Numerical Investigation of Modal Amplitude Saturation in Micromechanical Cantilever Beam Resonators

Volume 4: 22nd Design for Manufacturing and the Life Cycle Conference; 11th International Conference on Micro- and Nanosystems ◽

10.1115/detc2017-67720 ◽

2017 ◽

Author(s):

Tianyi Zhang ◽

Zhuangde Jiang ◽

Xueyong Wei

Keyword(s):

Cantilever Beam ◽

Mode Coupling ◽

Nonlinear Behavior ◽

Softening Effect ◽

Flexural Mode ◽

Micromechanical Resonators ◽

Beam Resonator ◽

Modal Amplitude ◽

Nonlinear Mode Coupling ◽

External Driving

Micromechanical resonators have extensive applications but unavoidably exhibit nonlinearities that may degrade the devices’ performances. A good understanding of their nonlinear dynamics is essential to the design of resonant devices. In this paper, we numerically investigated the dynamics of a cantilever beam resonator working at a coupled extensional and flexural vibrational modes with a 2:1 internal resonance. An amplitude saturation behavior is observed in the cantilever beam resonator by controlling the external driving force. The flexural mode shows a complex nonlinear behavior changing from a softening effect to a hardening effect and the extensional mode shows nonlinear behavior due to the nonlinear mode coupling.

Download Full-text

Utilization of 2:1 Internal Resonance in Microsystems

Micromachines ◽

10.3390/mi9090448 ◽

2018 ◽

Vol 9 (9) ◽

pp. 448 ◽

Cited By ~ 4

Author(s):

Navid Noori ◽

Atabak Sarrafan ◽

Farid Golnaraghi ◽

Behraad Bahreyni

Keyword(s):

Internal Resonance ◽

Mode Coupling ◽

Equations Of Motion ◽

Low Frequency ◽

Nonlinear Behavior ◽

Excitation Amplitude ◽

Beam Structure ◽

Nonlinear Mode Coupling ◽

T Beam ◽

Low Frequency Mode

In this paper, the nonlinear mode coupling at 2:1 internal resonance has been studied both analytically and experimentally. A modified micro T-beam structure is proposed, and the equations of motion are developed using Lagrange’s energy method. A two-variable expansion perturbation method is used to describe the nonlinear behavior of the system. It is shown that in a microresonator with 2:1 internal resonance, the low-frequency mode is autoparametrically excited after the excitation amplitude reaches a certain threshold. The effect of damping on the performance of the system is also investigated.

Download Full-text

An analytical model of a rotating radial cantilever beam considering the coupling between bending, stretching and torsion

Journal of Vibration and Acoustics ◽

10.1115/1.4051494 ◽

2021 ◽

pp. 1-30

Author(s):

Xianglin Wu ◽

Yinghou Jiao ◽

Zhao-Bo Chen

Keyword(s):

Analytical Model ◽

Cantilever Beam ◽

Rotational Speed ◽

Mode Coupling ◽

Twist Angle ◽

Equations Of Motion ◽

Ritz Method ◽

Arbitrary Cross Section ◽

Softening Effect ◽

Setting Angle

Abstract In this paper, the mode coupling between bending, stretching and torsional deformations is mainly studied by presenting an analytical model of a rotating cantilever beam with pre-twist angle and arbitrary cross section. Equations of motion of the beam are derived using Hamilton's principle. The Coriolis effect due to the coupling of the bending deformation and stretching deformation, the eccentricity caused by inconsistency between elastic center and centroid, spin softening effect, stress stiffening effect, shear deformation, and rotary inertia are included in the model. Equations of motion are solved by the Rayleigh-Ritz method. The natural frequencies obtained by the proposed analytical modal are in good agreement with those obtained by Finite Element Method (FEM) which proved the accuracy of the analytical model. Finally, the coupling between different mode components is studied in detail based on a quantitative method. The transformation/ conversion between different mode components is revealed, the influence of rotational speed, setting angle and pre-twist angle on this conversion mode is studied. Results show that a specific mode shape is usually composed of multiple mode components. The essence of mode coupling is the coupling between different mode components. The influence of rotational speed, setting angle and pre-twist angle on the mode coupling is that they cause the transformation/ conversion between different mode components.

Download Full-text