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Geomechanics and Engineering Volume 31, Number 1, October10 2022 , pages 099-112 DOI: https://doi.org/10.12989/gae.2022.31.1.099 |
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The influence of Winkler-Pasternak elastic foundations on the natural frequencies of imperfect functionally graded sandwich beams |
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Mehmet Avcar, Lazreg Hadji and Recep Akan
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| Abstract | ||
| The present study examines the natural frequencies (NFs) of perfect/imperfect functionally graded sandwich beams (P/IP-FGSBs), which are composed of a porous core constructed of functionally graded materials (FGMs) and a homogenous isotropic metal and ceramic face sheets resting on elastic foundations. To accomplish this, the material properties of the FGSBs are assumed to vary continuously along the thickness direction as a function of the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction represented using four distinct types of porosity distribution models. Additionally, to characterize the reaction of the two-parameter elastic foundation to the Perfect/Imperfect (P/IP) FGSBs, the medium is assumed to be linear, homogeneous, and isotropic, and it is described using the Winkler-Pasternak model. Furthermore, the kinematic relationship of the P/IP-FGSBs resting on the Winkler-Pasternak elastic foundations (WPEFs) is described using trigonometric shear deformation theory (TrSDT), and the equations of motion are constructed using Hamilton' principle. A closed-form solution is developed for the free vibration analysis of P/IP-FGSBs resting on the WPEFs under four distinct boundary conditions (BCs). To validate the new formulation, extensive comparisons with existing data are made. A detailed investigation is carried out for the effects of the foundation coefficients, mode numbers (MNs), porosity volume fraction, power-law index, span to depth ratio, porosity distribution patterns (PDPs), skin core skin thickness ratios (SCSTR), and BCs on the values of the NFs of the P/IP-FGSBs. | ||
| Key Words | ||
| boundary conditions; FGMs; free vibration; porosity; sandwich beams; Winkler-Pasternak elastic foundations | ||
| Address | ||
| Mehmet Avcar and Recep Akan: Department of Civil Engineering, Faculty of Engineering, Suleyman Demirel University, Cunur, Isparta, Türkiye Lazreg Hadji: Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam; Department of Civil Engineering, University of Tiaret, BP 78 Zaaroura, Tiaret, 14000, Algeria; Laboratory of Geomatics and Sustainable Development, University of Tiaret, 14000, Algeria | ||