A DIRECT ANALYSIS OF NONLINEAR SYSTEMS WITH EXTERNAL PERIODIC EXCITATIONS VIA NORMAL FORMS

机译：通过正规形式直接分析带有外部周期激励的非线性系统

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This study presents a direct methodology for the analysis of nonlinear dynamic systems with external periodic forcing via an application of the theory of normal forms. Rather than introducing a new state variable to reduce the problem to a homogenous one, we apply a set of time-dependant near-identity transformations to construct the normal forms. The proposed method can be applied to time-invariant as well as time varying systems. After discussing the time-invariant case, the methodology is extended to systems with time-periodic coefficients. The time periodic case is handled through an application of the Lyapunov-Floquet (L-F) transformation. It has been shown that all resonance conditions can be obtained in a closed form. Further, for time invariant case, if the superharmonic response is dominant, a simple modification can be made to yield accurate results. An example for each type of system, viz., constant coefficients and time-varying coefficients is included to demonstrate effectiveness of the method. It is observed that the linear parametric excitation term need not be small as generally assumed in perturbation and averaging techniques. The results obtained by proposed method are compared with numerical solutions.

机译：这项研究提出了一种通过应用规范形式理论来分析带有外部周期性强迫的非线性动力系统的直接方法。我们没有引入新的状态变量来将问题简化为同质的变量，而是应用了一组时间相关的近恒身份转换来构造普通形式。所提出的方法可以应用于时不变以及时变系统。在讨论了时不变情况后，该方法扩展到了具有时周期性系数的系统。通过应用Lyapunov-Floquet（L-F）变换来处理时间周期情况。已经表明，可以以封闭形式获得所有共振条件。此外，对于时不变的情况，如果超谐响应占主导，则可以进行简单的修改以产生准确的结果。包括每种类型的系统的示例，即常数系数和时变系数，以证明该方法的有效性。可以看出，线性参量激励项不必像扰动和平均技术中通常假定的那样小。将所提方法获得的结果与数值解进行比较。

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来源
《ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2007》|2007年|P.845852|共2页
会议地点 Las VegasNV(US);Las VegasNV(US);Las VegasNV(US)
作者
Amit P. Gabale; S. C. Sinha;
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作者单位

Nonlinear Systems Research Laboratory Auburn University, Auburn, USA;

Fellow ASME Nonlinear Systems Research Laboratory Auburn University. Auburn. USA;

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原文格式 PDF
正文语种 eng
中图分类柔性制造系统及柔性制造单元;
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专利

1. A direct analysis of nonlinear systems with external periodic excitations via normal forms [J] . Amit P. Gabale, S. C. Sinha Nonlinear Dynamics . 2009,第1a2期

机译：通过范式直接分析具有外部周期性激励的非线性系统
2. A direct analysis of nonlinear systems with external periodic excitations via normal forms [J] . Gabale AP, Sinha SC Nonlinear dynamics . 2009,第1a2期

机译：通过范式直接分析带有外部周期性激励的非线性系统
3. A direct approach for simplifying nonlinear systems with external periodic excitation using normal forms [J] . Nonlinear dynamics . 2020,第2期

机译：一种使用正常形式简化外周期激励的非线性系统的直接方法
4. A DIRECT ANALYSIS OF NONLINEAR SYSTEMS WITH EXTERNAL PERIODIC EXCITATIONS VIA NORMAL FORMS [C] . Amit P. Gabale, S. C. Sinha ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference . 2008

机译：通过正常形式直接分析外部周期性激励的非线性系统
5. External and parametric random excitation of nonlinear offshore systems. [D] . Thampi, Sreekumar Krishnan. 1989

机译：非线性海上系统的外部和参数随机激励。
6. Stochastic response analysis for nonlinear vibration systems with adjustable stiffness property under random excitation [O] . Shenlong Wang, Kaixin Han 2012

机译：随机激励下具有可调刚度的非线性振动系统的随机响应分析
7. Decision-making is the process of analyzing information about a problem situation and comparing it to a specific conclusion in order to solve a specific problematic (Yıkılmaz, 2001; Miller and Byrnes, 2001). Decision-making styles are a mechanism that is influenced by the internal and external conditions that determine the direction of the decisions of the individual, the content of the decision-making process, and the outcome of the decision-making process (Payne, Bettman and Johson, 1993; Bavol’ár and Orosová, 2015). ACT is a contemporary member of the Cognitive Behavioral Therapy family. ACT (Acceptance and commitment therapy) has both similar and different directions with Behavioral Therapies and Cognitive Therapies (Herbet and Forman, 2011; Hayes, 2004). KKT responds to classical behavioral treatments using both existential and cognitive approaches in the analysis of behavior. KKT is a science wing that tries to solve human problems with a wider perspective aimed at solving problematic human behaviors (Plumb, Stewart, Dahl and Lundgren, 2009). It is seen that there is very little research about the new approach of ACT approach when the aiming country of our country is screened and it is thought that our country will contribute to the field of psychological counseling with the work done. In the scope of the research, experimental and control groups and preliminary test, post-test and follow-up measurements of 2x3 experimental design were used. The study's study group consists of a total of 24 (12 experimental and 12 control groups) university students studying in different departments and levels, continuing their education in the academic year of 2015-2016 in Ağrı province and İbrahim Chechen University in 2015-2016 academic year. The average age of participants in the experiment and control group is 20. There were 12 participants in the experimental group, 7 female and 5 male, and 12 participants, 7 female and 5 male in the control group. Personal Information Form and Decision Making Style Scale prepared by the researcher were used in the research. In order to decide on the tests to be used in the course of analyzing the data, the scores of the participant's Decision Styles Scale pre-test, which are placed primarily in the experimental and control groups, it was analyzed whether the basic expectations of parametric tests were answered. As a result of the analysis made, the scores, skewness and kurtosis coefficients obtained from the Decision Making Styles Scale were given to the experimental and control groups. It was determined that the distribution was normal in the result of Shapiro-Wilk test, in which the skewness and kurtosis coefficients of each sub-scale were ranked between -1 and +1. Participants in the experimental and control groups; homogeneity test results for decision-style pre-test measurements indicate that the data are homogeneous. According to the results of the Mauchly Globalness Test, it has been determined that working supports the hypothesis. It was determined that there was no significant difference between the pre-test scores obtained from dependent decision-making style of experiment and control groups, but the test group showed lower mean scores at the significant level within the scores of post-test and follow-up tests. Therefore, it can be said that the ACT-oriented psychoeducation program applied to the experimental group reduces the dependent decision-making style scores from the decision style sub-dimensions and the psychoeducation program has a lasting effect. It was determined that there was no significant difference between pre-test, post-test and follow-up scores obtained from the Spontaneous-Instant Decision Style of experiment and control groups. Thus, it can be said that this situation does not cause a significant difference in the Spontaneous-Decision-Making Style scores from the decision style sub-dimensions of the ACT-oriented psychoeducation program applied to the experimental group. The ACT -oriented psychoeducation program had a decline in the intuitive decision-making styles of the individuals, but this decrease did not create significant differences. Thus, it can be said that this situation does not make a meaningful difference in the intuitive decision style scores from the decision style sub-dimensions of the KKT oriented psychoeducation program applied to the experimental group. The pre-test scores obtained from the rational decision-making style of the experimental and control groups showed that there was a difference between the post-test and the follow-up scores, but this difference was not significant. As a result of the analysis, it was determined that the test group had higher levels of rational decision style than the pre - test scores in the post test and follow - up scores, whereas the post test and follow - up test scores in the control group rational decision style showed a decrease compared to the pre - test scores. the pre - test scores. Decision-making Styles Scale Avoidant Decision Making As a result of the analysis of the mean scores of the subscale scores of pre-test, post-test and follow-up measures, the group effect was found to be insignificant. It was determined that the experimental and control groups differed significantly from the pre-test scores obtained from the avoidant decision-making style but did not show any significant change within the scores of the post-test and follow-up tests. [O] . mustafa ercengiz, ali haydar şar 2018

机译：决策是分析有关问题情况的信息并将其与特定结论进行比较的过程，以解决特定的问题（Yıkılmaz，2001; Miller和Byrnes，2001）。决策风格是一种机制，受到内部和外部条件的影响，确定个人决定的方向，决策过程的内容以及决策过程的结果（PAYNE，BETTMAN和BEDNE） Johson，1993;Bavol'ár和奥萨洛瓦，2015）。法案是认知行为治疗家庭的当代成员。行为（验收和承诺治疗）具有与行为疗法和认知疗法的类似和不同方向（Herbet和Forman，2011; Hayes，2004）。 KKT在分析行为中使用存在性和认知方法来响应古典行为治疗方法。 KKT是一个科学翼，试图解决人类问题，旨在解决有问题的人类行为（铅垂，斯图尔特，Dahl和Lundgren，2009）。有人认为，当我们国家的瞄准国家进行筛选时，有关行动方法的新方法几乎没有研究，并且认为我们的国家将为完成工作做出贡献的心理咨询领域。在研究的范围内，使用实验和对照组和初步测试，使用后测试和后续测量的2x3实验设计。该研究的研究小组包括共24名（12个实验和12个对照组）大学学生在不同的部门和水平上学习，在2015-2016学术上继续进行2015-2016的学术年度2015-2016学年年。实验和对照组参与者的平均年龄是20.实验组中有12名参与者，7名女性和5名男性，12名参与者，7名女性和5名男性。研究人员准备的个人信息表格和决策制定风格规模在研究中使用。为了决定在分析数据的过程中使用的测试，参与者的决策风格刻度预测的分数主要在实验和对照组中进行，分析了参数的基本期望吗？测试得到了回答。由于对实验和对照组给出了从决策曲调标度获得的分数，偏移和峰度分子系数。确定该分布是正常的在成熟的-WILK试验结果中，其中每亚级的偏差和刚度系数在-1到+1之间排名。实验和对照组的参与者;决策式预测测量的同质性测试结果表明数据是均匀的。根据毛毛环保试验的结果，已确定工作支持假设。据确定，从依赖决策风格的实验和对照组获得的预测分数之间没有显着差异，但测试组在测试后的分数内显示出较低的平均分数和后续的分数 - 测试。因此，可以说，应用于实验组的面向活动的心理教育程序减少了决策风格子维度的依赖决策风格分数，并且心理教育程序具有持久的效果。据确定，从实验和对照组自发决策风格获得的预测试，测试后和后续评分之间没有显着差异。因此，可以说这种情况不会导致从应用于实验组的活动导向的心理教育程序的决策风格分数的自发决策风格分数显着差异。行为的心理教育计划在个人直观的决策风格下降，但这种减少并没有产生显着的差异。因此，可以说，这种情况不会在从应用于实验组的KKT导向的心理教育程序的决策风格分数中产生有意义的决策风格分数。从实验和对照组的理性决策风格获得的预测分数显示后检验后和随访评分之间存在差异，但这种差异并不重要。由于分析，确定测试组的理性决策风格较高，而不是后测试和后续分数的预测分数，而对照组合理决策风格的后测试和后续测试分数显示出与预测试分数相比的减少。预测分数。决策款式扩展避免决策由于分析了预测试，测试后和后续措施的班次评分的平均分数，发现群体效应是微不足道的。确定实验和对照组从避免决策风格获得的预测评分中显着不同，但在测试后和后续测试的分数内没有显示出任何重大变化。
8. Normal Forms and Periodic Solutions in the Theory of Nonlinear Oscillations. Existence and Asymptotic Theory [R] . van der Beek, C. G. A. 1988

机译：非线性振动理论中的正规形式与周期解。存在与渐近理论

A DIRECT ANALYSIS OF NONLINEAR SYSTEMS WITH EXTERNAL PERIODIC EXCITATIONS VIA NORMAL FORMS

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