Dynamic Response of Large Complex Segmentally Periodic Structures by the Symplectic Matrix Method

2009 ◽  
Author(s):  
M. Zhou ◽  
F.W. Williams
Keyword(s):  
Dynamic Response ◽  
Matrix Method ◽  
Periodic Structures ◽  
Symplectic Matrix ◽  
Large Complex

Dynamic response of large complex systems

1960 ◽  
Vol 269 (4) ◽  
pp. 274-298
Author(s):  
Mihajlo D. Mesarović
Keyword(s):  
Dynamic Response ◽  
Complex Systems ◽  
Large Complex

Multimodal Transfer Matrix Method Applied to 3-D Periodic Structures

2021 ◽  
Author(s):  
Federico Giusti ◽  
Francisco Mesa ◽  
Qiao Chen ◽  
Guido Valerio ◽  
Oscar Quevedo-Teruel
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Periodic Structures

scholarly journals Dynamic Analysis of Flexible Rotor Based on Transfer Symplectic Matrix

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Hao Deng ◽  
Xi Fang ◽  
Huachun Wu ◽  
Yiming Ding ◽  
Jinghu Yu ◽  
...  
Keyword(s):  
Transfer Matrix ◽  
Matrix Method ◽  
Critical Speed ◽  
Reference Method ◽  
Rotor System ◽  
High Order ◽  
Symplectic Matrix ◽  
Hamilton System ◽  
System A ◽  
Relative Errors

In view of the numerical instability and low accuracy of the traditional transfer matrix method in solving the high-order critical speed of the rotor system, a new idea of incorporating the finite element method into the transfer matrix is proposed. Based on the variational principle, the transfer symplectic matrix of gyro rotors suitable for all kinds of boundary conditions and supporting conditions under the Hamilton system is derived by introducing dual variables. To verify the proposed method in rotor critical speed, a numerical analysis is adopted. The simulation experiment results show that, in the calculation of high-order critical speed, especially when exceeding the sixth critical speed, the numerical accuracy of the transfer symplectic matrix method is obviously better than that of the reference method. The relative errors between the numerical solution and the exact solution are 0.0347% and 0.2228%, respectively, at the sixth critical speed. The numerical example indicates the feasibility and superiority of the method, which provides the basis for the optimal design of the rotor system.

An Accurate and Efficient Method for Dynamic Analysis of Two-Dimensional Periodic Structures

2016 ◽  
Vol 08 (02) ◽  
pp. 1650013 ◽  
Author(s):  
Q. Gao ◽  
H. W. Zhang ◽  
W. X. Zhong ◽  
W. P. Howson ◽  
F. W. Williams
Keyword(s):  
Dynamic Response ◽  
Efficient Method ◽  
Algebraic Structure ◽  
Integration Method ◽  
Periodic Structures ◽  
Computational Effort ◽  
Two Dimensional ◽  
Great Efficiency ◽  
Energy Propagation ◽  
Precise Integration

In this paper, an accurate and efficient method is presented for analyzing the dynamic response of two-dimensional (2D) periodic structures. The algebraic structure of the corresponding matrix exponential is analyzed and, based on its special structure, an accurate and efficient method for its computation is proposed. Accuracy is maintained using the precise integration method (PIM), and great efficiency is achieved in the computational effort using the periodic properties of the structure and the energy propagation features of the dynamic system. The proposed method is compared with the conventional Newmark and Runge–Kutta (R–K) methods, and it is shown to be accurate, efficient and extremely frugal in its memory requirements.

SEA Subsystem Property Identification by Periodic FEM Approach

2011 ◽  
Vol 94-96 ◽  
pp. 1979-1982
Author(s):  
Jie Gao ◽  
Ke An Chen
Keyword(s):  
Dynamic Response ◽  
High Frequency ◽  
Periodic Structures ◽  
Low Frequency ◽  
Engineering Method ◽  
Complex Structures ◽  
High Frequency Range ◽  
Frequency Range ◽  
Remarkable Improvement ◽  
Property Identification

A study on SEA properties of periodically stiffened structure was accomplished based on the periodic theory. With application of certain software, a simulation was performed on a common periodically stiffened fuselage structure. The results indicate such modeling approach reflects relatively accurate property of subsystem in mid and high frequency range, while a remarkable improvement could also be expected in low frequency range, especially for complex structures. Such approach was approved as one reliable engineering method for solving dynamic response of periodic structures.

scholarly journals Multibody System Discrete Time Transfer Matrix Method for Nonlinear Shear Dynamic analysis of Immersed Tunnels

2021 ◽  
Vol 236 ◽  
pp. 02035
Author(s):  
Zhongyuan Shen ◽  
Xue Bai
Keyword(s):  
Dynamic Response ◽  
Transfer Matrix ◽  
Discrete Time ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody System ◽  
Dynamic Stiffness ◽  
Response Analysis ◽  
Time Transfer ◽  
Shear Response

Shear seismic response analysis is critical for seismic design of immersed tunnels. According to the structural characters of immersed tunnels and shear dynamic response of their joints, a multibody dynamic model consisting of multi-rigid body, shear hinge, and viscous damping hinge is proposed for shear response analysis, in which the dynamic stiffness of the shear hinge is divided into two stages based on a threshold. Following the discrete time transfer matrix method for multibody system dynamics (MS-DT-TMM), the mechanical model and mathematical expression of each tunnel element is derived first and then assembled for the whole tunnel system. A solution procedure is proposed to solve the shear dynamic response of immersed tunnels using the proposed multibody system model. It is shown that the MS-DT-TMM has the same computational accuracy as the finite element method (FEM) and the modeling process is more efficient and flexible when compared to FEM. Although the MS-DT-TMM discussed herein is only applied to shear response analysis, it can easily be extended to analyze axial force and bending moment of immersed tunnels leading to a complete, rapid yet accurate enough seismic analysis of immersed tunnels suitable for engineering practices.

Sign in / Sign up

Export Citation Format

Share Document