Advanced Vibration Analysis - Linear Multibody Systems
 

Analyze and design complex mechanical systems using modal analysis, transfer paths and learn engineering interpretation
What you'll learn
Derive equations of motion for coupled systems (first step towards multi-body and structural dynamics)
Model linear multi-degree-of-freedom mechanical systems in matrix form
Perform modal analysis and interpret eigenvalues and mode shapes physically
Understand how mass and stiffness distribution influence system dynamics
Compute and interpret system responses using frequency response functions and the frequency response matrix (MIMO)
Identify and evaluate transfer paths in complex system
Design absorber systems to reduce dynamic loads and improve resonance behavior
Apply all concepts to realistic engineering problems with focus on interpretation and decision-making
Requirements
Completion of the course 'Fundamentals of Dynamcis and Oscillations" is highly recommended (1-DOF vibrations)
Basic calculus and ordinary differential equations
Basic knowledge of matrices and linear algebr
Familiarity with mechanical concepts such as mass, stiffness, and energy
Basic exposure to MATLAB or Python is helpful, but not required (scripts are provided)
Description
Course Features
• Structured, step-by-step development of all concepts
• Focus on real engineering systems and applications
• Strong emphasis on interpretation and physical understanding
• Many guided exercises with complete solutions
• Engineering-oriented explanation of modal behavior and system response
• Direct relevance to multi-body dynamics, structural dynamics, and NVH applications
This course is designed for engineering students and practitioners who want to move beyond single-degree-of-freedom systems and learn how real mechanical systems behave.
You will learn how to model linear multi-degree-of-freedom systems in matrix form, perform modal analysis according to engineering practice, and interpret system behavior in a structured and physically meaningful way.
The focus is not on abstract mathematics or formal derivations, but on what is actually required to analyze and design real systems. All concepts are introduced step by step and immediately applied to realistic engineering problems from areas such as machinery, structural dynamics, and vibration engineering (NVH).
A strong emphasis is placed on interpretation and engineering decision-making. You will learn how mass and stiffness distribution influence eigenfrequencies and mode shapes, how excitation location affects modal participation, and how to identify and control critical transfer paths within a system.
Exercises play a central role throughout the course. Each problem is designed to be attempted independently first, followed by a complete, structured solution. The goal is not routine calculation, but the development of engineering intuition and the ability to solve problems in a controlled and reproducible way.
You will also learn how to professionally compute and interpret system responses using frequency response functions and the frequency response matrix (SIMO/MIMO systems) with provided python and matlab scripts, and how to design absorber systems to reduce dynamic loads and improve resonance robustness.
By the end of this course, you will be able to model, analyze, and interpret complex linear multi-body systems and make reliable engineering decisions based on their dynamic behavior.
Who this course is for
Mechanical engineering students and related fields (mechatronics, automotive, aerospace)
Learners and engineers who want to understand and analyze complex systems beyond simple 1-DOF models
Practitioners working in vibration engineering, NVH, or simulation who want a stronger theoretical foundation