Natural Frequencies Of Microbeam Research Articles

Dynamic analysis of straight stepped microbeams

This works aims to investigate the dynamics of Micro-electro-mechanical systems (MEMS) straight multi-stepped micro-beams. An analytical model is presented based on the Euler–Bernoulli beam theory and the Galerkin discretization. The effect of various parameters on the natural frequencies of micro-beams is examined, including the effects of varying the geometry (number of steps and their ratios), the axial force (including those from electrothermal actuation), and the nonlinear electrostatic forces. The analytical results are validated and compared with the simulation results of a Multiphysics Finite-Element (FE) model. Good agreement is found among all the results. The variations of the pull-in and buckling instabilities due to the various parameters are also reported. The results highlight the capability of both passive (geometry) and active (electrostatic and electrothermal/axial) methods to tune the natural frequencies of the structures, which can be useful in applications, such as tunable filters, switches, as well as for creating/avoiding internal resonance and energy exchanges among the various modes.

Vibrational behavior of variable section functionally graded microbeams carrying microparticles in thermal environment

Based on the modified strain gradient theory (MSGT) in conjunction with the Timoshenko beam theory, the vibrational behavior under thermal environment of variable section functionally graded (FG) microbeams carrying microparticles is studied. The eigenfrequency equations are derived using the Chebyshev–Ritz method. The effects of temperature dependence of material properties and the initial thermal stresses are considered. After validating the method, the influences of the width taper ratio, the position and values of the microparticle masses, temperature rise, length scale parameters and material gradient index on the free vibration behavior of microbeams are studied. In addition, comparisons between the results of the MSGT, the modified couple stress theory (MCST), and the classical theory (CT) are performed. It is found that in addition to the microparticle masses and locations, their influences on the natural frequencies depend on the vibration mode number and the edge restraints of microbeams. Also, it is shown that the temperature rise, length scale parameters and material gradient index have considerable effects on the natural frequencies of microbeams. Moreover, the results demonstrate that the MSGT and the CT provide the largest and the smallest natural frequencies, respectively.

Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

A size-dependent shear deformation beam model based on the strain gradient elasticity theory

A new size-dependent higher-order shear deformation beam model is developed based on modified strain gradient theory. The model captures both the microstructural and shear deformation effects without the need for any shear correction factors. The governing equations and boundary conditions are derived by using Hamilton’s principle. The static bending and free vibration behavior of simply supported microbeams are investigated. Analytical solutions including Poisson effect for deflections under point and uniform loads and for first three natural frequencies are obtained by Navier solution. The results are compared with other beam theories and other classical and non-classical models. A detailed parametric study is carried out to show the influences of thickness-to-material length scale parameter ratio, slenderness ratio and shear deformation on deflections and natural frequencies of microbeams. It is observed that effect of shear deformation becomes more significant for both smaller slenderness ratios and higher modes.

O.491 Long-term outcome following resection for IF malignancies

Based on the modified strain gradient theory (MSGT) in conjunction with the Timoshenko beam theory, the vibrational behavior under thermal environment of variable section functionally graded (FG) microbeams carrying microparticles is studied. The eigenfrequency equations are derived using the Chebyshev–Ritz method. The effects of temperature dependence of material properties and the initial thermal stresses are considered. After validating the method, the influences of the width taper ratio, the position and values of the microparticle masses, temperature rise, length scale parameters and material gradient index on the free vibration behavior of microbeams are studied. In addition, comparisons between the results of the MSGT, the modified couple stress theory (MCST), and the classical theory (CT) are performed. It is found that in addition to the microparticle masses and locations, their influences on the natural frequencies depend on the vibration mode number and the edge restraints of microbeams. Also, it is shown that the temperature rise, length scale parameters and material gradient index have considerable effects on the natural frequencies of microbeams. Moreover, the results demonstrate that the MSGT and the CT provide the largest and the smallest natural frequencies, respectively.