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1

Introduction to Vibration
- Generalized Coordinates
- Review of Dynamics
- Spring, Viscous Dampers ,etc

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2

Free Vibrations of One-Degree-of Freedom System

- Free-Body Diagram Method
- Equivalent Systems Method

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3

- Free Vibrations of Undamped / Viscous One-Degree-of-Freedom Systems

- Coulomb/ Hysteretic damping

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4

Harmonic Excitation of One-Degree-of-Freedom systems

- Differential Equations Governing Forced Vibrations
- an Undamped/ a Viscously Damped System to Single-Frequency Harmonic Excitation

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5

- Frequency-Squared Excitation

- Response Due to Harmonic Excitation of Support
- Systems with Coulomb/ Hysteretic Damping

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6

Transient Vibration of One-Degree-of-Freedom Systems

 

 

 

7

Multi-Degree-of-freedom Systems: Derivation of Governing Equation

 

 

 

 

8

Midterm Examination



9

- Lagrange’s Equation

- Matrix Formulation of Differential Equations for Linear Systems
- Stiffness/ Flexible Influence Coefficients

 

 

 

 

10

Free Vibrations of Multi-Degree-of-Freedom Systems

- Normal-Mode Solution
- Natural Frequencies and Mode Shape
- General Solution/ Special Cases

 

 

 

11

- Energy Scalar Products

- Normalized Mode Shapes
- Rayleigh’s Quotient
- Principal Coordinates
- Proportional Damping

 

 

 

12

Forced Vibrations of Multi-Degree-of Freedom Systems

- Harmonic Excitations
- Laplace transform Solutions

 

 

 

 

13

- Modal Analysis for Undamped Systems and Proportional Damping Systems

- Modal Analysis for Systems with General Damping
-Numerical Solution

 

 

 

 

14

Vibration Control

 

 

 

 

15 Vibration of Continuous System

 

 

 

16

Finite Element Method

 

 

 

17

Final Examination