## Course Title : Dynamics of Soil and Structures

Code 35120 3rd year 1st term Monday・1 Kyoutsuu4 2 Lecture English Furukawa

### Course Description

This course deals with fundamentals and application of vibration theory and elastic wave propagation in civil engineering.

Based on the performance during the course (including homework) and the results of a final examination.

### Course Goals

At the end of this course, students will be required to have a good understanding of:
- Vibration phenomena, response to dynamic loads, fundamental principle of vibration measurement, including manipulation of mathematical manipulation and calculation.
- Treatment of vibration problems for multi-degree-of-freedom systems and elastic media.
- Fundamental properties of elastic waves that propagate in elastic media and layers.

### Course Topics

Theme Class number of times Description
Vibration of structures and equation of motion 1 Vibration phenomena encountered in civil engineering structures. Importance and engineering issues of vibration. Derivation of equation of motion.
Free vibration Definition of the natural period and damping ratio for single degree-of-freedom systems. Derivation of free vibration response.
Forced vibration Resonance curves and phase response curves for forced harmonic vibration. Frequency response characteristics.
Principle of vibration measurement Background theory of vibration measurement. Accelerometers and seismometers.
Response to arbitrary input 2 Evaluation of dynamic response to arbitrary forcing and earthquake excitation. Response spectra.
Nonlinear vibration Fundamental properties of nonlinear dynamic response of structures associated with elasto-plastic behavior.
Vibration of 2-DOF systems 1 Solution of equations of motions for 2-degree-of-freedom systems representing free vibration. Concept of normal vibration modes.
Natural frequencies and natural modes of vibration 1 Relationship between the natural frequencies, normal vibration modes of multi-degree-of-freedom systems and eigenvalue analysis.
Damped free vibration of MDOF systems 1 Vibration of multi-degree-of-freedom systems with damping. Analysis of MDOF systems using damping using normal vibration modes.
Forced vibration and response to arbitrary input for MDOF systems 1 Modal analysis to evaluate the dyanmic response of multi-degree-of-freedom systems for harmonic and arbitrary excitation.
Vibration of continuum 1 Vibration of shear beams. Flexural vibration. Wave equation. Solution of shear vibration problem.
Elastic wave 2 Properties of elastic waves travelling in elastic media and elastic layers. Fundamental concept in deriving solutions of elastic wave propagation problems.
Achievement evaluation 1 Students' achievements in understanding of the course material are evaluated.

### Textbook

Not used; Class hand-outs are distributed when necessary.

### Prerequisite(s)

Calculus, Linear Algebra, Structural Mechanics I and Exercises (35110), Structural Mechanics II and Exercises (35140).