple stress theory. This theory is a nonclassical continuum theory that allows one to capture the small-scale size effects in the vibrational behavior of micro structures. More realistic boundary conditions are represented with elastic edge conditions. The effect of Poisson’s ratio on the micro beam characteristics is also analyzed. The present results revealed that the characterization of real boundary conditions is much more important for micro beams than for macro beams, and this is an assessment that cannot be ignored.

Nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam resting on nonlinear elastic foundation based on modified couple stress theory

“…The relevant effective material properties that are determined using equation 1are as follows: Young's modulus ðE f Þ, Poisson's ratio ð f Þ, thermal expansion coefficient ð f Þ, and density ð f Þ. The effective shear modulus G f is determined using the relationship 25,32…”

“…Substituting equations (13), (14), (17), (18), (21a) or (21b), and (24) in equation (5) and considering the displacement and rotation fields, given by equation (25), the equations governing forced beam vibration at peak response amplitude in the frequency domain are derived and are given below in matrix form as…”

“…Considering the equilibrium of moments of couples, MCST is developed by Yang et al 3 based on classical couple stress theory [15][16][17][18] that originally required two material length scale parameters. Research reports on static and dynamic analyses of homogeneous microbeams based on MCST are available in the literature and some of them 4,[19][20][21][22][23][24][25][26] are briefly mentioned here. The static and free vibration analysis of Euler-Bernoulli microbeams based on variational approach is reported by Park and Gao 4 and Kong et al 19 respectively.…”

“…Dehrouyeh-Semnani and Nikkhah-Bahrami 24 studied the effect of size-dependent shear deformation on static, buckling, and free vibration behavior of microbeams. Considering EBT, Bambill et al 25 presented the free vibration analysis of elastically restrained microbeams and concluded that the effect of nonrigid boundary condition is more prominent for microbeams than macrobeams. It is to be mentioned that the studies mentioned in this paragraph so far for homogeneous microbeams are geometrically linear.…”

Mechanical Behaviors of Electrostatic Microbeams with Nonideal Supports

“…ese cause the boundary conditions of the actual system to deviate from the ideal support conditions such that the displacement and rotation angle of the two fixed ends are not equal to zero. Bambill et al [27] drew the conclusion that the characterization of real boundary conditions was much more important for microscale beams than for macroscale beams. In addition, Muthukumaran et al [28] proposed that the boundary condition became one of the techniques responsible for the structural tuning of particular note in order to obtain a desired harmonic relation among its natural frequencies.…”