Mode shape analysis of dynamic behaviour of cracked nanobeam on elastic foundation

Hossain, Mainul; Lellep, Jaan

doi:10.1088/2631-8695/ac2a75

Cited by 5 publications

(5 citation statements)

References 54 publications

(59 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The beam length is considerably longer than the cross-sectional dimension and the deformation is very small. According to the Euler-Bernoulli beam theory, the displacement field along the axial and transverse direction can be written as [24][25][26]:…”

Section: Equation Of Motionmentioning

confidence: 99%

Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

Hossain¹,

Lellep²

2022

Eng. Res. Express

View full text Add to dashboard Cite

In the study, the Maclaurin series technique is presented to analyse the vibration of cracked tapered double nanobeams. The equation of motion is derived from the Euler-Bernoulli beam theory based on the Hamiltonian principle and Eringen's nonlocal theory of elasticity. The double-nanobeam system consists of two parallel nanobeams attached by a Winkler elastic layer. Both beams are identical and their widths vary along the x-axis. A single crack is considered at the upper beam of the system. The mechanical behaviour of cracked cross-sections is simulated by the local stiffness model. According to the model, the cracked double-beam system is divided into two intact segments. A numerical investigation is carried out to scrutinize the effects of nonlocal parameters, crack severity, taper ratio, and spring constant on the vibration of the double nanobeam. The results reveal that the effects of crack depth, crack location, nonlocal parameters, taper ratio, and spring constant influence the natural frequency and dynamic response of the system significantly. This study highlights that a crack at the upper beam influences the mode shape of the upper beam as well as the intact lower beam. Numerical results have been examined with the previously published works and found a good agreement with them.

show abstract

Section: Equation Of Motionmentioning

confidence: 99%

Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

Hossain¹,

Lellep²

2022

Eng. Res. Express

View full text Add to dashboard Cite

show abstract

“…There are a few points to note from all studies above. Firstly, the beam theories used are the Euler-Bernoulli beam theory 33,[35][36][37][38][39][40][41][42][43]45,47,50 and the Timoshenko beam theory. 20,34,44,46,48,49 Secondly, the crack is modelled as an elastic spring connected by two intact segments to each other at cracked sections.…”

Section: Introductionmentioning

confidence: 99%

“…Loghmani and Yazdi, 36 Hossain and Lellep, 37 Lellep and Lenbaum 38–40 studied free vibration frequencies of multiple cracked and stepped nanobeams. Hossain and Lellep 41 analysed changes in mode shapes of cracked nanobeams rested on elastic foundation. Ebrahimi and Mahmoodi, 42 Aria et al, 43 Abdullah et al 44 and Karličić et al 45 studied free vibration frequencies of cracked nanobeams in thermal environment.…”

Section: Introductionmentioning

confidence: 99%

Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams

Lien,

Dinh,

Thang

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams with arbitrary boundary conditions based on the Nonlocal Elasticity Theory (NET) and the Timoshenko beam theory are presented. The NET considering the size effect of nanostructures is applied. FGM properties vary nonlinearly along the height of the beam. A crack model using two springs with stiffness depending on the crack depth is applied. The proposed solutions are provided explicitly as functions of integration constants determined from the standard boundary conditions. Frequency equations, that established in the form of the determinant of the matrix 3 × 3 order for arbitrary boundary conditions, are applied to analyse free vibration. Expressions for the mode shapes are given explicitly. The effects of geometry, material, nonlocal and crack parameters on the free vibration of the multiple cracked nanobeam are then analysed in detail.

show abstract

“…It appeared that together with the Ritz method another effective method of solution of problems of this kind is the differential quadrature method (see Shu [48], Pradhan and Kumar [41]). The same numerical procedure was employed by Hossain and Lellep [21,22] as well when studying the natural frequencies of nanobeams with cracks. Note that in these studies, the effect of the rotatory inertia of an element was taken into account in contrast to the classical approach.…”

Section: Introductionmentioning

confidence: 99%

Natural vibrations of circular nanoarches of piecewise constant thickness

Mubasshar,

Lellep

2023

ACUTM

View full text Add to dashboard Cite

The free vibrations of elastic circular arches made of a nano-material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch.

show abstract

Mode shape analysis of dynamic behaviour of cracked nanobeam on elastic foundation

Cited by 5 publications

References 54 publications

Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams

Natural vibrations of circular nanoarches of piecewise constant thickness

Contact Info

Product

Resources

About