Size-dependent three-dimensional free vibration of rotating functionally graded microbeams based on a modified couple stress theory

Raman spectroscopy to study thermal maturity and elastic modulus of kerogen

https://iopscience.iop.org/article/10.1088/2053-1591/aabe62/pdf

Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory

In this paper, to improve the vibrational response of microstructures, the impact of the nonlinear modal analysis of axially functionally graded (AFG) truncated conical micro-scale tube including the thermal loading for the different type of cross sections such as uniform section, linear tapered section, convex section, the exponential section are studied that are applicable for various application, for example, the micro-thermal fins, macro-/micro-fluid-flow diffuser, fluid-flow nozzle, fluid-flow throat, micro-sensor, etc. The nonlinear equations are obtained applying Hamilton’s principles based on the modified couple stress to determine the size effect and Euler–Bernoulli beam theory considering the von-Karman’s nonlinear strain. The material combination varies along the tube’s length, denouncing the AFG tube made by metal and ceramic phases. The nonlinear equations are solved by applying a couple of homotopy perturbation methods (HPM) to calculating the nonlinear results and the generalized differential quadrature method (GDQM) to providing the initial conditions. The linear and nonlinear results presented the effect of various cross sections and other parameters on the micro-tube frequency that are valuable to design and manufacture the micro-electro-mechanical systems (MEMS).

Computer simulation via a couple of homotopy perturbation methods and the generalized differential quadrature method for nonlinear vibration of functionally graded non-uniform micro-tube

Thermodynamic modeling of viscoelastic thin rotating microbeam based on non-Fourier heat conduction

In this paper free vibration analysis of functionally graded micro-beam is investigated based on the modified couple stress theory. The model is established using the Euler–Bernoulli beam theory. The thermal and mechanical properties of the micro-beam are assumed to be temperature-dependent and vary smoothly through the thickness direction. The power law distribution is used for exerting the material gradation. The micro-beam is initially stressed by temperature change thorough the thickness. The temperature field is supposed to be constant in the cross section plane. The induced thermal stress, and the power index affect dynamic responses of the micro-beam. The Hamilton’s principle is utilized to derive the governing equation of motion, and Galerkin’s method is used in the solution procedure. Upon using the modified couple stress theory, non-classical results are obtained, moreover by neglecting the non-classical parameter, classical results are reported. For verification, the numerical results are compared with those of benchmark. Present results denote the vitality of temperature and material gradation upon dynamic responses of micro-systems.

Temperature-dependent free vibration analysis of functionally graded micro-beams based on the modified couple stress theory

Free longitudinal vibration analysis of a rotating rod based on the Eringen’s nonlocal elasticity is studied in this paper. Rod is supposed to rotate around a fixed axis with a constant angular velocity. To capture the effect of the rotational motion into analysis of the continuous system, a linear proportional relation is introduced between axial and angular velocities. For the first time the mentioned relation is presented based on the internal motions of the infinitesimal element. This novelty makes the rotational displacement as a dependent function of axial displacement playing a significant role through the analysis. Variational approach is adopted to derive the equations of motion for clamped–clamped and clamped-free boundary conditions. For verification of the results obtained from the Galerkin approach, comparison with technical literature is reported. Finally current results illustrate the dependency of the dynamic-vibration analysis of the presented system on the nonlocality and the rotational velocity parameter. This dependency shows the decrement of the frequency with increment in both the angular velocity and the nonlocal parameter. As a result, the mentioned parameters are key factors in the design and analysis of such systems.

Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field

In this research paper, lateral vibration analysis of simply-supported microbeam under thermal stress is investigated. Microbeam model is presented based on the modified couple stress theory and Ti...

On dynamic-vibration analysis of temperature-dependent Timoshenko microbeam possessing mutable nonclassical length scale parameter

Axial vibration analysis of an optimized MEMS gyroscope is investigated in this paper. For this purpose; a model of rotating, axially functionally graded (tapered) nano-rod is represented. Along with classical continuum mechanics, Eringen’s non-local theory is adopted. Using Hamilton’s variational approach along with coupled displacement field concept which is derived from Babaei and Yang, governing equations of motion are derived. Rayleigh–Ritz approximate method is used to solve the equation for both clamped–clamped and clamped-free rod model. Verification of current results is ratified by comparison with results available in technical literature. Incorporation of taper parameter, non-local effect and rotation effects reveals predictable patterns along with unpredictable chaotic behavior of the optimized gyroscope. Such outcomes report necessity of precise and case-by-case perusal as for some specific values of taper and non-local parameters; system results unpredictable responses. In such chaotic regimes, pattern detection based on response of the gyroscope is impossible and a kind of real-time monitoring and analysis is required. Excluding critical values of the mentioned parameters of non-locality and taper; generally rotations around a fixed axis leads to lessening the oscillations, enhancing the non-locality yields weak vibrations, and intensifying the taper effects makes the system oscillate with greater frequencies wherein for quite high values of taper parameter, gyroscope model behavior turns out independent. It is good to mention that only case in which increment of taper parameter suppresses vibrations occurs when cross-section area of clamped-free nano-rod model is increasing. Eventually, influential factors of current model are revealed.

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Longitudinal vibration responses of axially functionally graded optimized MEMS gyroscope using Rayleigh–Ritz method, determination of discernible patterns and chaotic regimes

Free lateral vibration analysis of gyroscope model is studied in this paper. This gyroscope is modeled as a rotating simply-supported beam which is under an initial thermal stress. Thermo-mechanica...

Alireza Babaei

Papers

Temperature-dependent free vibration analysis of functionally graded micro-beams based on the modified couple stress theory

Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field

On dynamic-vibration analysis of temperature-dependent Timoshenko microbeam possessing mutable nonclassical length scale parameter

Longitudinal vibration responses of axially functionally graded optimized MEMS gyroscope using Rayleigh–Ritz method, determination of discernible patterns and chaotic regimes

Vibration analysis of rotating thermally-stressed gyroscope, based on modified coupled displacement field method