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Double‐mode modeling of nonlinear flexural vibration analysis for a symmetric rectangular honeycomb sandwich thin panel by the homotopy analysis method
Author(s) -
Li Yongqiang,
Yao WenKai
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6703
Subject(s) - homotopy analysis method , nonlinear system , galerkin method , mathematics , vibration , mathematical analysis , transverse plane , flexural strength , honeycomb , honeycomb structure , ordinary differential equation , homotopy , structural engineering , differential equation , materials science , geometry , physics , composite material , acoustics , engineering , quantum mechanics , pure mathematics
Nonlinear flexural vibration of a symmetric rectangular honeycomb sandwich thin panel with simply supported along all four edges is studied in this paper. The nonlinear governing equations of the symmetric rectangular honeycomb sandwich panel subjected to transverse excitations are simplified to a set of two ordinary differential equations by the Galerkin method. Based on the homotopy analysis method, the average equations of the primary resonance and harmonic resonance are obtained. The influence of structural parameters, the transverse exciting force amplitude, and transverse damping to the symmetric rectangular honeycomb sandwich panel are discussed by using the analytic approximation method. Compared with the results obtained by single‐mode modeling technique, the results obtained by double‐mode modeling technique change the softening and hardening nonlinear characteristics when Ω ≈ ω 1 , ω 1 /3, and ω 2 /3.