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Mechanical Vibrations' Fundamentals

Prof Dr Farid Khan

This course of mechanical vibrations will cover the basic and fundamental nature and concepts on the vibration of mechanical systems including: review of systems for mechanical vibrations, existence of vibrations in daily life and industry, causes of vibrations in machines and equipment, why the control of vibration is necessary, catastrophe of harsh and abnormal vibrations, why vibration control is necessary, classification of vibratory systems, type of vibration excitation, free/natural vibrations, resonance, damped and undamped vibrations, free undamped vibrations, free damped vibrations, forced undamped vibrations, forced damped vibrations, vibration amplification and its control through damping, damped natural frequency, Newton's method for equation of motion, energy method for equation of motion, frequency of excitation, torsional systems, modeling of vibratory systems, lumped parameter modeling, linear vibrations, systems' response to free and  harmonic excitation, single and multiple degree of freedom systems, rotatory machines vibrations, modeling of rotating unbalance, base-excitation, vibration transmissiblity and isolation, vibration displacement, velocity and acceleration, fundamental frequency, natural frequencies and mode shapes, time and frequency response, simulations of systems response to interpret systems' behavior at frequency ratios below less than 1, equal to 1 and above 1. Critical frequencies for machine's operation, how to avoid critical frequencies during machines design and functioning.

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What's inside

Syllabus

Able to know about mechanical vibration, causes and nature of vibration, degree of freedom,dependent and independent co-ordinate, discrete(lumped), distributed(continuous) modeling of vibration system
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Learn and identify about vibrations. Be able to know where the mechanical vibrations exist and why, what is the cause of vibrations in machines and equipment?

Vibration's basics, Causes of vibrations, Vibrations' classification
Degree of freedom (DOF) of a vibration-system, SDOF, 2-DOF, multi-DOF systems
Capable to know and identify free vibrations, harmonic vibration, undamped system, determining equation of motion using Newton's and energy methods, to find resonant frequency and systems' response
Undamped natural frequency, equation of motion of SDOF, Newton's & Energy method
Modeling of simple pendulum under free/natural vibration, solution linearization
Equation of motion of SDOF undamped system under free vibration(harmonic motion)
Rayleigh's method: to determine natural frequency of SDOF undamped system
Be able to know what is damped free vibration, how to develop the equation of motion of a SDOF system. Moreover, be capable to determine the natural frequency
Damping, Spring-Mass-damper system under free vibrations
Finding damping ratio with logarithmic decrement method, effect of spring mass
Be able to model forced vibrations (undamped and damped) under harmonic vibrations, determining equation of motion and resonant frequency and response of the SDOF system, magnification and isolation
SDOF forced vibrations, damped system
Response of SDOF damped system under forced vibrations (harmonic excitation)
Base excitation (displacement transmissibility) of SDOF damped system
Base excitation (force transmissibility) of SDOF damped system
Rotating unbalance
Vibration isolation (force transmitted to the base)
Vibration isolation (simulation for amplification and isolation regions)
Capable to model multi-degree of freedom systems under harmonic excitation, determining equation of motion of the vibratory system, finding resonant frequency and response of the system
2-DOF system under free vibrations

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Mechanical Vibrations' Fundamentals with these activities:
Review Dynamics and Kinematics
Reinforce your understanding of dynamics and kinematics concepts, which are fundamental to understanding the equations of motion used in vibration analysis.
Browse courses on Dynamics
Show steps
  • Review notes and textbooks on dynamics and kinematics.
  • Work through practice problems related to Newton's laws and energy methods.
  • Focus on understanding concepts like displacement, velocity, acceleration, and force.
Read 'Mechanical Vibrations' by Singiresu S. Rao
Supplement your learning with a comprehensive textbook on mechanical vibrations to gain a deeper understanding of the subject matter.
View Vibration of Continuous Systems on Amazon
Show steps
  • Read chapters related to the topics covered in the course.
  • Work through the examples and exercises provided in the book.
  • Use the book as a reference for clarifying concepts and solving problems.
Solve SDOF Vibration Problems
Practice solving problems related to single degree of freedom (SDOF) systems to solidify your understanding of free, damped, and forced vibrations.
Show steps
  • Find problems related to SDOF systems in textbooks or online resources.
  • Solve for natural frequency, damping ratio, and system response to harmonic excitation.
  • Compare your solutions with provided answers or solutions manuals.
Three other activities
Expand to see all activities and additional details
Show all six activities
Create a Vibration Analysis Tutorial
Solidify your understanding by creating a tutorial explaining a specific vibration analysis technique, such as modal analysis or frequency response analysis.
Show steps
  • Choose a specific vibration analysis technique to focus on.
  • Research the technique and gather relevant information.
  • Create a step-by-step tutorial with clear explanations and examples.
  • Share your tutorial with classmates or online forums for feedback.
Simulate Vibration Response
Develop a simulation using software like MATLAB or Python to model the response of a vibrating system to different inputs and parameters.
Show steps
  • Choose a specific vibrating system to model (e.g., a spring-mass-damper system).
  • Write code to simulate the system's response to free and forced vibrations.
  • Vary parameters like mass, stiffness, and damping to observe their effects.
  • Visualize the results using plots of displacement, velocity, and acceleration over time.
Read 'Theory of Vibration with Applications' by William Tyrrell Thomson and Marie Dillon Dahleh
Explore a more advanced textbook on vibration theory to delve deeper into the mathematical foundations and advanced topics.
View Theory of Vibrations with Applications on Amazon
Show steps
  • Focus on chapters that expand on the course material.
  • Pay attention to the mathematical derivations and proofs.
  • Attempt to solve the more challenging problems presented in the book.

Career center

Learners who complete Mechanical Vibrations' Fundamentals will develop knowledge and skills that may be useful to these careers:
Vibration Analyst
A Vibration Analyst ensures the reliability and performance of machinery by identifying and diagnosing vibration-related issues. This role involves collecting vibration data, analyzing it to detect anomalies, and recommending solutions to prevent equipment failures. This course helps build a foundation for understanding the fundamental principles of mechanical vibrations, including free, damped, and forced vibrations, which are critical for accurately interpreting vibration data in real-world scenarios. Moreover, the course's coverage of resonance and vibration isolation will be useful when troubleshooting vibration problems in industrial machinery. Learning about modeling techniques will also help a Vibration Analyst understand complex systems. The simulations of system response will improve their ability to interpret system behavior.
See salaries and explore the career path for Vibration Analyst
Mechanical Engineer
The Mechanical Engineer designs, develops, and tests mechanical devices and systems. This often includes addressing vibration issues to ensure the durability and performance of these systems. This course will be helpful for understanding the causes and effects of mechanical vibrations, enabling them to design systems that minimize unwanted vibrations. The course's modules on modeling vibratory systems and analyzing system responses to harmonic excitation are directly applicable to the design of vibration-resistant mechanical components. The course also focuses on the importance of avoiding critical frequencies during machine design. Anyone interested in becoming a Mechanical Engineer should take this course.
See salaries and explore the career path for Mechanical Engineer
Aerospace Engineer
The Aerospace Engineer designs and tests aircraft and spacecraft, where managing vibration is crucial for structural integrity and passenger comfort. This course helps build a foundation for understanding and mitigating vibrations in aerospace structures. It equips the learner with the necessary knowledge to analyze and control vibrations in aircraft components. This course's coverage of natural frequencies, mode shapes, and time/frequency response of vibrating systems is especially relevant for aerospace applications. Base excitation, vibration transmissibility, and vibration isolation are covered as well. An aspiring Aerospace Engineer may find the course helpful for addressing vibration challenges in aircraft design.
See salaries and explore the career path for Aerospace Engineer
Automotive Engineer
The Automotive Engineer designs and develops vehicles, focusing on performance, safety, and comfort. Vibration analysis is essential for optimizing vehicle ride quality and minimizing component fatigue. This course helps build a foundation for understanding the principles of mechanical vibrations, enabling them to analyze and address vibration issues in automotive systems. The course content on damped and undamped vibrations, forced vibrations, and vibration isolation is particularly relevant for designing suspension systems and reducing noise and vibration harshness in vehicles. The modeling of rotating unbalance will be useful in this role. Automotive Engineers may find this course helpful.
See salaries and explore the career path for Automotive Engineer
Test Engineer
The Test Engineer designs and conducts tests to evaluate the performance and reliability of products and systems. Vibration testing is often a critical part of the evaluation process. This course may be useful for understanding the fundamental concepts of mechanical vibrations, enabling them to design and interpret vibration tests effectively. The course will introduce methods for calculating equations of motion. Knowledge of frequency response, simulations, and resonant frequencies are helpful for designing effective tests and simulations. Base excitation, vibration transmissibility, and vibration isolation are covered as well.
See salaries and explore the career path for Test Engineer
Robotics Engineer
The Robotics Engineer designs, builds, and programs robots for various applications. Vibration analysis is important for ensuring the stability and precision of robotic systems. This course helps build a foundation for understanding the principles of mechanical vibrations that affect robot performance. The course's modules on modeling vibratory systems, analyzing system responses to harmonic excitation, and controlling vibration through damping are directly applicable to the design of stable and precise robots. The course also focuses on the importance of avoiding critical frequencies during machine design. Aspiring Robotics Engineers may find this course useful.
See salaries and explore the career path for Robotics Engineer
Structural Engineer
The Structural Engineer designs and analyzes structures to ensure their stability and safety. They must understand how structures respond to dynamic loads, including vibrations. This course may be useful for understanding the principles of mechanical vibrations, which is crucial in assessing the impact of vibrations on buildings and bridges. The course's coverage of natural frequencies, mode shapes, and time/frequency response helps structural engineers evaluate the dynamic behavior of structures under various loading conditions. The knowledge of vibration isolation may be useful for mitigating vibrations in structures.
See salaries and explore the career path for Structural Engineer
Acoustical Engineer
The Acoustical Engineer focuses on controlling noise and vibration in various environments. While primarily concerned with sound, understanding mechanical vibrations is foundational since sound is often caused by vibrating structures. While this course may not directly cover acoustics, it helps build a foundation for understanding the principles of mechanical vibrations. An understanding of resonance, damped vibration, and free vibration can be helpful for an Acoustical Engineer when working to reduce noise and unwanted sounds. This course also focuses on the importance of avoiding critical frequencies during machine design.
See salaries and explore the career path for Acoustical Engineer
Manufacturing Engineer
The Manufacturing Engineer designs and optimizes manufacturing processes, including minimizing vibrations that can affect product quality and equipment lifespan. This course may be useful in understanding the basics of mechanical vibrations. The course covers causes of vibrations in machines and equipment and discusses why controlling vibration is necessary. The basics of vibration isolation may also be useful for mitigating vibrations in manufacturing equipment. Aspiring Manufacturing Engineers may find this course helpful.
See salaries and explore the career path for Manufacturing Engineer
Mechatronics Engineer
The Mechatronics Engineer integrates mechanical, electrical, and computer systems. Understanding mechanical vibrations is important for designing and controlling mechatronic devices. This course may be helpful for understanding the fundamental principles of mechanical vibrations, which is crucial for designing mechatronic systems that operate smoothly and reliably. The course covers modeling vibratory systems and analyzing system responses to harmonic excitation, which are directly applicable to mechatronic design problems. A Mechatronics Engineer may wish to take this course.
See salaries and explore the career path for Mechatronics Engineer
Naval Architect
The Naval Architect designs ships and other marine vessels. Vibration analysis is carried out to ensure structural integrity and passenger comfort. This course may be helpful for understanding the fundamental principles of mechanical vibrations, which includes methods for calculating equations of motion. An understanding of resonance, damped vibration, and free vibration can be helpful for a Naval Architect when working to reduce noise and unwanted sounds. This course also focuses on the importance of avoiding critical frequencies during machine design.
See salaries and explore the career path for Naval Architect
CAD Designer
The CAD Designer creates technical drawings and models of mechanical components and systems. Though not directly related to vibration analysis, understanding the principles of mechanical vibrations can inform design choices to minimize vibration-related problems. This course may be somewhat useful for understanding the nature of vibration. The course spends some time on modeling of vibratory systems. As an Engineer, the person may find this course helpful.
See salaries and explore the career path for CAD Designer
Data Analyst
The Data Analyst collects, processes, and analyzes data to identify trends and insights. In manufacturing and engineering contexts, data analysts may work with vibration data to monitor equipment health. This course may be useful for understanding the root causes of the vibration. The Data Analyst may be interested in the simulations of systems response to interpret systems' behavior at frequency ratios. This knowledge may be helpful to a Data Analyst.
See salaries and explore the career path for Data Analyst
Technical Writer
The Technical Writer creates documentation for technical products and systems. While not directly involved in vibration analysis, a basic understanding of the concepts can be helpful for creating accurate and informative documentation. This course may be useful for understanding the basics of mechanical vibration, including the vibrations' classification. The Technical Writer may wish to take this course.
See salaries and explore the career path for Technical Writer
Project Manager
The Project Manager oversees engineering projects, ensuring they are completed on time and within budget. While not directly involved in vibration analysis, a general understanding of potential vibration issues can help in planning and risk management. This course may be useful for an overview of vibration basics. The Project Manager may wish to take this course.
See salaries and explore the career path for Project Manager

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Mechanical Vibrations' Fundamentals.
Cover image
Vibration of Continuous Systems
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Comprehensive resource on mechanical vibrations, covering both theoretical concepts and practical applications. It provides a detailed explanation of single and multiple degree of freedom systems, as well as vibration control techniques. It is commonly used as a textbook in mechanical engineering courses and offers a wealth of examples and exercises. This book will add depth to the course by providing alternative explanations and more advanced topics.
Vibration of Continuous Systems
Paperback
Check
Vibration of Continuous Systems
Kindle Edition
Check
Cover image
Theory of Vibrations with Applications
Save
Provides a rigorous treatment of vibration theory, with a focus on mathematical modeling and analysis. It covers advanced topics such as nonlinear vibrations and random vibrations. While it may be more valuable as additional reading, it offers a deeper understanding of the underlying principles. This book is often used in graduate-level courses and useful reference for researchers and engineers.
Theory of Vibrations with Applications
Paperback
Check
Theory of Vibrations with Applications
Kindle Edition
Check

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Effort
12.5 total hours
Via
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Instructor
Prof Dr Farid Khan
Language
English
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