Analysis of modified structures by Rayleigh quotient

2021 ◽  
Vol 150 (4) ◽  
pp. A344-A344
Author(s):  
Allison Kaminski ◽  
James McDaniel
Keyword(s):  
Rayleigh Quotient

scholarly journals The Optimum Design of Stepped Shafts: A Study in Computational Optimization

1982 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Optimum Design ◽  
Critical Speed ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Minimum Principle ◽  
Problem Formulation ◽  
Rayleigh Quotient ◽  
Computational Optimization ◽  
Stepped Shaft ◽  
Determine Step

Optimum stepped shaft designs are obtained through an application of Pontryagin’s Minimum Principle. Optimum designs are obtained for a given critical speed of specified order. Indexes of Performance to be minimized include mass and rotating inertia. A general problem formulation illustrates how constraints on stress, deflections, and geometric design are taken in account. Numerical solutions are obtained to nonlinear multi-point-boundary-value-problems. A Newton-Raphson algorithm was developed to determine step locations precisely in order to facilitate the convergence of the shooting method used to solve the boundary value problem. Numerical solutions are determined with an assumed critical speed; a Rayleigh quotient calculation is used to verify that the optimum design possesses the assumed value.

Optical results with Rayleigh quotient discrimination filters

1999 ◽  
Author(s):  
Richard D. Juday ◽  
John M. Rollins ◽  
Stanley E. Monroe, Jr. ◽  
Michael V. Morelli
Keyword(s):  
Rayleigh Quotient

Performance Quality, Sensitivity, and Tolerance Specification of Mechanisms

1994 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Yufeng Long
Keyword(s):  
Signal To Noise Ratio ◽  
Rayleigh Quotient ◽  
Sensitivity Index ◽  
Signal To Noise ◽  
Mechanism Synthesis ◽  
Performance Quality ◽  
Mechanical Assemblies ◽  
Tolerance Specification ◽  
Position Synthesis ◽  
The Ideal

Abstract By employing Taguchi’s concept to mechanism synthesis, this paper presents the theory and technique to identify a robust design, which is the least sensitive to the tolerances, for mechanisms and to determine the tolerance specification for the best performance and manufacturability. The method is demonstrated in finite and infinitesimal position synthesis. The sensitivity Jacobian is first introduced to relate the performance tolerances and the dimensional tolerances. The Rayleigh quotient of the sensitivity Jacobian, which is equivalent to Taguchi’s signal to noise ratio, is then used to define the performance quality and a sensitivity index is introduced to measure the sensitivity of the performance quality to the dimensional tolerances for the whole system. The ideal tolerance specification is obtained in closed form. It shows how the tolerance specification affects the performance quality and that the performance quality can be significantly improved by tightening a key tolerance while loosening the others. The theory is general and the technique is readily adaptable to almost any form and type of mechanical system, including multiple-loop linkages and mechanical assemblies or even structures.

scholarly journals A Paneitz–Branson type equation with Neumann boundary conditions

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Denis Bonheure ◽  
Hussein Cheikh Ali ◽  
Robson Nascimento
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Type Equation ◽  
Neumann Boundary ◽  
Rayleigh Quotient ◽  
Neumann Boundary Conditions ◽  
Asymptotic Estimates ◽  
Best Constant ◽  
Order Elliptic Problem ◽  
Nonconstant Solution

AbstractWe consider the best constant in a critical Sobolev inequality of second order. We show non-rigidity for the optimizers above a certain threshold, namely, we prove that the best constant is achieved by a nonconstant solution of the associated fourth order elliptic problem under Neumann boundary conditions. Our arguments rely on asymptotic estimates of the Rayleigh quotient. We also show rigidity below another threshold.

scholarly journals The Rayleigh quotient and dynamic programming

1978 ◽  
Vol 1 (4) ◽  
pp. 401-405
Author(s):  
Richard Bellman
Keyword(s):  
Differential Equation ◽  
Dynamic Programming ◽  
Nonlinear Partial Differential Equation ◽  
Rayleigh Quotient ◽  
Programming Approach ◽  
Nonlinear Characteristic ◽  
Dynamic Programming Approach ◽  
Computational Aspects ◽  
Characteristic Values ◽  
Matrix Problems

The purpose of this paper is to derive a nonlinear partial differential equation for whichλgiven by (1.3), is one value of the solution. In Section 2, we derive this equation using a straightforward dynamic programming approach. In Section 3, we discuss some computational aspects of derermining the solution of this equation. In Section 4, we show that the same method may be applied to the nonlinear characteristic value problem. In Section 5, we discuss how the method may by applied to find the higher characteristic values. In Section 5, we discuss how the same method may be applied to some matrix problems. Finally, in Section 7, we discuss selective computation.

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