About Course
Mechanical vibration (MV) is one of the most important applications of Mechanics. In MV, we deal with many important and practical problems that finding their solution is critical. In most cases, solutions for vibratory systems can save many human lives.
The prerequisites for studying MV are courses such as statics, dynamics, and mechanics of material. To solve problems in Mechanical vibration and a better understanding of its application a solid knowledge of all these areas is needed.
A student of MV must learn how to use the knowledge that exists to model a mechanical system with appropriate assumptions. Assumptions like a number of degrees of freedom, famous mechanics principles. The student will get familiar with deriving the equations governing the model and then solve them. Sometimes the solution for modeling results is easy to find (a small group of differential equations) and sometimes some other assumptions are needed.
The purpose of this course is to draw a guideline for students who study mechanical vibrations through many aspects of vibration analysis. Also, the course is planned to give the student the ability to design useful structures for damping annoying vibrations.
In the first chapter, you will get familiar with basic concepts in Mechanical vibrations, and also different elements used in modeling vibratory systems are introduced.
In the second and third chapters, two general cases in vibratory systems are considered, free and harmonic vibration.
in each chapter there are many practical examples that are directly connected with problems in the real world, we use these examples for more illustration.
Who this course is for:
 Mechanical Engineers
 Chemical Engineers
 Civil Engineer
 Material Engineer
 Mechanical Engineer Students
 Chemical Engineer Students
 Civil Engineer students
 Material Engineer Students
Course Content
Mechanical Vibrations

Differential Equations Primer (1 of 2) – Finding the Homogeneous (Transient) Solution
00:00 
Differential Equations Primer (2 of 2) – Finding the Particular (SteadyState) Solution
00:00 
Free Vibrations of a Single Degree of Freedom Problem (Simple Harmonic Oscillator)
00:00 
Harmonic Motion
00:00 
Single Degree of Freedom (SDOF) System with Gravitational Effects
00:00 
Free Vibrations of a Single Degree of Freedom (SDOF) System with Viscous Damping
00:00 
Free Vibrations of a Single Degree of Freedom (SDOF) System with Coulomb Damping
00:00 
Numerical Solution to the Single Degree of Freedom (SDOF) Problem – Part 1 – Mathematical Derivation
00:00 
Numerical Solution to the Single Degree of Freedom (SDOF) Problem – Part 2 – Coding in Python
00:00 
A Better Integrator? The RungeKutta Family of Integrators – Part 1 of 2 – Mathematical Foundation
00:00 
So What Is A Mode Shape Anyway? – The Eigenvalue Problem
00:00 
A Better Integrator? The RungeKutta Family of Integrators – Part 2 of 2 – Method
00:00 
Implementing The RungeKutta 4th Order Integrator Using Python
00:00 
Equation of Motion for the Simple Pendulum (SDOF)
00:00 
Coding a Numerical Solution to the Simple Pendulum Problem using Python
00:00 
Shock Absorber Problem
00:00 
Static Instability (Divergence)
00:00 
Forced Vibrations of a Single Degree of Freedom System (SDOF) & Dynamic Instability
00:00 
Dynamic Amplification Factor
00:00 
General Harmonic Loading of a Damped System (SDOF)
00:00 
Base Motion (Ground Motion) Effects
00:00 
Aeroelastic Instability – Single DegreeofFreedom System (SDOF)
00:00 
Two Degree of Freedom (2DOF) Problem Without Damping – Equations of Motion (EOMs)
00:00 
Solving a System of Coupled Ordinary Differential Equations of Motion
00:00 
Equations of Motion for a Torsional 2DOF System Using Newton’s 2nd Law and Lagrange’s Equations
00:00 
Two Degree of Freedom (2DOF) Problem With Damping – Equations of Motion (EOMs)
00:00 
SemiDefinite (Unrestrained) Two Degree of Freedom (2DOF) Problem
00:00 
Equations of Motion for a Car (2DOF) Using Lagrange’s Equations
00:00 
Equations of Motion for a Pendulum on a Cart (2DOF) Using Method of Lagrange’s Equations
00:00 
Solving Equations of Motion by Direct Time Integration
00:00 
Equations of Motion for the Elastic Pendulum (2DOF) Using Lagrange’s Equations
00:00 
Equations of Motion for the Double Pendulum (2DOF) Using Lagrange’s Equations
00:00 
Equations of Motion for the Double Compound Pendulum (2DOF) Using Lagrange’s Equations – Part 1 of 2
00:00 
Equations of Motion for the Double Compound Pendulum (2DOF) Using Lagrange’s Equations – Part 2 of 2
00:00 
Equations of Motion for the Inverted Pendulum (2DOF) Using Lagrange’s Equations
00:00 
Equations of Motion for the Spherical Pendulum (2DOF) Using Lagrange’s Equations
00:00 
Equations of Motion for an Airfoil (2DOF) Using Lagrange’s Equations
00:00 
Equations of Motion for a Cylinder Riding on a Cart (2DOF) Using Lagrange’s Equations
00:00 
Dynamic Vibration Absorbers
00:00 
Equations of Motion for the Multi Degree of Freedom (MDOF) Problem Using LaGrange’s Equations
00:00 
Multidegree of Freedom Systems (MDOF) – Numerical Solution to the Equations of Motion (EOM)
00:00 
Coding a Numerical Solution to the Multidegree of Freedom (MDOF) System Using Python
00:00 
Equations of Motion for the Nonlinear Oscillator (2DOF)
00:00 
Longitudinal Vibration of a Bar (Continuous System)
00:00 
Transverse Vibration of a String (Continuous System)
00:00 
Transverse Vibration Analysis of an EulerBernoulli Beam (Continuous System)
00:00 
Response of a Simply Supported EulerBernoulli Beam (Continuous System)son
00:00 
Response of a ClampedClamped EulerBernoulli Beam (Exam Problem)
00:00 
Transverse Vibration Analysis of an AxiallyLoaded EulerBernoulli Beam (Continuous System)
00:00 
Column Buckling (Continuous System)
00:00