Mechanical Vibrations

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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:

  1. Mechanical Engineers
  2. Chemical Engineers
  3. Civil Engineer
  4. Material Engineer
  5. Mechanical Engineer Students
  6. Chemical Engineer Students
  7. Civil Engineer students
  8. Material Engineer Students
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What Will You Learn?

  • A depth understanding of vibration
  • Modeling different vibratory systems
  • Ability to derive the equation of motion of different vibratory systems
  • Ability to apply proper method for solution of different equation of motions
  • Ability to analyze different kinds of vibration including free and forced vibration
  • Ability to design vibration absorber or shock absorber for different vehicles and reciprocating machines like pumps

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 (Steady-State) 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 Runge-Kutta 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 Runge-Kutta Family of Integrators – Part 2 of 2 – Method
    00:00
  • Implementing The Runge-Kutta 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 Degree-of-Freedom 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
  • Semi-Definite (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
  • Multi-degree 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 Euler-Bernoulli Beam (Continuous System)
    00:00
  • Response of a Simply Supported Euler-Bernoulli Beam (Continuous System)son
    00:00
  • Response of a Clamped-Clamped Euler-Bernoulli Beam (Exam Problem)
    00:00
  • Transverse Vibration Analysis of an Axially-Loaded Euler-Bernoulli Beam (Continuous System)
    00:00
  • Column Buckling (Continuous System)
    00:00

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