A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Free Vibration Analysis of Pre-deformed Bi-directionally Graded Beam Supported on Nonlinear Elastic Foundation
https://orcid.org/http://orcid.org/0000-0003-0968-2258
https://orcid.org/http://orcid.org/0000-0003-3530-9123
The present article considers a bi-directional functionally graded (BDFG) beam on nonlinear elastic foundation to investigate nonlinear free vibration behaviour. A power-law distribution function is considered to describe material gradation in both the longitudinal and transverse directions. The beam foundation is considered as a nonlinear elastic one that consists of a cubic nonlinear layer and a shear layer. The beam kinematics is modelled following the principle of Timoshenko beam theory. A whole domain semi analytical formulation which considers von Kármán type geometric nonlinearity, is adopted to derive the detailed nonlinear equation sets. The solution is obtained by using an iterative numerical method. The results are furnished to study the influences of material gradation indices of BDFG beam, as well as, the influences of various stiffness parameters of nonlinear foundation, on the natural frequencies of the system. In a few cases, linear and nonlinear mode shape plots are obtained.
Free Vibration Analysis of Pre-deformed Bi-directionally Graded Beam Supported on Nonlinear Elastic Foundation
https://orcid.org/http://orcid.org/0000-0003-0968-2258
https://orcid.org/http://orcid.org/0000-0003-3530-9123
The present article considers a bi-directional functionally graded (BDFG) beam on nonlinear elastic foundation to investigate nonlinear free vibration behaviour. A power-law distribution function is considered to describe material gradation in both the longitudinal and transverse directions. The beam foundation is considered as a nonlinear elastic one that consists of a cubic nonlinear layer and a shear layer. The beam kinematics is modelled following the principle of Timoshenko beam theory. A whole domain semi analytical formulation which considers von Kármán type geometric nonlinearity, is adopted to derive the detailed nonlinear equation sets. The solution is obtained by using an iterative numerical method. The results are furnished to study the influences of material gradation indices of BDFG beam, as well as, the influences of various stiffness parameters of nonlinear foundation, on the natural frequencies of the system. In a few cases, linear and nonlinear mode shape plots are obtained.
Free Vibration Analysis of Pre-deformed Bi-directionally Graded Beam Supported on Nonlinear Elastic Foundation
https://orcid.org/http://orcid.org/0000-0003-0968-2258
https://orcid.org/http://orcid.org/0000-0003-3530-9123
The present article considers a bi-directional functionally graded (BDFG) beam on nonlinear elastic foundation to investigate nonlinear free vibration behaviour. A power-law distribution function is considered to describe material gradation in both the longitudinal and transverse directions. The beam foundation is considered as a nonlinear elastic one that consists of a cubic nonlinear layer and a shear layer. The beam kinematics is modelled following the principle of Timoshenko beam theory. A whole domain semi analytical formulation which considers von Kármán type geometric nonlinearity, is adopted to derive the detailed nonlinear equation sets. The solution is obtained by using an iterative numerical method. The results are furnished to study the influences of material gradation indices of BDFG beam, as well as, the influences of various stiffness parameters of nonlinear foundation, on the natural frequencies of the system. In a few cases, linear and nonlinear mode shape plots are obtained.
Free Vibration Analysis of Pre-deformed Bi-directionally Graded Beam Supported on Nonlinear Elastic Foundation
J. Inst. Eng. India Ser. C
Lohar, Hareram (author) / Mitra, Anirban (author)
Journal of The Institution of Engineers (India): Series C ; 106 ; 157-169
2025-02-01
13 pages
Article (Journal)
Electronic Resource
English
Nonlinear Free Vibration of Functionally Graded Nanobeams on Nonlinear Elastic Foundation
| Springer Verlag | 2016
| British Library Online Contents | 2012
| British Library Online Contents | 2017
| British Library Online Contents | 2017