Derivatives of Eigenvalues for Torsional Vibration of Geared Shaft Systems

1993 ◽  
Vol 115 (3) ◽  
pp. 277-279 ◽  
Author(s):  
Liu Zhong-Sheng ◽  
Chen Su-Huan ◽  
Xu Tao
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Design Parameter ◽  
Practical Importance ◽  
Design Sensitivity ◽  
Shaft System ◽  
Eigenvalue Derivatives ◽  
Derivatives Of

Design sensitivity analysis of natural frequency for geared shaft systems is of practical importance in the optimal design of these systems. This note provides a simple and easily implemented method to calculate the eigenvalue derivatives of a geared shaft system with respect to a design parameter ν, including gear inertia J, shaft stiffness K, and transmission ratio Q, when the eigensolution is known. An example is given to illustrate the method.

Design sensitivity analysis for optimal design of geometrically nonlinear lattice structures

2018 ◽  
Vol 168 ◽  
pp. 915-928 ◽  
Author(s):  
Ji-Yang Fu ◽  
Ben-Gang Wu ◽  
Jiu-Rong Wu ◽  
Ting Deng ◽  
Yong-Lin Pi ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Geometrically Nonlinear ◽  
Lattice Structures ◽  
Nonlinear Lattice

Analysis and Optimal Design of Spatial Mechanical Systems

1987 ◽  
Author(s):  
H. Ashrafeiuon ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Sensitivity ◽  
General Purpose ◽  
Design Sensitivity Analysis ◽  
Analysis And Design ◽  
Spatial Systems

Abstract This paper presents a new approach to optimal design of large multibody spatial mechanical systems. This approach uses symbolic computing to generate the necessary equations for dynamic analysis and design sensitivity analysis. Identification of system topology is carried out using graph theory. The equations of motion are formulated in terms of relative joint coordinates through the use of velocity transformation matrix. Design sensitivity analysis is carried out using the Direct Differentiation method applied to the relative joint coordinate formulation for spatial systems. Symbolic manipulation programs are used to develop subroutines which provide information for dynamic and design sensitivity analysis. These subroutines are linked to a general purpose computer program which performs dynamic analysis, design sensitivity analysis, and optimization. An example is presented to demonstrate the efficiency of the approach.

Sensitivity Analysis and Application of Natural Frequency of Torsional Vibration of Rotor System

2008 ◽  
Author(s):  
Qing He ◽  
Dongmei Du
Keyword(s):  
Sensitivity Analysis ◽  
Electric Power ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Electric Power System ◽  
Rotor System ◽  
Analysis Method ◽  
Turbine Generator ◽  
Sensitivity Analysis Method

The disturbance of electric power system makes large-scale turbine-generator shafts generate torsional vibration. A available method to restrain the torsional vibration of turbine-generator shafts is that all the natural frequencies of torsional vibration of turbine-generator shafts must keep away from the working frequency and its harmonic frequencies as well as all the frequencies that possibly bring on interaction between turbine-generator and electric power system so that the torsional resonation of shafts may not occur. A dynamic design method for natural frequencies of torsional vibration of rotor system based on sensitivity analysis is presented. The sensitivities of natural frequency of torsional vibration to structure parameters of rotor system are obtained by means of the theory of sensitivity. After calculated the torsional vibration dynamic characteristics of original shafts of a torsional vibration stand that simulates the real shafts of 300MW turbine-generator, the dynamic modification for the torsional vibration natural frequency is carried out by the sensitivity analysis method, which makes the first-five natural frequencies of torsional vibration of the stand is very close to the design object. It is proved that the sensitivity analysis method can be used to the dynamic adjustment and optimal design of real shafts of turbine-generator.

Analysis and Optimal Design of Spatial Mechanical Systems

1990 ◽  
Vol 112 (2) ◽  
pp. 200-207 ◽  
Author(s):  
H. Ashrafiuon ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Sensitivity ◽  
General Purpose ◽  
Design Sensitivity Analysis ◽  
Sensitivity Analyses ◽  
Spatial Systems ◽  
Spatial System

This paper presents a new approach to optimal design of large multibody spatial mechanical systems which takes advantage of both numerical analysis and symbolic computing. Identification of system topology is carried out using graph theory. The equations of motion are formulated in terms of relative joint coordinates through the use of a velocity transformation matrix. Design sensitivity analysis is carried out using the direct differentiation method applied to the relative joint coordinate formulation for spatial systems. The symbolic manipulation program MACSYMA is used to automatically generate the necessary equations for both dynamic and design sensitivity analyses for any spatial system. The symbolic equations are written as FORTRAN statements that are linked to a general purpose computer program which performs dynamic analysis, design sensitivity analysis, and optimization, using numerical techniques. Examples are presented to demonstrate reliability and efficiency of this approach.

Probabilistic Optimal Design Using Second Moment Criteria

1988 ◽  
Vol 110 (3) ◽  
pp. 324-329 ◽  
Author(s):  
A. D. Belegundu
Keyword(s):  
Finite Element Method ◽  
Sensitivity Analysis ◽  
Optimal Design ◽  
Design Sensitivity ◽  
Design Criterion ◽  
Second Order ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Programming Technique ◽  
Second Moment

Probability-based optimal design of structures is presented. The emphasis here is to develop a practical approach to optimal design given random design parameters. The method is applicable to structures which are modeled using the finite element method. The Hasofer-Lind (H-L) second-moment design criterion is used to formulate the general design problem. A method for calculating the sensitivity coefficients is presented, which involves second-order design sensitivity analysis. The importance of second order derivatives is established. A nonlinear programming technique is used to solve the problem. Numerical results are presented, where stiffness parameters are treated as random variables.

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