Abstract
This paper is concerned with the free vibration of cantilever microbeams with attached tip mass in a systematical manner. Small size effects on the vibrations of the microbeam are taken into consideration by introducing a scale parameter. A Fourier sine series is used to represent the lateral displacement function. Stokes’ transformation is applied in the present formulation and corresponding derivatives are presented explicitly. The present formulations can be readily reduced to those for others classical elasticity models by setting corresponding small scale parameter to zero. Several parametric studies are performed to validate the present solutions and the effects of various important physical parameters (scale parameter, tip mass) are investigated.
Highlights
Microbeams (MEMS) and nanobeams (NEMS) such as doubly clamped and cantilever microbeam are the major components of MEMS and NEMS devices, and the preferred actuation method is always the electric actuation
Beam model based on the classical theory (CT), such as Euler-Bernoulli [10,11,12], Timoshenko [11, 12] and some higher-order shear deformation [12, 13] beam theories is not capable of capturing size effect in micro/nano-structures as a result of lacking of the material length scale parameter [14]
Strain gradient elasticity models of continuum mechanics are recognized within the wide literature as material models capable to capture and describe a number of experimentally detected microstructural phenomena featured by an internal length scale, such as size effects, surface effects, dispersion effects of wave propagation, along with the possibility to dispense with stress/strain singularities at, typically, crack tips and dislocation cores [16, 17]
Summary
Microbeams (MEMS) and nanobeams (NEMS) such as doubly clamped and cantilever microbeam are the major components of MEMS and NEMS devices, and the preferred actuation method is always the electric actuation The analysis of this actuation and sensing has been a topic of interest over the past several years. In order to determine the effects of attached mass on the resonant frequency of micro/nanoscale application, the continuum models based on microbeam as well as nanaobeam is used by several researchers [18,19,20]. The method of Stokes’ transformation is more efficient than the analytical series methods because this method gives more flexibility in boundary conditions This is in particular essential for determining the dynamic response of microbeams other than supported. The present analytical solutions can be readily reduced to those for the classic beam without mass effect, by setting small scale parameter to zero
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