2024/04/26 by Jun Chen, Wenchao Qu, Chao Ye +2 · 4 citations
Engineering · #Composite Structure Analysis and Optimization #Composite material #Elasticity and Material Modeling #Engineering #Foundation (evidence) #Hyperelastic material #Materials science #Nonlinear system #Ogden #Physics #Structural Behavior of Reinforced Concrete #Structural engineering
paper · doi:10.1142/s0219455425500968
published in International Journal of Structural Stability and Dynamics 25(09) (World Scientific)
openalex publication_date 2024/04/26 · crossref created 2024/04/26 · crossref issued 2024/06/01 · crossref published 2024/06/01 · crossref published-online 2024/06/01 · crossref deposited 2025/04/24 · crossref published-print 2025/05/15 · openalex created_date 2025/10/10 · crossref indexed 2026/08/05 · openalex updated_date 2026/08/06
Hyperelastic functionally graded materials have a wide range of application prospects in soft robotics and biomedical fields. This paper investigates the nonlinear free and forced vibrations of a hyperelastic functionally graded beam (HFGB) based on higher-order shear deformation beam theory. The geometrical nonlinearity is considered by using the von-Kármán’s nonlinear theory. The three-material-parameter free energy function named as Ishihara model is employed to characterize the hyperelastic material. The power-law gradient form along the thickness direction is adopted. The HFGB is resting on the elastic foundation. The Winkler, Pasternak and nonlinear stiffness coefficients are considered. The time-harmonic external force is applied to the HFGB. The nonlinear governing equations for the vibration of the HFGB are derived by using Hamilton’s principle, and are subsequently transformed into ordinary differential equations via Galerkin’s method. The nonlinear free vibration and primary resonance of the HFGB are investigated analytically by employing the extended Hamiltonian method and multiple scales method, respectively. The results indicate that the power-law index, slenderness ratio, material properties, and elastic foundation parameters have significant influences on the nonlinear frequency of free vibration as well as the frequency–response and force–response curves of forced vibration. The phase plane method is employed to analyze the system’s stability states under various excitation amplitudes. The relative error between the results of the current computational model and the published literature is less than 0.1 percent.