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Summary of doctoral thesis on solid mechanics: Analysis of nonlinear vibration by weighted averaging approach

The thesis has developeda technique by combining the equivalent linearization method and the weighted averagingvalueto analyze the responses of some undamped free nonlinear vibrations. | MINISTRY OF EDUCATION VIETNAM ACADEMY OF AND TRAINING SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY - Dang Van Hieu ANALYSIS OF NONLINEAR VIBRATION BY WEIGHTED AVERAGING APPROACH Major Mechanics of Solid Code 9440107 SUMMARY OF DOCTORAL THESIS IN SOLID MECHANICS Ha Noi 2021 The thesis has been completed at Graduate University Science and Technology Vietnam Academy of Science and Technology. Supervisors 1. Assoc. Prof. Dr. Ninh Quang Hai 2. Dr. Duong The Hung Reviewer 1 Reviewer 2 Reviewer 3 . Thesis is defended at Graduate University Science and Technology Vietnam Academy of Science and Technology at on . Hardcopy of the thesis be found at - Library of Graduate University Science and Technology - Vietnam national library 1 PREFACE 1. The necessity of the thesis Vibration is a common phenomenon in nature and technology. In fact almost all vibrations of technical systems are nonlinear linear vibration is just the idealization of a vibration phenomenon that we encounter. Only a very small class of the nonlinear vibration problem has the exact solution. The approximate analytical methods are effective tools to find the solutions of the nonlinear vibration problem. Among the approximate analytical methods the Equivalent Linearization method 1 is a simple but effective method for analyzing nonlinear vibration problems. However like other approximate analytical methods the linearization method equivalent with the classical averaging value often has disadvantages that the obtained results are often inaccurate and sometimes unacceptable when the nonlinearity of the problem increases. Many authors have tried to improve this disadvantage of the equivalent linearization method in which in 2015 Nguyen Dong Anh 2 proposed a new method for estimating the averaging value of a determistic function instead of using the classical averaging value which is called the weighted averaging technique. The weighted averaging technique has partially overcome the .