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Mechanical Vibrations

  • Course level: All Levels

Description

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

What Will I 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

Topics for this course

50 Lessons

Mechanical Vibrations

Differential Equations Primer (1 of 2) – Finding the Homogeneous (Transient) Solution00:00:00
Differential Equations Primer (2 of 2) – Finding the Particular (Steady-State) Solution00:00:00
Free Vibrations of a Single Degree of Freedom Problem (Simple Harmonic Oscillator)00:00:00
Harmonic Motion00:00:00
Single Degree of Freedom (SDOF) System with Gravitational Effects00:00:00
Free Vibrations of a Single Degree of Freedom (SDOF) System with Viscous Damping00:00:00
Free Vibrations of a Single Degree of Freedom (SDOF) System with Coulomb Damping00:00:00
Numerical Solution to the Single Degree of Freedom (SDOF) Problem – Part 1 – Mathematical Derivation00:00:00
Numerical Solution to the Single Degree of Freedom (SDOF) Problem – Part 2 – Coding in Python00:00:00
A Better Integrator? The Runge-Kutta Family of Integrators – Part 1 of 2 – Mathematical Foundation00:00:00
So What Is A Mode Shape Anyway? – The Eigenvalue Problem00:00:00
A Better Integrator? The Runge-Kutta Family of Integrators – Part 2 of 2 – Method00:00:00
Implementing The Runge-Kutta 4th Order Integrator Using Python00:00:00
Equation of Motion for the Simple Pendulum (SDOF)00:00:00
Coding a Numerical Solution to the Simple Pendulum Problem using Python00:00:00
Shock Absorber Problem00:00:00
Static Instability (Divergence)00:00:00
Forced Vibrations of a Single Degree of Freedom System (SDOF) & Dynamic Instability00:00:00
Dynamic Amplification Factor00:00:00
General Harmonic Loading of a Damped System (SDOF)00:00:00
Base Motion (Ground Motion) Effects00:00:00
Aeroelastic Instability – Single Degree-of-Freedom System (SDOF)00:00:00
Two Degree of Freedom (2DOF) Problem Without Damping – Equations of Motion (EOMs)00:00:00
Solving a System of Coupled Ordinary Differential Equations of Motion00:00:00
Equations of Motion for a Torsional 2DOF System Using Newton’s 2nd Law and Lagrange’s Equations00:00:00
Two Degree of Freedom (2DOF) Problem With Damping – Equations of Motion (EOMs)00:00:00
Semi-Definite (Unrestrained) Two Degree of Freedom (2DOF) Problem00:00:00
Equations of Motion for a Car (2DOF) Using Lagrange’s Equations00:00:00
Equations of Motion for a Pendulum on a Cart (2DOF) Using Method of Lagrange’s Equations00:00:00
Solving Equations of Motion by Direct Time Integration00:00:00
Equations of Motion for the Elastic Pendulum (2DOF) Using Lagrange’s Equations00:00:00
Equations of Motion for the Double Pendulum (2DOF) Using Lagrange’s Equations00:00:00
Equations of Motion for the Double Compound Pendulum (2DOF) Using Lagrange’s Equations – Part 1 of 200:00:00
Equations of Motion for the Double Compound Pendulum (2DOF) Using Lagrange’s Equations – Part 2 of 200:00:00
Equations of Motion for the Inverted Pendulum (2DOF) Using Lagrange’s Equations00:00:00
Equations of Motion for the Spherical Pendulum (2DOF) Using Lagrange’s Equations00:00:00
Equations of Motion for an Airfoil (2DOF) Using Lagrange’s Equations00:00:00
Equations of Motion for a Cylinder Riding on a Cart (2DOF) Using Lagrange’s Equations00:00:00
Dynamic Vibration Absorbers00:00:00
Equations of Motion for the Multi Degree of Freedom (MDOF) Problem Using LaGrange’s Equations00:00:00
Multi-degree of Freedom Systems (MDOF) – Numerical Solution to the Equations of Motion (EOM)00:00:00
Coding a Numerical Solution to the Multidegree of Freedom (MDOF) System Using Python00:00:00
Equations of Motion for the Nonlinear Oscillator (2DOF)00:00:00
Longitudinal Vibration of a Bar (Continuous System)00:00:00
Transverse Vibration of a String (Continuous System)00:00:00
Transverse Vibration Analysis of an Euler-Bernoulli Beam (Continuous System)00:00:00
Response of a Simply Supported Euler-Bernoulli Beam (Continuous System)son00:00:00
Response of a Clamped-Clamped Euler-Bernoulli Beam (Exam Problem)00:00:00
Transverse Vibration Analysis of an Axially-Loaded Euler-Bernoulli Beam (Continuous System)00:00:00
Column Buckling (Continuous System)00:00:00
Mechanical vibration
35 £

Enrolment validity: Lifetime

Requirements

  • Calculus
  • A good understanding of statics or RAHME201 course on Udemy
  • A good understanding of Dynamics or RAHME101 course on Udemy
  • Familiarity with mechanical of materials and fluid mechanics helps