Comprehensive investigation of vibration of sigmoid and power law FG nanobeams based on surface elasticity and modified couple stress theories

Shanab, Rabab A.; Mohamed, S.A.; Mohamed, Norhan A.; Attia, Mohamed A.

doi:10.1007/s00707-020-02623-9

Cited by 19 publications

(6 citation statements)

References 76 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(22.5). So, these terms act as self-excitation loading and cause deformation of the nanostructure at no external load [63].…”

Section: Solution Proceduresmentioning

confidence: 99%

“…Gurtin and Murdoch ([23,24]) proposed a surface elasticity theory to approximate the contribution of surface energy by assuming an elastic body with elastic surface layers of zero thickness that is perfectly bonded to the surface of the bulk continuum. The Gurtin and Murdoch surface elasticity theory (GM-SET) has been successfully employed in conjunction with the other nonclassical continuum theories in the analysis of homogeneous and one-dimensional FG structures, i.e., GM-SET combined with the DNET ( [47][48][49]), GM-SET combined with the SGT ( [50]), GM-SET combined with the DNSGT ( [51]), GM-SET combined with the MCST ( [52][53][54][55][56][57][58][59][60][61][62][63][64]), and GM-SET combined with the MCST in the framework of DNET ( [65,66]). Based on these studies, it has been shown that incorporating the influence of surface energy may show a stiffness-hardening or stiffness-softening of the studied nanostructures depending on whether the signs of the surface elastic constants are positive or negative.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Attia

Shanab

2022

Acta Mech

Self Cite

View full text Add to dashboard Cite

This paper presents an investigation of the dynamic behavior of bi-directionally functionally graded (BDFG) micro/nanobeams excited by a moving harmonic load. The formulation is established in the context of the surface elasticity theory and the modified couple stress theory to incorporate the effects of surface energy and microstructure, respectively. Based on the generalized elasticity theory and the parabolic shear deformation beam theory, the nonclassical governing equations of the problem are obtained using Lagrange’s equation accounting for the physical neutral plane concept. The material properties of the beam smoothly change along both the axial and thickness directions according to power-law distribution, accounting for the gradation of the material length scale parameter and the surface parameters, i.e., residual surface stress, two surface elastic constants, and surface mass density. Using trigonometric Ritz method (TRM), the trial functions denoting transverse, axial deflections, and rotation of the cross sections of the beam are expressed in sinusoidal form. Then, with the aid of Lagrange’s equation, the system of equations of motion are derived. Finally, Newmark method is employed to find the dynamic responses of BDFG subjected to a moving harmonic load. To validate the present formulation and solution method, some comparisons of the obtained fundamental frequency and dynamic response with those available in the literature are performed. A parametric study is performed to extensively explore the impact of the key parameters such as the gradient indices in both directions, moving speed, and excitation frequency of the acting load on the dynamic response of BDFG nanobeams. The obtained results can serve as a guideline for assessing the multi-functional and optimal design of micro/nanobeams acted upon by a moving load.

show abstract

“…(22.5). So, these terms act as self-excitation loading and cause deformation of the nanostructure at no external load [63].…”

Section: Solution Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Attia

Shanab

2022

Acta Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…Later, Lam et al [15] and Yang et al [16] put forward a modified strain gradient model and couple stress model that contains three and one materiallength scale parameters, respectively. With the application of strain gradient and couple stress models, a large number of studies are performed to investigate the toughening effect of materials-length scale parameter on the buckling loads and vibration frequencies of micro-and nano-scale beams, for example [17][18][19][20][21]. Furthermore, mechanical behaviors of microbeams embedded in the elastic medium were also investigated [22].…”

Section: Introductionmentioning

confidence: 99%

Elastic buckling and free vibration of nonlocal strain gradient Euler‐Bernoulli beams using Laplace transform

Bian

Qing

2021

Z Angew Math Mech

View full text Add to dashboard Cite

Previous studies have shown that Lim's nonlocal strain gradient differential model would lead to some inconsistencies for the static bending of Bernoulli-Euler and Timoshenko beams, though it is widely applied to address both softening and toughening size-effect. In this work, nonlocal strain gradient integral model is applied to study the elastic buckling and free vibration of Bernoulli-Euler beam under different boundary conditions. The differential governing equation and corresponding boundary conditions are derived via the Hamilton's principle, and the relation between strain and nonlocal stress is expressed in integral form. The Laplace transform technique is applied to solve the integro-differential equations directly, and the explicit expression for bending deflections and moments is obtained with six unknown constants. The nonlinear characteristic equations to determine the characteristic buckling load and vibration frequency are derived explicitly in consideration of corresponding boundary conditions. The buckling load and vibration frequency from present model are validated against to the existed results in literature. Consistent softening and toughening responses respect to length-scale parameters can be obtained for both elastic buckling and free vibration.

show abstract

“…In the case of a large number of consumers, some enterprises use the tools of intelligent service centres, but due to the limitation of technical level, for some intelligent services, the information is inaccurate and the service efficiency is low. To make intelligent decisions, it is necessary to provide accurate information resources according to the needs of customers [18]. Considering that the customer service centre is still a new field in the electric power enterprise, and the electric power enterprise is an important part of the national economy leapfrog.…”

Section: Introductionmentioning

confidence: 99%

Intelligent Assistant Decision-Making Method for Power Enterprise Customer Service Based on IoT Data Acquisition

Long

Liu

et al. 2021

Mobile Information Systems

View full text Add to dashboard Cite

The prevailing era of the Internet of Things (IoT) has renewed all fields of life in general, but, especially with the advent of artificial intelligence (AI), has drawn the attention of researchers into a new paradigm of life standards. This revolution has been accepted around the world for making life comfortable with the use of intelligent devices. AI-enabled machines are more intelligent and capable of completing a specific task which saves a lot of time and resources. Currently, diverse methods are available in the existing literature to handle different issues of real life based on AI and IoT systems. The role of decision-making has its prominence in the AI-enabled and IoT systems. In this article, an AI- and IoT-based intelligent assistant decision-making method is presented for power enterprise customer service. An intelligent model of the customer service data network is designed, and the method of collecting data from IoT to assist decision-making is presented. Then, the semantic relationship of customer service data is defined, and the sharing scope of data transmission and resources are determined to realize intelligent assistant decision-making of customer service in power enterprises. Simulation results show that the proposed method improves the decision data transmission speed and shortens the transmission delay, and the network performance of data interaction is better than that of the existing methods.

show abstract

Comprehensive investigation of vibration of sigmoid and power law FG nanobeams based on surface elasticity and modified couple stress theories

Cited by 19 publications

References 76 publications

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Elastic buckling and free vibration of nonlocal strain gradient Euler‐Bernoulli beams using Laplace transform

Intelligent Assistant Decision-Making Method for Power Enterprise Customer Service Based on IoT Data Acquisition

Contact Info

Product

Resources

About