Nonlinear dynamic analysis of a double curvature honeycomb sandwich shell with simply supported boundaries by the homotopy analysis method

2019 ◽  
Vol 221 ◽  
pp. 110884 ◽  
Author(s):  
Yingjie Zhang ◽  
Yongqiang Li
Keyword(s):  
Dynamic Analysis ◽  
Homotopy Analysis Method ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Sandwich Shell ◽  
Analysis Method ◽  
Simply Supported ◽  
Double Curvature ◽  
Honeycomb Sandwich ◽  
Homotopy Analysis

The homotopy analysis for the nonlinear dynamics of planetary gear trains

2020 ◽  
Vol 234 (16) ◽  
pp. 3154-3165
Author(s):  
Chao Xun ◽  
Sujuan Jiao ◽  
He Dai ◽  
Xinhua Long
Keyword(s):  
Numerical Integration ◽  
Homotopy Analysis Method ◽  
Nonlinear Dynamic Analysis ◽  
Primary Resonance ◽  
Planetary Gear ◽  
Analysis Method ◽  
Planetary Gear Trains ◽  
Homotopy Analysis ◽  
Gear Trains ◽  
Harmonic Resonance

In this paper, the nonlinear oscillation of planetary gear trains is investigated by the homotopy analysis method. The nonlinearity of planetary gear trains due to the periodically time-varying mesh stiffness and contact loss are included. In contrast to the perturbation analysis, the homotopy analysis method is independent of the contact loss ratio, and then can be applied to both small and large contact loss ratios. In this article, firstly the closed-form approximations for the primary resonance, sub-harmonic resonance, and super-harmonic resonance are obtained by homotopy analysis method. The accuracy of homotopy analysis method solutions is evaluated by numerical integration simulations. Results indicate that with relatively large contact loss ratios, the amplitude–frequency curves obtained by homotopy analysis method agree better with the results obtained by numerical integration than those obtained by the method of multiple scales. This study lays a higher accurate foundation for more complex nonlinear dynamic analysis of planetary gear trains.

scholarly journals A new nonlinear dynamic analysis method of rotor system supported by oil-film journal bearings

2014 ◽  
Vol 38 (21-22) ◽  
pp. 5239-5255 ◽  
Author(s):  
Li-Hua Yang ◽  
Wei-Min Wang ◽  
Shi-Quan Zhao ◽  
Yan-Hua Sun ◽  
Lie Yu
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Journal Bearings ◽  
Rotor System ◽  
Analysis Method ◽  
Oil Film

An Efficient and Robust Nonlinear Dynamic Analysis Method for Framed Structures Using the Rigid Body Rule

2021 ◽  
Author(s):  
Zhaohui Chen ◽  
Min He ◽  
Yuchen Tao ◽  
Y. B. Yang
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Integration Method ◽  
Nonlinear Dynamic Analysis ◽  
Direct Integration ◽  
Analysis Method ◽  
Framed Structures ◽  
Geometric Stiffness ◽  
Highly Nonlinear

In this paper, by implanting the rigid body rule (RBR)-based strategy for static nonlinear problems into the implicit direct integration procedure, an efficient and robustness nonlinear dynamic analysis method for the response of framed structures with large deflections and rotations is proposed. The implicit integration method proposed by Newmark is improved by inserting an intermediate time into the time step and by adding the 3-point backward difference in the second substep so as to preserve the momentum conservation and to maintain the stability of the direct integration method. To solve the equivalent incremental equations of motion, the RBR is built in to deal with the rigid rotations and the resulting additional nodal forces of element. During the increment-iterative procedure, the use of RBR-qualified geometric stiffness in the predictor reduces the numbers of iterations, while the elastic stiffness alone in the corrector to update the element nodal forces makes the computation efficiency and convergence with no virtual forces caused by the ill geometric stiffness. The proposed algorithm is advanced in the applications of several framed structures with highly nonlinear behavior in the dynamic response by its simplicity, efficient and robustness.

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