Engineering Vibration I: Introduction: Single-Degree-of-Freedom Systems

Overview

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This course is an introduction to exploring the topic of engineering systems undergoing vibration. The methods taught in the course are used to predict the response of engineering structures to various types of input and to analyze the resulting vibratory motion. The free vibration of Single Degree-of-Freedom (SDOF) systems will be the focus of this course.

Syllabus

Week 1 – Vibration System Modeling Elements

Module 1 – Introduction and Importance of Vibrations
Module 2 – Vibrations Modeling System Elements - Mass
Module 3 – Vibrations Modeling System Elements – Linear and Torsional Springs
Module 4 – Equivalent Spring Constants for Multiple Springs
Module 5 – Equivalent Spring Constants for Axially and Torsionally Loaded Members
Module 6 – Equivalent Spring Constants for Beam Structures
Module 7 – Vibrations Modeling System Elements – Damper

Week 2 – Vibration System Differential Equations of Motion

Module 8 – Generalized Coordinates and Degrees of Freedom
Module 9 – Model Real World Systems
Module 10 – Static Equilibrium – SDOF
Module 11 – Derive Differential Equation of Motion – SDOF translational motion
Module 12 – Solve Differential Equation of Motion – SDOF translational motion

Week 3 – Undamped Single Degree-of-Freedom Vibration Systems

Module 13 – Natural Frequency/Period of Oscillation
Module 14 – Transient Response Solution
Module 15 – Phase Angle Form of Solutions
Module 16 – Analyze Position, Velocity, Acceleration Solutions – SDOF systems
Module 17 – Solve for Undamped, Free Vibration
Module 18 – Derive Differential Equation of Motion – SDOF rotational motion
Module 19 – Derive Differential Equation of Motion – SDOF rotational motion
Module 20 – Solve Differential Equation of Motion – SDOF rotational motion/Stability
Module 21 – Solve Undamped, Free Vibration problems

Week 4 – Damped, Single-Degree-of-Freedom Vibration Systems

Module 22 – Derive Differential Equation of Motion – SDOF damped, free vibration
Module 23 – Cases of Damping/Critical Damping
Module 24 – Derive Differential Equation of Motion – SDOF damped, free vibration
Module 25 – Plot and Interpret Transient Underdamped Vibration
Module 26 – Solve Differential Equation of Motion – SDOF damped, free vibration

Week 5 – Damped, Single-Degree-of-Freedom Vibration Systems

Module 27 – Logarithmic Decrement
Module 28 – Solve Differential Equation of Motion - SDOF rotational damped, free vibration
Module 29 – Solve for natural frequency, damping factor, and time to decay
Module 30 – Overdamped Vibration
Module 31 – Critically Damped Vibration
Module 32 – Course Conclusion