Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation
Апстракт
This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method... and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.
Кључне речи:
Nonlocal strain gradient theory / Incremental harmonic balance method / Functionally graded beams / Fractional Pasternak layer / Fractional damping / Duffing oscillatorИзвор:
Nonlinear Dynamics, 2022, 107, 3, 2003-2026Издавач:
- Springer, Dordrecht
Финансирање / пројекти:
- Serbian Ministry of Education, Science, and Technological Development
- Marie Sklodowska-Curie Actions-European Commission fellowship [799201-METACTIVE, 896942-METASINK]
Напомена:
- This is the peer reviewed version of the article: Nešić, N.; Cajić, M.; Karličić, D.; Obradović, A.; Simonović, J. Nonlinear Vibration of a Nonlocal Functionally Graded Beam on Fractional Visco-Pasternak Foundation. Nonlinear Dynamics 2022, 107 (3), 2003–2026. https://doi.org/10.1007/s11071-021-07081-z
Повезане информације:
- Друга верзија
https://doi.org/10.1007/s11071-021-07081-z - Друга верзија
https://machinery.mas.bg.ac.rs/handle/123456789/3789
DOI: 10.1007/s11071-021-07081-z
ISSN: 0924-090X
WoS: 000743008200002
Scopus: 2-s2.0-85123125987
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Nešić, Nikola AU - Cajić, Milan AU - Karličić, Danilo AU - Obradović, Aleksandar AU - Simonović, Julijana PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4360 AB - This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed. PB - Springer, Dordrecht T2 - Nonlinear Dynamics T1 - Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation EP - 2026 IS - 3 SP - 2003 VL - 107 DO - 10.1007/s11071-021-07081-z ER -
@article{ author = "Nešić, Nikola and Cajić, Milan and Karličić, Danilo and Obradović, Aleksandar and Simonović, Julijana", year = "2022", abstract = "This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.", publisher = "Springer, Dordrecht", journal = "Nonlinear Dynamics", title = "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation", pages = "2026-2003", number = "3", volume = "107", doi = "10.1007/s11071-021-07081-z" }
Nešić, N., Cajić, M., Karličić, D., Obradović, A.,& Simonović, J.. (2022). Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics Springer, Dordrecht., 107(3), 2003-2026. https://doi.org/10.1007/s11071-021-07081-z
Nešić N, Cajić M, Karličić D, Obradović A, Simonović J. Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics. 2022;107(3):2003-2026. doi:10.1007/s11071-021-07081-z .
Nešić, Nikola, Cajić, Milan, Karličić, Danilo, Obradović, Aleksandar, Simonović, Julijana, "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation" in Nonlinear Dynamics, 107, no. 3 (2022):2003-2026, https://doi.org/10.1007/s11071-021-07081-z . .