## Structural DynamicsBack JP / EN

Numbering Code Year/Term G-ENG02 5F227 LJ73G-ENG01 5F227 LJ73 2021 ・ First semester 2 Lecture Japanese Tue.2 TAKAHASHI YOSHIKAZU (Graduate School of Engineering Professor)IGARASHI AKIRA (Disaster Prevention Research Institute Professor) This course deals with dynamics of structural systems and related topics, to provide the theoretical basis to deal with the problems of vibration, safety under dynamic loads and health monitoring associated with infrastructures. The students will study the dynamic response, properties of natural modes and methods of eigenvalue analysis for multi-DOF systems. The topics on the numerical time integration schemes, probabilistic evaluation of structural response to random excitation, and dynamic response control techniques for structures are also studied. (1) To aquire the knowledge on theories and principles of analysis of MDOF systems (2) Systematic understanding of frequency-domain structural response analysis (3) Concept of analysis of numerical time integration schemes (4) Understanding of fundamentals of the random vibration theory Introduction (1 week) The fundamental concepts of structural dynamics and the scope of the problem to be treated are described, and the outline of the theoretical framework of methodologies for analysis is overviewed. Dynamics of Multi-Degree-Of-Freedom Systems (2 weeks) Basic concepts, including the formulation of vibration model of multi-degree of freedom systems, eigenvalue analysis, normal modes and modal analysis of linear systems and modeling of system damping, are described. Frequency-Domain Analysis of System Response (1 week) Methodology of response analysis of linear systems based on the concept of the frequency response function, and the relationship between the frequency-domain analysis and time-domain response via Fourier integral, mathematical operation and numerical procedure are described. Numerical Time Integration (2 weeks) Overview of the step-by-step time integration method used for numerical response analysis in the time domain is followed by the implication and mathematical analysis of the characteristics of the integration method, including stability and accuracy. Random Vibration (6 weeks) The methodology for stochastic modeling of inputs when the dynamic load on the structure can not be deterministically specified is shown, and the concept, theory and method for probabilistic evaluation of the dynamic response of the structures are described. Structural Response Control (2 weeks) The concept of dynamic response control of structures, in particular the active control and semi-active control, is described, and the standard theories for analysis and design are introduced. Achievement Evaluation (1 week) Students' achievements in understanding of the course material are evaluated. Based on the results of a final examination (90%), plus homework assignments (10%) Mechanical vibration (undergraduate level), Complex calculus (integration of analytic functions, Fourier transform, etc.), Probability theory, Linear algebra There will be homework assignments at the end of most of the lectures. Not used; Class hand-outs are distributed when necessary.