**Course Instructors:**

Dr. Saeed Asiri

**Office:**24E38**Website:**https://www.asiri.net**WhatsApp:**+966565555275**Email:**saeed@asiri.net**Twitter:**@drsaeedasiri**Facebook:**saeedasiri

**Course TA:**

Eng. Salah Fatani

**Office:**TBA**Cell. No.:**+966504543238**WhatsApp:**+966504543238**Email**:

**Prerequisites:**

- MENG 262 Dynamics
- MENG 270 Mechanics of Materials
- EE 300 Complex Variables & Linear Algebra

**Course description**: Free and damped vibration of single degree of freedom systems, Viscous damping, Forced vibration, Resonance, Harmonic excitation; Rotating unbalance, Base motion, Vibration isolation, Fourier analysis, Vibration measuring, General excitation, Step and impulse response, Two degree of freedom systems, Frequencies and mode shapes, Modal analysis, Undamped vibration absorber, Multi degrees of freedom systems, Introduction to Continuous systems, Applications with computer programs.

**Textbook:** Singiresu Rao, *Mechanical Vibrations*, Prentice-Hall, Fifth Edition.

**Course Learning Objectives**:

By the end of the course the student will be to:

- Model linear and nonlinear mechanical systems as combinations of springs, masses and dampers.
- Determine and define the degrees of freedom of a given mechanical system.
- Extract the equations of motion of a given mechanical system.
- Analyze and interpret the response of mechanical systems to various types of excitations.
- Analyze and interpret the response of mechanical systems to different cases of damping.
- Predict qualitatively the response of systems based on the spectral content of the excitation.
- Minimize the effects of transient and harmonic excitations on systems and their support structures.
- Decouple equations of motion
- Understand the significance of vibration control in various applications

** ****Grading Policy:**

Laboratory | 10% |

Quizzes | 40% |

Term Project | 10% |

Collaborative Learning Activities | 10% |

Final Opportunity To Shine | 30% |

**Note**: 75% attendance is required. No makeup for any quiz. Student must attend the laboratory to pass the course.

**Contribution of the course to meet the ABET professional Component:**

Engineering science: 2 credit, Engineering design: 1 credit.

**How to Succeed**

- Accept that it is your responsibility to learn the material (in spite of the book or teacher)
- Show up and become engaged with the topics
- Do the homework daily so you can ask questions in class
- Use you resources for help (classmates, upperclassmen, faculty, the library)

** **

**Prerequisites by Topic:**

- Students should be familiar with free and forced vibration of
**S**ingle**D**egree**O**f**F**reedom (**SDOF**) systems. - Students should be familiar with the kinematics and kinetics of two and three-dimensional rigid bodies.
- Students should have a good understanding of the mechanics of solids including the ability to determine effective spring constants of common structural members.
- Students should be able to solve linear ordinary differential equations.
- Students should be familiar with concepts from linear algebra including matrix vector arithmetic, determinants, matrix inversion, eigenvalues, and eigenvectors.
- Students must have the ability to formulate and solve problems using
**MATLAB.**

No. | ReadingAssign. | Topic | PDF | Video |

0 | NN | Introduction | NN | NN |

1 | 1.4 – 1.10 | Fundamentals of Vibrations | Click here | Click here |

2 | 6.7 – 6.8 | Lagrange’s Equations of SDOF | Click here | Click here |

3 | 2.1 – 2.3 | Undamped Free Vibration of SDOF | Click here | Click here |

4 | 2.6 | Damped Free Vibration of SDOF | Click here | Click here |

5 | 3.1 – 3.5 | Undamped Forced Vibration of SDOF | Click here | Click here |

6 | 3.6 | Damped Forced Vibration of SDOF Direct Excitation & Rotating Unbalance | Click here | Click here |

7 | 3.7 | Damped Forced Vibration of SDOF Base Excitation | Click here | Click here |

8 | 5.1 – 5.5 | Free Vibrations of 2-DOF | Click here | Click here |

9 | 5.6, 5.9 9.10, 9.11 | Forced Vibrations of 2-DOF | ||

10 | 6.1- 6.15 | Modal Analysis | Click here | Click here |

Final OTS | ||||

All files are “PDF”, if you don’t already have the reader you can get free from: |

**Lab. Engineer: ** Eng. Salah Fatani

**WhatsApp :** +966504543238

__General Format for Lab Reports (30 Points)__

- TITLE PAGE (
**1 point**): Report title, course, your name, date lab performed, date lab due, date report submitted. - OBJECTIVE OF THE EXPERIMENT (
**1 point**): Statement of objective or purpose of the experiment/lab - THEORY/EQUATIONS USED (
**3 points**): List the equations used for your lab calculations(if any). - SAMPLE CALCULATIONS/DATA GENERATED (
**5 points**) A sample of the calculations you performed to get your results. - PROGRAM LISTING (
**5 points**)A listing of your MATLAB program (if any) - CONCLUSIONS/ANSWERS TO QUESTIONS (
**5 points**): List your conclusions. Include answers to**all**questions asked in the lab handout here. Make sure your answers are well explained - RESULTS(
**5 points**): Your results, any problems you have had in this lab, your comments on the lab - TEAM PARTICIPATION (
**5 points**): Your active participation in the*Virtual*Lab is crucial to the experience. Additional unique insight presented in your report may also be represented here.

Please remember, it’s **what **you put in your report that counts and **not **how **much **you put in it. Some of these labs require you to turn in MATLAB plots, do not turn in **all **that you have printed out, but **only **what has been asked for. Please ask the lab engineer if you are unsure what you need to turn in. Once again, remember that most of the points you get for a lab come from your answers to the questions at the experiment site. Points may be taken off for grammar/spelling and sloppy presentation. The reports should be typewritten.

- All students should know how to operate the virtual experiment and take part in the execution of the virtual experiment. It will be reflected in your grades.
- Question/s about the virtual labs will be asked on exams. Not specifics, but concepts, methods, and techniques.

**Experiment List:**

No. | Exp. Title | Exp. Link |

1 | Free vibration of a cantilever beam | |

2 | Free vibration of the simply supported beam | |

3 | Free vibration of fixed beam | |

4 | Forced vibration of SDOF system | |

5 | Base Excitation | |

6 | Rotating Unbalance | |

7 | 2DOF Forced vibration | |

8 | Dynamic Vibration Absorber |

Project weight: 10% of the final grade

This is an open-ended project, where each group designs its own project according to some restrictions and requirements. The project includes:

- Written report.
- Poster.
- Oral Presentation.
- Physical model to validate the mathematical model.

Each group should work independently but can share their experience by teaching their colleagues some of their useful skills. Groups should NOT have similar designs, even if the parameters are different.

1- Design a vibration system that includes the following:

- At least 2 independent DOFs.
- At least 2 spring components.
- At least one damping component.
- At least one harmonic force component with changing amplitude and velocity.
- The system should be underdamped.

2- Draw your design using a drawing program (Pro/E, SolidWorks, etc.) or clean and professional hand drawing. Write down all the dimensions and parameters of the designed system on the drawing.

3- **(10 points) ****On Sunday, **April**. 2:** Final design drawings are due. Show Eng. Hafiz a clear drawing of your design before this date, and get the approval by this date.

4- Once approved, use the general system parameters [which are: the spring constants (*K*_{1}, *K*_{2}, etc.), the damping coefficients (*C*_{1}, etc.), the masses (*M*_{1}, *M*_{2}, etc.), the force amplitude (*F*_{0}) and the force-frequency (*ω*)] to find the following: (use a word processor, no handwriting)

- The differential equations of motion.
- The transient and steady-state responses.
- The natural frequencies and mode shapes
- Check if the system can be decoupled or not (only check!).

5- Build your designed system in such a way that the force amplitude can be changed within a reasonable range, and the force frequency (speed) can be changed within a range that covers at least the first two mode natural frequencies. You should also measure the actual parameters of the system (*K*_{1}, *K*_{2}, *C*_{1}, *M*_{1}, *M*_{2}, etc.) and test the actual model using reasonable values for *F*_{0} and *ω*.

6- Write the differential equations of motion, the transient and steady-state responses, the natural frequencies, and the mode shapes (from parts “4_{a}, 4_{b}, 4_{c}” above) by substituting with the actual values of the parameters *K*_{1}, *K*_{2}, *C*_{1}, *M*_{1}, *M*_{2}, etc. and reasonable values for *F*_{0} and *ω*.

7- Design a vibration absorber to reduce the vibration of the primary system at a specific excitation frequency by adding a proper secondary system.

8- Validate your vibration absorber design experimentally to show that the vibration of the primary system has been reduced.

9- Write a report that includes the following:

- Introduction and presentation of the problem.
- Your design drawings (from “2”).
- How the model is built, the material used, challenges faced, final model and parameter values, pictures of your model throughout building it, etc.
- Your vibration problem and solution (from “4” and “6”).
- Your results from testing the actual model (from “5”) with some explanations.
- The theoretical results and experimental validation of the vibration absorber (from “7” and “8”)
- Discussion and conclusions (how your results can vary if the model parameters vary, how your model might be improved, etc.).

10- Prepare a poster that includes brief summary of all of the items presented in step “9”.

11- **On Th, May. 25:** Do the following:

**(30 points)**Prepare and present a 10-minute presentation to show your design steps, all of the items presented in step “9”, and some videos of building and testing your model**(40 points)**Demonstrate the model motion and response at resonance using at least the first two natural frequencies so that the two mode shapes can be identified clearly from the motion. Each group member will be asked for thorough details about the project, and the grade will vary from one member to member based on their participation.**(40 points)**Submit: (1) The project model; (2) A printed copy of the report; (3) The poster; (4) A soft copy of the report and the presentation. Clarity, proficiency, and organization in your work will carry points toward your grade.25T

No. | Reading Assign. | Topic | Video | |

0 | NN | Introduction | NN | NN |

1 | 1.4 - 1.10 | Fundamentals of Vibrations | Click here | Click here |

2 | 6.7 - 6.8 | Lagrange’s Equations of SDOF | Click here | Click here |

3 | 2.1 - 2.3 | Undamped Free Vibration of SDOF | Click here | Click here |

4 | 2.6 | Damped Free Vibration of SDOF | Click here | Click here |

5 | 3.1 - 3.5 | Undamped Forced Vibration of SDOF | Click here | Click here |

6 | 3.6 | Damped Forced Vibration of SDOF Direct Excitation & Rotating Unbalance | Click here | Click here |

7 | 3.7 | Damped Forced Vibration of SDOF Base Excitation | Click here | Click here |

8 | 5.1 - 5.5 | Free Vibrations of 2-DOF | Click here | Click here |

9 | 5.6, 5.9 9.10, 9.11 | Forced Vibrations of 2-DOF | ||

10 | 6.1- 6.15 | Modal Analysis | Click here | Click here |

Final OTS |