About the course

"Mechanical Vibration Theory" is one of the core courses for postgraduates in fields of mechanics, mechanical engineering, aerospace engineering and vehicle engineering. By taking this course, the students are expected to have a good grasp of systematic knowledge of mechanical vibration theory, analysis methods and application skills to engineering practice. It is required for the students to understand dynamic behaviors of typical vibration systems and to know how to establish vibration models and carry out modal analysis. Based on that, the students should be familiar with approximation methods for vibration problem solving, vibration isolation techniques, rotational system vibration, random vibration analysis and fundamentals of nonlinear system vibration.

This course is organized into 6 chapters and consists of the following topics:

Chapter 1 Introduction (2 hours)

1.1 Introduction

1.2 Fundamentals of Vibration

Chapter 2 Vibrations of Single DoF Systems (10 hours)

  2.1 Free Vibrations of Undamped Systems

  2.2 Free Vibrations with Damping

  2.3 Harmonically Excited Vibration

  2.4 Vibration under General Forcing

Chapter 3 Vibrations of Multiple DoF Systems (12 hours)

  3.1 Equation of Motion for Multi DoF Systems

  3.2 Free vibrations of Undamped MDoF Systems

  3.3 Forced vibrations of Undamped MDoF system

  3.4 Forced vibrations of Proportional Damped Systems

  3.5 Determination of Natural Frequencies

Chapter 4 Vibrations of Continuous Systems (10 hours)

  4.1 Transverse Vibration of a String or Cable

  4.2 Longitudinal Vibration of a Bar or Rod

  4.3 Lateral Vibration of Beams

  4.4 Special Vibration problems of Beams

  4.5 Determination of Natural Frequencies

Chapter 5 Random Vibration (4 hours)

  5.1 Random Process

  5.2 Power Spectrum of Vibration Signals

  5.3 Response due to Random Excitation

Chapter 6 Nonlinear Vibration (10 hours)

  6.1 Introduction and Basic Concepts

  6.2 Qualitative Analysis of Nonlinear Autonomous Systems

  6.3 Analytical Analysis of Nonlinear Autonomous Systems

  6.4 Forced Vibration of Nonlinear Nonautonomous Systems

About the teacher

Dr. Li Zhang received Ph. D. in General and Fundamental Mechanics from Nanjing University of Aeronautics and Astronautics (NUAA), China in 2012. She is currently an associate professor of mechanics at the College of Aerospace Engineering, NUAA. Her research fields are delayed dynamical systems and nonlinear dynamics with applications in human balancing and machine tool vibrations.

Dr. Zhang has been recognized as an experienced lecturer by many prestigious teaching awards, including the 1st prize in National Universities Micro-teaching Competition and 1st prize in Jiangsu teaching competition for youth university teachers.

All materials are contributed by Nanjing University of Aeronautics and Astronautics.