Free vibrations of stepped nano-beams

Modern Building Materials, Structures and Techniques (MBMST)

Hossain

2019

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Natural vibrations of nanobeams and nanosheets are investigated with the help of nonlocal theories of elasticity. The vibration analysis is based on the size-dependent non-local theory of elasticity developed by A. C. Eringen. It is assumed that the nano-structures under consideration have rectangular cross sections with piece wise constant dimensions and that the nanoplates are weakened with defects. The influence of the crack on the vibration of the nanoplate is assessed with the aid of additional local compliance developed in previous papers. Numerical results are presented for one- and two-stepped nanoplates.

Section:  mentioning

confidence: 53%

Section:  mentioning

confidence: 99%

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Free vibration of rectangular nanoplate strips

Modern Building Materials, Structures and Techniques (MBMST)

Hossain

2019

Self Cite

“…Eringen (2002) introduced also differential approach to the specific class of kernel functions which admitted to transform the constitutive equations into the form of differential equations. Following Eringen (2002), Reddy (2007aReddy ( , 2007b, Lellep and Lenbaum (2018), we shall use the constitutive equations for the bending moment M as…”

Section: Constitutive Equations In Nonlocal Elasticitymentioning

confidence: 99%

“…Several researchers among Lellep and Kraav (2016), Lellep and Liyvapuu (2016), Lellep and Lenbaum (2018) Tada, Paris, and Irwin (2000). Consider the case of one-stepped nanobeam (see Figure 2) with simply supported ends in a greater detail.…”

Section: The Local Compliancementioning

confidence: 99%

Buckling of nanobeams and nanorods with cracks

Arif

Modern Building Materials, Structures and Techniques (MBMST)

2019

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Buckling of nanobeams and nanorods is treated with the help of the nonlocal theory of elasticity. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with cracks or cracklike defects emanating at the re-entrant corners of steps. A general method for determination of critical buckling loads of stepped nanobeams with cracks is developed. The influence of defects on the critical buckling load is evaluated numerically and compared with similar results of other researchers.

Buckling analysis of cantilever nanobeams with defects

Arif

2021

Appl Nanosci

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Cantilever nanobeams subjected to the axial pressure are considered under the assumption that the material behaviour can be modelled with the help of the nonlocal theory of elasticity. The nanobeams and nanocolumns under consideration have rectangular cross section with piecewise constant dimensions and are weakened by crack-like defects at the re-entrant corners of the steps. The critical buckling loads of stepped nanobeams are calculated and the sensitivity of critical loads with respect to crack parameters is studied. Results show the significant effect of crack parameters on the stability of stepped nanobeams. The numerical results are presented with the aid of MATLAB tools and are found to be in a close agreement with the available work in the literature.