Investigation of Size-Dependency in Free-Vibration of Micro-Resonators Based on the Strain Gradient Theory

Vatankhah, Ramin; Kahrobaiyan, M. H.

doi:10.1590/1679-78252430

Cited by 10 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Static and dynamic behavior of microbeams based on size‐dependent theories has been well‐investigated in previous studies. For example, Vatankhah and Kahrobaiyan 42 investigated the size‐dependency in free‐vibration of micro‐resonators based on the strain gradient theory. Kong et al 43 solved the static and dynamic problem of Euler‐Bernoulli beams on the basis of MSG theory.…”

Section: Introductionmentioning

confidence: 99%

A modified strain gradient beam constraint model

Arhami

Moeenfard

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

The objective of the present paper is to develop a modified strain gradient beam constraint model (MSGBCM) to improve the modeling accuracy of small‐scale compliant mechanisms. First, a simple nano/micro flexure beam under the effect of end loads is considered. The virtual work principle is employed to formulate the nonlinear load–displacement behavior of the system, based on the modified strain gradient theory. It is observed that as the size of the structure becomes smaller, the elements of the elastic stiffness and load stiffening matrices severely deviate from their corresponding values in the beam constraint model (BCM). A closed‐form nonlinear strain energy expression is also derived for nano/micro flexure beams in terms of their tip displacements. This energy expression is utilized to model the nonlinear load–displacement relationships of small‐scale parallelogram (P) flexures. Moreover, analytical formulas are derived for the axial, transverse, and rotational stiffness values of P‐flexures. The most important observation is that in the small‐scale P‐flexures, the axial stiffness loss of small‐scale P‐flexures resulted from the movement of the stage in the transverse direction, may be seriously overestimated by BCM. The developed MSGBCM can be easily extended for investigating the static and dynamic behavior of more complicated micron and submicron size flexures.

show abstract

Section: Introductionmentioning

confidence: 99%

A modified strain gradient beam constraint model

Arhami

Moeenfard

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Experiments show that ignoring the internal length scale, which is the case in the classical continuum mechanics, in micro and nano structures can result in inaccurate structural predictions. To overcome this problem, a number of theories like couple stress theory and strain gradient theory [1][2][3][4][5] have been developed. In the couple stress theory, the effect of couple per unit area along with the effect of normal and shear forces is considered [6].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Alimoradzadeh

Salehi

Esfarjani

2020

Period. Polytech. Mech. Eng.

View full text Add to dashboard Cite

In this study, a non-classical approach was developed to analyze nonlinear free and forced vibration of an Axially Functionally Graded (AFG) microbeam by means of modified couple stress theory. The beam is considered as Euler-Bernoulli type supported on a three-layered elastic foundation with Von-Karman geometric nonlinearity. Small size effects included in the analysis by considering the length scale parameter. It is assumed that the mass density and elasticity modulus varies continuously in the axial direction according to the power law form. Hamilton's principle was implemented to derive the nonlinear governing partial differential equation concerning associated boundary conditions. The nonlinear partial differential equation was reduced to some nonlinear ordinary differential equations via Galerkin's discretization technique. He's Variational iteration methods were implemented to obtain approximate analytical expressions for the frequency response as well as the forced vibration response of the microbeam with doubly-clamped end conditions. In this study, some factors influencing the forced vibration response were investigated. Specifically, the influence of the length scale parameter, the length of the microbeam, the power index, the Winkler parameter, the Pasternak parameter, and the nonlinear parameter on the nonlinear natural frequency as well as the amplitude of forced response have been investigated.

show abstract

“…Vatankhah and Kahrobaiyan [48] studied vibration of a micro-resonator based on MSGT to capture size e ect on the system. They modeled the microresonator as a clamped-clamped micro-beam subjected to a tensile axial force with a concentrated mass attached to the micro-beam.…”

Section: Introductionmentioning

confidence: 99%

Size Effect Investigation on Lateral Vibrations of a Micro Drill Subjected to an Axial Load Using the Modified Couple Stress Theory

Rahi

2018

Scientia Iranica

View full text Add to dashboard Cite

In this paper, the modi ed couple stress theory is used to capture size e ect on dynamic behavior of a micro-drill subjected to an axial load and a concentrated mass, which is attached to its free end. Governing equations of lateral vibrations of the system and associated boundary conditions were derived by rst, obtaining the total kinetic and potential energy of the system and then, using Hamilton's principle. The Assumed Modes method was applied for transforming the governing partial di erential equations into a set of in nite ordinary di erential equations. Considering two terms of the equations, the rst two natural frequencies and instability rotational speeds of the micro-drill system were determined semi-analytically. Finally, numerical results of natural frequencies and the threshold of instability speeds of the system were derived with respect to di erent values of the system parameters such as rotational speed, axial load, rotor length, concentrated mass, and material length scale. The results showed that the material length scale parameter was extremely e ective on natural frequencies and the threshold of instability speeds of the micro-drill.

show abstract

Investigation of Size-Dependency in Free-Vibration of Micro-Resonators Based on the Strain Gradient Theory

Cited by 10 publications

References 29 publications

A modified strain gradient beam constraint model

A modified strain gradient beam constraint model

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Size Effect Investigation on Lateral Vibrations of a Micro Drill Subjected to an Axial Load Using the Modified Couple Stress Theory

Contact Info

Product

Resources

About