The following is an article entitled "Sincerely Thanks for Doctoral Thesis" for reference only.

The tutor's accurate grasp of the subject direction and comprehensive understanding of students' characteristics create good conditions for research work, so that students can successfully complete doctoral course study and thesis work within two years. Because of the tutor's persuasive and strict requirements, students' scientific research ability has been improved and their basic knowledge has become more solid, thus gaining a valuable opportunity to enter Shanghai Institute of Applied Mathematics and Mechanics for postdoctoral research. The tutor's profound academic attainments, unyielding demeanor, tireless loyalty and professionalism, and academic attitude left a deep impression on the students. People have the ability to spread the word, and the tutor's words and deeds have played and will continue to play an extremely important role in the professional development of students.

I sincerely thank my wife Hong Qi for her consistent understanding and support of the author's academic research. During my stay in Shanghai, while she finished her job and took on housework, she also handled the daily work of the unit such as statements, letters and reimbursement on behalf of the author. The author also thanks his parents and other relatives for their care and help. The author especially thanks her daughter Chen Wenyuan, who just turned six. More than a dozen loving and childlike letters gave me special support. I'd like to think about it and keep it in the center.

Thanks to the leaders of Anshan Iron and Steel Institute at all levels, especially Professor Sui Yougong, Professor Wang Chengjiu, Professor Liu Zheng and Professor Cui. They take care of themselves and their families' lives during the author's directional degree study, and actively support the author to strive for postdoctoral opportunities. Professor Zheng Liu and Professor Cui are also the author's first teachers of advanced mathematics and vibration mechanics respectively.

Thanks to the master tutor, Professor Wang Tieguang of Northeastern University. Professor Wang Tieguang introduced me to the research field of nonlinear vibration ten years ago, and has been concerned about and supporting the author's academic and professional development since then.

Thanks to Professor Hong, director of the Department of Engineering Mechanics, Associate Professor Yang Changjun, director of the General Mechanics Teaching and Research Section, and Professor Bao Guangwei for their concern for the author's study, work and life during his stay in Shanghai Jiaotong University. Professor Hong also put forward some enlightening suggestions for the author's academic development.

Professor Zhu Zhaoxuan of Peking University once put forward suggestions to the author in his letter. In May, he attended the annual meeting of China Control and Decision-making 1996, and studied under Professor Zhang Siying of Northeastern University and researcher Zheng Yingping of Institute of Systems Science. During attending the expert seminar on nonlinear dynamics in July1996, I was guided by Academician Wen Bangchun of Northeastern University, Academician of Harbin Institute of Technology, Professor An Jiaotong University, Professor Liu Zengrong of Suzhou University and Professor P. Yu of the University of Western Ontario. In August, he attended the Mechanics Science Popularization Conference and studied under Professor Wu from Peking University, 1996. September 1996 studied under Professor Chen from Fudan University. I would like to express my gratitude to all the experts.

Thanks to Dr. Qing Yu, my roommate, for his timely and meticulous help in computer application. Associate Professor Ge Xinsheng, a visiting scholar of Beijing Institute of Mechanical Engineering, had fruitful cooperation with the author. His fellow disciples Dr. Chen Li, Dr. Peng Jianhua, Dr. Chenggong, Dr. Qu Qiuzhen and Dr. Gu had a useful discussion with the author. Dr. Ni Chunshuang, Dr. Li, Dr. Zhai Jun, Dr. Li and Dr. Shu also provided help in computer word processing. I want to thank you.

The author's work has been supported by the National Natural Science Foundation, the doctoral research fund of the State Education Commission and the applied basic science research fund of the Ministry of Metallurgical Industry, and I would like to express my gratitude.