## Course Title : Dynamics of Solids and Structures

Code 10G230 Master and Doctor Course 2nd term Mon 2nd C3-Lecture Room 3 2 No Restriction Lecture Japanese S. Biwa and T. Hayashi

### Course Description

Fundamental principles for dynamic deformations of solids and structures are examined. In particular, basic characteristics of elastic wave motion in solid media are emphasized. Responses of materials and structures to impact loading are also considered.

### Grading

Grading is based on the attendance, homework reports and the final examination.

### Course Goals

This course aims to establish the understanding of basic characteristics of dynamic deformations and elastic waves in solid media, as well as to learn about technological applications of ultrasound in a variety of fields. Particular emphasis is put on the mathematical aspects of the physical phenomena involved.

### Course Topics

Theme Class number of times Description
Fundamentals of elastodynamics 1 Expressions of stress and strain; Conservation laws; Hooke's law; Principle of virtual work; Hamilton's principle and its applications
Basics of wave propagation 2 One-dimensional wave equation; D'Alembert's solution; Harmonic waves; Spectral analysis; Waves in structural members; Dispersive waves; Phase and group velocities
Stress waves in a bar 1 Reflection and transmission at bi-material connection; Reflection at a free end; Stress wave by tensile loading at a bar end; Plastic wave
Waves in isotropic elastic media 1 Navier's equations; Longitudinal and transverse waves; Plane elastic waves in isotropic solids
Waves in anisotropic elastic media 1 Voigt representation; Plane elastic waves in anisotropic solids; Christoffel's equation; Propagation and polarization directions; Slowness surfaces
Reflection and transmission 2 Reflection and transmission of normal incident waves; Snell's law; Mode conversion; Reflection and refraction of oblique incident waves.
Guided elastic waves 3 Bulk waves and guided waves; Rayleigh wave; Love wave; Lamb wave.
Numerical analysis of elastic waves 2 Finite difference method; Finite element method; Boundary element method
Measurements of vibration and waves 2 Comparison of various measurement techniques; Analogue and digital data analysis

### Textbook

No textbooks are assigned. Print-outs are handed in when needed.

### Prerequisite(s)

Basic knowledge of mechanics of materials (solid mechanics, continuum mechanics) is expected.

### Independent Study Outside of Class

Enrolling students are expected to work on the lecture materials and the homework problems.

### Additional Information

The time units and weights for each item on the above list are subject to possible changes.