Investigating nonlinear vibrations of higher-order hyper-elastic beams using the Hamiltonian method
Abstract
This paper presents a higher-order shear deformation beam theory for modeling and nonlinear vibration analysis of hyper-elastic beams made of silicon rubber and unfilled natural rubber. Four models named neo-Hookean, Mooney–Rivlin, Ishihara, and Yeoh models are presented, and their efficacy in nonlinear dynamic modeling of hyper-elastic beams has been explored. Geometric nonlinearity of the hyper-elastic beam is considered based on von-Kármán-type nonlinearity. The hyper-elastic beam is resting on a nonlinearly hardening elastic foundation. It is shown that the Ishihara model is a suitable model for nonlinear vibration analysis of hyper-elastic beams accounting for the shear deformation effect. The nonlinear governing equations based on the presented beam theory are analytically solved via the Hamiltonian method to find nonlinear vibration frequencies. It is shown that the nonlinear vibration behavior of hyper-elastic beams is influenced by rubber-material type and material parameters of the hyper-elastic model.
Collections
- Mechanical & Industrial Engineering [1342 items ]
Related items
Showing items related by title, author, creator and subject.
-
State-dependent adaptive dynamic programing for a class of continuous-time nonlinear systems
Batmani, Yazdan; Davoodi, Mohammadrez; Meskin, Nader ( Institute of Electrical and Electronics Engineers Inc. , 2016 , Conference Paper)The state-dependent Riccati equation (SDRE) technique can be used to solve optimal control problems for a wide class of nonlinear dynamical systems. In this method, instead of solving a complicated Hamilton-Jacobi-Bellman ... -
Parameter Set-mapping using kernel-based PCA for linear parameter-varying systems
Rizvi, S.Z.; Mohammadpour, J.; Toth, R.; Meskin, Nader ( Institute of Electrical and Electronics Engineers Inc. , 2014 , Conference Paper)This paper proposes a method for reduction of scheduling dependency in linear parameter-varying (LPV) systems. In particular, both the dimension of the scheduling variable and the corresponding scheduling region are shrunk ... -
Adaptive cooperative control of nonlinear multi-agent systems with uncertain time-varying control directions and dead-zone nonlinearity
Shahriari-kahkeshi, M.; Meskin, Nader ( Elsevier B.V. , 2021 , Article)This paper investigates the development of an adaptive cooperative control scheme for the consensus of uncertain nonlinear multi-agent systems subjected to uncertain time-varying control direction, disturbances, and dead-zone ...