Geodesic
Nonlinear statics and dynamics of porous functional-gradient nanobeam taking into account transverse shifts
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 4, pp. 587-597.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, nonlinear mathematical models of functionally gradient porous nanobeams are constructed taking into account transverse shifts. Transverse shifts are described using kinematic models of the second (S. P. Timoshenko) and third approximations (Sheremetyev – Pelekh). From the Sheremetyev – Pelekh model, as a special case, the kinematic models of the second (S. P. Timoshenko) and first approximation (Bernoulli – Euler) follow. Geometric nonlinearity is accepted according to T. von Karman, nanoeffects are accepted according to the modified Yang moment theory of elasticity. The required equations are derived from the Ostrogradsky – Hamilton principle. An efficient algorithm has been developed that allows us to consider both static and chaotic dynamics problems. Numerical examples are given. 
@article{ISU_2024_24_4_a9,
     author = {A. V. Krys'ko and A. N. Krechin and M. V. Zhigalov and V. A. Krys'ko},
     title = {Nonlinear statics and dynamics of porous functional-gradient nanobeam taking into account transverse shifts},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {587--597},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2024_24_4_a9/}
}
TY  - JOUR
AU  - A. V. Krys'ko
AU  - A. N. Krechin
AU  - M. V. Zhigalov
AU  - V. A. Krys'ko
TI  - Nonlinear statics and dynamics of porous functional-gradient nanobeam taking into account transverse shifts
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2024
SP  - 587
EP  - 597
VL  - 24
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2024_24_4_a9/
LA  - ru
ID  - ISU_2024_24_4_a9
ER  - 
%0 Journal Article
%A A. V. Krys'ko
%A A. N. Krechin
%A M. V. Zhigalov
%A V. A. Krys'ko
%T Nonlinear statics and dynamics of porous functional-gradient nanobeam taking into account transverse shifts
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2024
%P 587-597
%V 24
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2024_24_4_a9/
%G ru
%F ISU_2024_24_4_a9
A. V. Krys'ko; A. N. Krechin; M. V. Zhigalov; V. A. Krys'ko. Nonlinear statics and dynamics of porous functional-gradient nanobeam taking into account transverse shifts. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 4, pp. 587-597. http://geodesic.mathdoc.fr/item/ISU_2024_24_4_a9/

[1] Kumar R., Lal A., Singh B. N., Singh J., “Non-linear analysis of porous elastically supported FGM plate under various loading”, Composite Structures, 233 (2020), 111721 | DOI

[2] Shafiei N., Mirjavadi S. S., Afshari B. M., Rabby S., Kazemi M., “Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams”, Computer Methods Applied Mechanics and Engineering, 322 (2017), 615–632 | DOI

[3] Shafiei N., Mirjavadi S. S., Afshari B. M., Rabby S., Hamouda A. M. S., “Nonlinear thermal buckling of axially functionally graded micro and nanobeams”, Composite Structures, 168 (2017), 428–439 | DOI

[4] Changho Oh, Stovall C. B., Dhaouadi W., Carpick R. W., de Boer M. P., “The strong effect on MEMS switch reliability of film deposition conditions and electrode geometry”, Microelectronics Reliability, 98 (2019), 131–143 | DOI

[5] Fan F., Xu Y., Sahmani S., Safaei B., “Modified couple stress-based geometrically nonlinear oscillations of porous functionally graded microplates using NURBS-based isogeometric approach”, Computer Methods in Applied Mechanics and Engineering, 372 (2020), 113400 | DOI

[6] Ebrahimi F., Barati M. R., “Small-scale effects on hygro-thermo-mechanical vibration of temperaturedependent nonhomogeneous nanoscale beams”, Mechanics of Advanced Materials and Structures, 24:11 (2017), 924–936 | DOI

[7] Jouneghani F. Z., Dimitri R., Tornabene F., “Structural response of porous FG nanobeams under hygro-thermo-mechanical loadings”, Composites Part B: Engineering, 152 (2018), 71–78 | DOI

[8] Ebrahimi F., Dabbagh A., “Wave dispersion characteristics of heterogeneous nanoscale beams via a novel porosity-based homogenization scheme”, The European Physical Journal Plus, 134 (2019), 157 | DOI

[9] Messai A., Fortas L., Merzouki T., Houari M. S. A., “Vibration analysis of FG reinforced porous nanobeams using two variables trigonometric shear deformation theory”, Structural Engineering and Mechanics, 81:4 (2022), 461–479 | DOI

[10] Xu X., Karami B., Shahsavari D., “Time-dependent behavior of porous curved nanobeam”, International Journal of Engineering Science, 160 (2021), 103455 | DOI

[11] Yang F., Chong A. C. M., Lam D. C. C., Tong P., “Couple stress based strain gradient theory for elasticity”, International Journal of Solids and Structures, 39 (2002), 2731–2743 | DOI

[12] Awrejcewicz J., Krysko A. V., Smirnov A., Kalutsky L. A., Zhigalov M. V., Krysko V. A., “Mathematical modeling and methods of analysis of generalized functionally gradient porous nanobeams and nanoplates subjected to temperature field”, Meccanica, 57 (2022), 1591–1616 | DOI

[13] Miller R. E., Shenoy V. B., “Size-dependent elastic properties of nanosized structural elements”, Nanotechnology, 11:3 (2000), 139–147 | DOI

[14] Krysko V. A., Awrejcewicz J., Komarov S. A., “Nonlinear deformations of spherical panels subjected to transversal load action”, Computer Methods Applied Mechanics and Engineering, 194 (2005), 3108–3126 | DOI

[15] Gulick D., Encounters with chaos, McGraw-Hill College, New York, 1992, 224 pp.

[16] Awrejcewicz J., Krysko A. V., Erofeev N. P., Dobriyan V., Barulina M. A., Krysko V. A., “Quantifying chaos by various computational methods. Part 1: Simple systems”, Entropy, 20:3 (2018), 175 | DOI