A Direct Integration Technique for the Transient Analysis of Rotating Shafts

1982 ◽  
Vol 104 (2) ◽  
pp. 384-388
Author(s):  
F. H. Chu ◽  
W. D. Pilkey
Keyword(s):  
Transfer Matrix ◽  
Discrete Time ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Transient Analysis ◽  
Direct Integration ◽  
Structural Members ◽  
Integration Technique ◽  
Continuous Space ◽  
Rotating Shafts

The continuous space discrete time Riccati transfer matrix method is a new direct integration technique for transient analysis of structural members. This method is applied to rotating shafts with bearing systems containing masses. Numerical results are given for a rotor with isotropic bearings.

A Direct Integration Technique for the Transient Analysis of Rotating Shafts

1981 ◽  
Vol 103 (1) ◽  
pp. 244-248
Author(s):  
F. H. Chu ◽  
W. D. Pilkey
Keyword(s):  
Transfer Matrix ◽  
Discrete Time ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Transient Analysis ◽  
Direct Integration ◽  
Structural Members ◽  
Integration Technique ◽  
Continuous Space ◽  
Rotating Shafts

The Continuous Space Discrete Time Riccati Transfer Matrix Method is a new direct integration technique for transient analysis of structural members. This method is applied to rotating shafts with bearing systems containing masses. Numerical results are given for a rotor with isotropic bearings.

The Riccati Transfer Matrix Method

1978 ◽  
Vol 100 (2) ◽  
pp. 297-302 ◽  
Author(s):  
G. C. Horner ◽  
W. D. Pilkey
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
New Technique ◽  
Computational Time ◽  
Structural Members ◽  
Rotating Shaft ◽  
Rotating Shafts ◽  
A New Technique ◽  
And Storage

The Riccati transfer matrix method is a new technique for analyzing structural members. This new technique makes use of an existing large catalog of transfer matrices for various structural members such as rotating shafts. The numerical instability encountered when calculating high resonant frequencies, static response of a flexible member on a stiff foundation, or the response of a long member by the transfer matrix method is eliminated by the Riccati transfer matrix method. The computational time and storage requirements of the Riccati transfer matrix method are about half the values for the transfer matrix method. A rotating shaft analysis demonstrates the numerical accuracy of the method.

Discrete Time Finite Element Transfer Matrix Method Development for Modeling and Decentralized Control

2015 ◽  
Author(s):  
Nick Cramer ◽  
Sean Swei ◽  
Kenny Cheung ◽  
M. Teodorescu
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Discrete Time ◽  
Flight Control ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Structural Control ◽  
Method Development ◽  
Time Step ◽  
Element Transfer

The current emphasis on increasing aeronautical efficiency is leading the way to a new class of lighter more flexible airplane materials and structures, which unfortunately can result in aeroelastic instabilities. To effectively control the wings deformation and shape, appropriate modeling is necessary. Wings are often modeled as cantilever beams using finite element analysis. The drawback of this approach is that large aeroelastic models cannot be used for embedded controllers. Therefore, to effectively control wings shape, a simple, stable and fast equivalent predictive model that can capture the physical problem and could be used for in-flight control is required. The current paper proposes a Discrete Time Finite Element Transfer Matrix (DT-FETMM) model beam deformation and use it to design a regulator. The advantage of the proposed approach over existing methods is that the proposed controller could be designed to suppress a larger number of vibration modes within the fidelity of the selected time step. We will extend the discrete time transfer matrix method to finite element models and present the decentralized models and controllers for structural control.

A Method for the Calculation of Natural Frequencies of Orthotropic Axisymmetrically Loaded Shells of Revolution

1994 ◽  
Vol 116 (1) ◽  
pp. 16-25 ◽  
Author(s):  
A. Kayran ◽  
J. R. Vinson ◽  
E. Selcuk Ardic
Keyword(s):  
Numerical Integration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Shell Of Revolution ◽  
Initial Stresses ◽  
Integration Technique ◽  
Shells Of Revolution ◽  
Axisymmetric Loading

A methodology is presented for the calculation of the natural frequencies of orthotropic axisymmetrically loaded shells of revolution including the effect of transverse shear deformation. The fundamental system of equations governing the free vibration of the stress-free shells of revolution are modified such that the initial stresses due to the axisymmetric loading are incorporated into the analysis. The linear equations on the vibration about the deformed state are solved by using the transfer matrix method which makes use of the multisegment numerical integration technique. This method is commonly known as frequency trial method. The solution for the initial stresses due to axisymmetric loading is omitted; since the application of the transfer matrix method, making use of multisegment numerical integration technique for both linear and nonlinear equations are available in the literature. The method is verified by applying it to the solution of the natural frequencies of spinning disks, for which exact solutions exist in the literature, and a deep paraboloid for which approximate solutions exist. The governing equations for a shell of revolution are used to approximate circular disks by decreasing the curvature of the shell of revolution to very low values, and good agreement is seen between the results of the present method and the exact solution for spinning disks and the approximate solution for a deep paraboloid.

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