A shear deformable cylindrical shell model based on couple stress theory

Zeighampour, Hamid; Beni, Yaghoub Tadi

doi:10.1007/s00419-014-0929-8

Cited by 63 publications

(19 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast to the classical theory which is not able to justify the mechanical response of the micro-scale structures, non-classical theories, such as couple stress theory [14][15][16] and modi ed couple stress theory [17][18][19], are appropriately able to explain this phenomenon and cover the gap between the experimental and classical theory results. Couple stress theory as a theory is capable of explaining the size-dependent behavior of mechanisms proposed for the rst time by Mindlin and Tiersten [14].…”

Section: Introductionmentioning

confidence: 93%

Effect of size dependency on in-plane vibration of circular micro-rings

2017

View full text Add to dashboard Cite

KEYWORDSMicro-ring; Modi ed couple stress theory; Resonant frequency.Abstract. In this paper, based on the modi ed couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The ndings are compared with classical beam theories. Response of the micro-ring under application of static and dynamic loads is investigated and compared with the classical theories. Results show that when the thickness of the ring is in the order of the length scale of the ring material, the natural frequencies evaluated using the modi ed couple stress are considerably more than those predicted based on the classical beam theories, while the de ection and natural frequencies of the classical and non-classical beam theories approach one another for the rings with thickness much larger than the material length scale.

show abstract

Section: Introductionmentioning

confidence: 93%

Effect of size dependency on in-plane vibration of circular micro-rings

2017

View full text Add to dashboard Cite

show abstract

“…The micro-plates and micro-beams have found to be extensively applied in nano-/micro-electrical mechanical systems (NEMS/MEMS). The size-dependent behavior of these microscale structures also has been indicated in many experiments [10]. This phenomenon was first realized in much plastic deformation in metals and polymers.…”

Section: Introductionmentioning

confidence: 68%

Vibration and dynamic behavior of electrostatic size-dependent micro-plates

Karimipöur

Beni

Zeighampour

2020

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

The recent trend of using thin micro-plate structures in severe operational conditions caused the classical theory (CT) to be no longer suited in analyzing the dynamic characteristics of them. For this study, the modified version of the couple stress theory (MCST) is adopted. Then, using Hamilton's principle and Kirchhoff plate theory, the dynamic form of the size-dependent equation of motion for micro-plates stimulated by electrostatic dynamic excitation is acquired. The mixed extended Kantorovich and differential transformation methods on partial differential equations are applied to obtain the mode shapes and natural frequencies. The mode shapes from the linear free vibration solution are used as the mode shapes of the assumed multi-mode displacement field. The displacement field is required to solve the dynamical equation of motion. The equations are subsequently solved by the fourth-order Runge-Kutta method. Some universal graphs are also presented using the MCST to predict the effects of the size effect, tensile and compressive residual stresses, and aspect ratio of micro-plate on the free vibration and dynamic behaviors of micro-plates around their static configuration. It is found that the non-dimensional natural frequency parameter varies linearly versus the other non-dimensional parameters of the micro-plate. Various interesting phenomena are observed from the current simulations of the dynamic response of micro-plates to both DC and AC excitation, as well as the boundary of the frequency behavior conversion. A comparison is drawn between the responses of the micro-plate based on the modified couple stress and CT taking the size dependency into account. To facilitate understanding of the physical phenomena observed in the results, a simple physical analog to the micro-plates is suggested. This physical analog, which describes the boundary of frequency behavior conversion, is the linear relationship between the non-dimensional parameters of the system. The study of this model can help to realize some of the complex responses of the micro-plates. Keywords Vibration analysis • Modified couple stress theory • Clamped rectangular micro-plates • Extended Kantorovich method (EKM) • Modal method • Galerkin method • Differential transformation method (DTM)

show abstract

“…Based on the Navier solution method and according to FSDT cylindrical shell model, for simply supported ends, the MT displacement field solutions are considered as follows: 32,62 u = U cos mπ L x cos (nθ) e iωt ;…”

Section: Solving Methodsmentioning

confidence: 99%

Using a New Size Dependent Orthotropic Elastic Shell Model for the Investigation of Free Vibration of Protein Microtubules

Beni¹,

Zeverdejani²

2019

The International Journal of Acoustics and Vibration

View full text Add to dashboard Cite

Protein microtubules are one of the most effective intracellular components. The microtubules structure is in a manner that their behaviour is similar to that of the orthotropic materials. Therefore, in this paper, size-dependent vibration of the anisotropic protein microtubule is studied. For this purpose, using a first shear deformable shell model and based on couple stress theory, new equations are developed for the dynamic behavior of anisotropic protein microtubule. After solving the governing equations of microtubule motion, the effects of cytoplasm environment, microtubule dimensions and its mechanical properties, and material length scale parameters on the natural frequency of microtubules are investigated.

show abstract

A shear deformable cylindrical shell model based on couple stress theory

Cited by 63 publications

References 21 publications

Effect of size dependency on in-plane vibration of circular micro-rings

Effect of size dependency on in-plane vibration of circular micro-rings

Vibration and dynamic behavior of electrostatic size-dependent micro-plates

Using a New Size Dependent Orthotropic Elastic Shell Model for the Investigation of Free Vibration of Protein Microtubules

Contact Info

Product

Resources

About