VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION
Abstract
This study investigates the stability of periodic solutions of a nonlinear nonlocal strain gradient functionally graded Euler–Bernoulli beam model resting on a visco-Pasternak foundation and subjected to external harmonic excitation. The nonlinearity of the beam arises from the von Kármán strain-displacement relation. Nonlocal stress gradient theory combined with the strain gradient theory is used to describe the stress-strain relation. Variations of material properties across the thickness direction are defined by the power-law model. The governing differential equation of motion is derived by using Hamilton's principle and discretized by the Galerkin approximation. The methodology for obtaining the steady-state amplitude-frequency responses via the incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the numerical integration method and stability analysis is performed by utilizing the Floquet theory.
Keywords:
Nonlocal strain gradient theory / Functionally graded beams / Pasternak layer / Duffing oscillator / Incremental harmonic balance method / Floquet multipliersSource:
FACTA UNIVERSITATIS Series: Mechanical Engineering, 2023Publisher:
- University of Niš
Funding / projects:
- Ministry of Science, Technological Development and Innovation of the Republic of Serbia, institutional funding - 200105 (University of Belgrade, Faculty of Mechanical Engineering) (RS-MESTD-inst-2020-200105)
- Marie Skłodowska-Curie grant agreement No. 896942 (METASINK)
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Nešić, Nikola AU - Cajić, Milan AU - Karličić, Danilo AU - Lazarević, Mihailo AU - Adhikari, Sondipon PY - 2023 UR - https://machinery.mas.bg.ac.rs/handle/123456789/7064 AB - This study investigates the stability of periodic solutions of a nonlinear nonlocal strain gradient functionally graded Euler–Bernoulli beam model resting on a visco-Pasternak foundation and subjected to external harmonic excitation. The nonlinearity of the beam arises from the von Kármán strain-displacement relation. Nonlocal stress gradient theory combined with the strain gradient theory is used to describe the stress-strain relation. Variations of material properties across the thickness direction are defined by the power-law model. The governing differential equation of motion is derived by using Hamilton's principle and discretized by the Galerkin approximation. The methodology for obtaining the steady-state amplitude-frequency responses via the incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the numerical integration method and stability analysis is performed by utilizing the Floquet theory. PB - University of Niš T2 - FACTA UNIVERSITATIS Series: Mechanical Engineering T1 - VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION DO - 10.22190/FUME230419022N ER -
@article{ author = "Nešić, Nikola and Cajić, Milan and Karličić, Danilo and Lazarević, Mihailo and Adhikari, Sondipon", year = "2023", abstract = "This study investigates the stability of periodic solutions of a nonlinear nonlocal strain gradient functionally graded Euler–Bernoulli beam model resting on a visco-Pasternak foundation and subjected to external harmonic excitation. The nonlinearity of the beam arises from the von Kármán strain-displacement relation. Nonlocal stress gradient theory combined with the strain gradient theory is used to describe the stress-strain relation. Variations of material properties across the thickness direction are defined by the power-law model. The governing differential equation of motion is derived by using Hamilton's principle and discretized by the Galerkin approximation. The methodology for obtaining the steady-state amplitude-frequency responses via the incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the numerical integration method and stability analysis is performed by utilizing the Floquet theory.", publisher = "University of Niš", journal = "FACTA UNIVERSITATIS Series: Mechanical Engineering", title = "VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION", doi = "10.22190/FUME230419022N" }
Nešić, N., Cajić, M., Karličić, D., Lazarević, M.,& Adhikari, S.. (2023). VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION. in FACTA UNIVERSITATIS Series: Mechanical Engineering University of Niš.. https://doi.org/10.22190/FUME230419022N
Nešić N, Cajić M, Karličić D, Lazarević M, Adhikari S. VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION. in FACTA UNIVERSITATIS Series: Mechanical Engineering. 2023;. doi:10.22190/FUME230419022N .
Nešić, Nikola, Cajić, Milan, Karličić, Danilo, Lazarević, Mihailo, Adhikari, Sondipon, "VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION" in FACTA UNIVERSITATIS Series: Mechanical Engineering (2023), https://doi.org/10.22190/FUME230419022N . .