Response Analysis of Acoustic Field With Convex Parameters

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Baizhan Xia ◽  
Dejie Yu

The acoustic field with convex parameters widely exists in the engineering practice. The vertex method and the anti-optimization method are not considered as appropriated approaches for the response analysis of acoustic field with convex parameters. The shortcoming of the vertex method is that the local optima out of vertexes cannot be identified. The disadvantage of the anti-optimization method is that the analytical formulation of response may be not obtained. To analyze the acoustic field with convex parameters efficiently and effectively, a first-order convex perturbation method (FCPM) and a second-order convex perturbation method (SCPM) are presented. In FCPM, the response of the acoustic field with convex parameters is expanded with the first-order Taylor series. In SCPM, the response of the acoustic field with convex parameters is expanded with the second-order Taylor series neglecting the nondiagonal elements of Hessian matrix. The variational bounds of the expanded responses in FCPM and SCPM are yielded by the Lagrange multiplier method. The accuracy and efficiency of FCPM and SCPM are investigated by numerical examples.

2012 ◽  
Vol 204-208 ◽  
pp. 2824-2831
Author(s):  
You Fa Yang ◽  
Shuai Li ◽  
Ling Ling

First order iterative algorithm, mixed iterative algorithm, structural damage identification using static and dynamic data were put forward. The first and second order sensitivity matrixes of modal parameters that respect to the damage member were derived, and the modal truncation error which produced during the derivation of modal mode sensitivity was improved. The first and second order sensitivity equations were established respectively based on the principle of Taylor series expansion. And the solving method of these sensitivity equations was studied. Mixed iterative algorithm took up the second order nonlinear analytical solution as the first substituting value, and then the first substituting value was modified based on the Taylor series bias error using the solution of the first order sensitivity equation. It showed that the mixed iterative algorithm in this paper had a better convergence and a faster iteration speed because the higher precision second order nonlinear analytical solution was adopted. Because the method using static and dynamic data combined the static information and dynamic information of the structure, it could react the inside information of the structure more comprehensively, the result of damage identification was more accurate and it would be adapted more widely.


2017 ◽  
Vol 868 ◽  
pp. 201-206
Author(s):  
Han Hui ◽  
Li Na Hao ◽  
Zhang Qi ◽  
Gao Xiang

Steam turbine generator unit, water pump and other high speed revolution symmetric flexible rotor were regarded as research objects in this paper. According to variation characteristic of rotor shaft in rigid and flexible working mode, nine-reel high pressure water pump rotor was analyzed. The former four-order intrinsic frequency of flexible rotor was obtained by modal analysis and harmonic response analysis. The methods of reaction force response and unbalance response were been studied after first order and second order resonance region eliminating in different modes of simple harmonic exciting force. Based on above theoretical research results, trapezoid counterweight method was proposed for dynamic balance of flexible rotor. This method solved problem that rigid dynamic balance of low speed rotor was destroyed after first order and second order resonance region counter weight in dynamic balance of flexible rotor. The dynamic balancing techniques of flexible rotor could be improved the qualities of rotor and its relative products by this method, eliminating the vibration of unbalance mass of products radically.


Author(s):  
M. Bugra Akin ◽  
Wolfgang Sanz

Optimal shape design is widely used today to improve a variety of designs. It is a challenging task and several methods have been developed. These methods are generally classified by the order of derivatives used. They are zero, first and second order methods, which, as their names imply, use only the function values, first and second order derivatives, respectively. There are two common approaches to first order methods. These are the finite difference method and the adjoint method. The finite difference method requires an additional CFD calculation for each parameter, which quickly becomes computationally very expensive as the number of parameters rise. The adjoint method provides a computationally efficient alternative in such cases. But the computational cost of the adjoint method also becomes expensive if additional constraints are introduced or when multi-objective optimizations are considered. This paper presents a novel optimization strategy which can be classified as a quasi-gradient based optimization method. As with the finite differences method an additional CFD calculation is performed for each parameter. But in order to save computational time the simulations are not performed to full convergence so that the derivatives are not calculated accurately. The only information that can be obtained in this way is whether the chosen contour manipulation leads to an improvement. A line search method is introduced that can find an optimum using this incomplete gradient information. The optimization method is demonstrated by the quasi-3d optimization of a U-bend.


Electronics ◽  
2021 ◽  
Vol 10 (21) ◽  
pp. 2649
Author(s):  
Hyeong-Woo Ham ◽  
Joon-Ho Lee

In this paper, it is shown how the performance of the monopulse algorithm in the presence of an additive noise can be obtained analytically. In a previous study, analytic performance analysis based on the first-order Taylor series and the second-order Taylor series was conducted. By adopting the third-order Taylor series, it is shown that the analytic performance based on the third-order Taylor series can be brought closer to the performance of the original monopulse algorithm than the analytic performance based on the first-order Taylor series and the second-order Taylor series.


2000 ◽  
Author(s):  
Leslie Ng ◽  
Richard Rand

Abstract We investigate the nonlinear dynamics of the classical Mathieu equation to which is added a nonlinearity which is a general cubic in x, ẋ. We use a perturbation method (averaging) which is valid in the neighborhood of 2:1 resonance, and in the limit of small forcing and small nonlinearity. By comparing the predictions of first order averaging with the results of numerical integration, we show that it is necessary to go to second order averaging in order to obtain the correct qualitative behavior. Analysis of the resulting slow flow equations is accomplished both analytically as well as by use of the software AUTO.


2016 ◽  
Vol 33 (2) ◽  
Author(s):  
Mengwu Guo ◽  
Hongzhi Zhong ◽  
Kuan You

Purpose For eigenvalue problems containing uncertain inputs characterized by fuzzy basic parameters, first-order perturbation methods have been developed to extract eigen-solutions, but either the result accuracy or the computational efficiency of these methods is less satisfactory. This paper presents an efficient method for estimation of fuzzy eigenvalues with high accuracy. Design/methodology/approach Based on the first order derivatives of eigenvalues and modes with respect to the fuzzy basic parameters, expressions of the second order derivatives of eigenvalues are formulated. Then a second-order perturbation method is introduced to provide more accurate fuzzy eigenvalue solutions. Only one eigenvalue solution is sought for the perturbed formulation, and quadratic programming is performed to simplify the alpha-level optimization. Findings Fuzzy natural frequencies and buckling loads of some structures are estimated with good accuracy, illustrating the high computational efficiency of the proposed method. Originality/value Up to the second order derivatives of the eigenvalues with respect to the basic parameters are represented in functional forms, which are used to introduce a second-order perturbation method for treatment of fuzzy eigenvalue problems. The corresponding alpha-level optimization is thus simplified into quadratic programming. The proposed method provides much more accurate interval solutions at alpha-cuts for the membership functions of fuzzy eigenvalues. Analogously, third- and higher-order perturbation methods can be developed for more stringent accuracy demands or for the treatment of stronger nonlinearity. The present work can be applied to realistic structural analysis in civil engineering, especially for those structures made of dispersed materials such as concrete and soil.


1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.


2017 ◽  
Vol 9 (3) ◽  
pp. 17-30
Author(s):  
Kelly James Clark

In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms (the kinds of religion we find in the world), there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican (hereafter M&M), are “beliefs that claim unique authority for some particular religious tradition in preference to all others” (3). According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according to M&M, we have perfectly natural explanations of the causes that underlie such beliefs (they seem to conceive of such natural explanations as debunking explanations). They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes” (3). Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal (according to contemporary psychology of religion), empirically supported (according to philosophy in the form of the Fine-Tuning Argument), and beneficial (and so justified pragmatically). With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good(s) of religion (cooperation, trust, etc) without its bad(s) (conflict and violence). Second-order supernaturalism is thus rational (and possibly true) and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that (first-order) religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too.Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good (agatheism), is rational (agreeing that their particular claims are not) and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world.While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that (a) belief in first-order religion is not a primary motivator of conflict and violence (and so eliminating first-order religion won’t reduce violence). Second, partly contra Salamon, who I think is half right (but not half wrong), I will argue that (b) the religious resources for compassion can and should come from within both the particular (often exclusivist) and the universal (agatheistic) aspects of religious beliefs. Finally, I will argue that (c) both are guilty, as I am, of the philosopher’s obsession with belief. 


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