Free vibrations of nanobeams under non-ideal supports based on modified couple stress theory

2021 ◽  
Vol 76 (5) ◽  
pp. 427-434
Author(s):  
Duygu Atcı
Keyword(s):  
Size Effect ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Linear Functions ◽  
Stress Theory ◽  
Fundamental Frequencies ◽  
Resonance Frequencies ◽  
Modified Couple Stress

Abstract In this study, free vibration analysis of nanobeams under various non-ideal supports have presented. Size effect of nanobeams has applied by utilizing modified couple stress theory. Hamilton’s principle has been used to derive the equation of motion. Governing equation has subjected to non-ideal boundary conditions which are modeled as linear functions including an introduced weighting factor (k). Obtained numerical results have verified by comparing with the published results. Results show that fundamental resonance frequencies of non-ideal clamped nanobeams are significantly decreased when it is compared to ideal supports. However, non-ideal simply supports creates a minor increase effect on fundamental frequencies with respect to clamped ones. Also, nano-size effect has investigated for non-ideal supports. It has found that, the smaller cross-sectional size of nanobeam causes increasing effect of non-ideal supports on fundamental frequencies.

Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST

2017 ◽  
Vol 22 (1) ◽  
pp. 55-86 ◽  
Author(s):  
Mohammad Arefi ◽  
Masoud Kiani ◽  
Ashraf M Zenkour
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length ◽  
Exponentially Graded

The present work is devoted to the free vibration analysis of elastic three-layered nano-/micro-plate with exponentially graded core and piezomagnetic face-sheets using the modified couple stress theory. To capture size-dependency for a nano-/micro-sized rectangular plate, the couple stress theory is used as a non-classical continuum theory. The rectangular elastic three-layered nano-/micro-plate is resting on Pasternak’s foundation. The present model contains one material length scale parameter and can capture the size effect. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on the modified couple stress theory and first-order shear deformation theory. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually the natural frequency is scrutinized for different side length ratio, thickness ratio, inhomogeneity parameter, material length scale, and parameters of foundation numerically.

scholarly journals Free Vibration Analysis of Rotating Beams Based on the Modified Couple Stress Theory and Coupled Displacement Field

2021 ◽  
Vol 2 (2) ◽  
pp. 226-238
Author(s):  
Alireza Babaei ◽  
Masoud Arabghahestani
Keyword(s):  
Displacement Field ◽  
Vibration Analysis ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Slenderness Ratio ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Analysis And Design ◽  
Modified Couple Stress

In this paper, transverse vibration analysis of rotating micro-beam is investigated based on the modified couple stress theory. The simply-supported micro-beam is modeled utilizing Euler-Bernoulli and Timoshenko beam theories. The system is rotating around a fixed axis perpendicular to the axial direction of the beam. For the first time, displacement filed is introduced as a coupled field to the translational field. In other words, the mentioned rotational displacement field is expressed as a proportional function of translational displacement field using first (axial), second (lateral), and third (angular or rotational) velocity factors. Utilizing Hamilton’s approach as a variational method, dynamic-vibration equations of motion of the proposed model are derived. Galerkin’s method is adopted to solve the equation corresponding to the Euler–Bernoulli and Timoshenko beams. For the case considering shear deformation effects, Navier method is chosen. For evaluation of current results and models, they are compared with those available at the benchmark. In this paper; effects of slenderness ratio, axial, lateral, and angular velocity factors, and rotations of the beam on the frequency are reported. Based on the results presented, mentioned factors should be counted in the analysis and design of such rotating micro-systems.

Flexural Vibration of an Atomic Force Microscope Cantilever Based on Modified Couple Stress Theory

2015 ◽  
Vol 15 (07) ◽  
pp. 1540025 ◽  
Author(s):  
Li-Na Liang ◽  
Liao-Liang Ke ◽  
Yue-Sheng Wang ◽  
Jie Yang ◽  
Sritawat Kitipornchai
Keyword(s):  
Size Effect ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Flexural Vibration ◽  
Modified Couple Stress Theory ◽  
Length Scale ◽  
Stress Theory ◽  
Atomic Force ◽  
Modified Couple Stress

This paper is concerned with the flexural vibration of an atomic force microscope (AFM) cantilever. The cantilever problem is formulated on the basis of the modified couple stress theory and the Timoshenko beam theory. The modified couple stress theory is a nonclassical continuum theory that includes one additional material parameter to describe the size effect. By using the Hamilton's principle, the governing equation of motion and the boundary conditions are derived for the AFM cantilevers. The equation is solved using the differential quadrature method for the natural frequencies and mode shapes. The effects of the sample surface contact stiffness, length scale parameter and location of the sensor tip on the flexural vibration characteristics of AFM cantilevers are discussed. Results show that the size effect on the frequency is significant when the thickness of the microcantilever has a similar value to the material length scale parameter.

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