Modal Analysis in Excel
In Modal Analysis in Excel, you'll learn ...
- The fundamentals of free vibrations in structures and mechanical systems
- Single degree of freedom system free response
- Multiple degrees of freedom system modal analysis
- How to verify the solution of a system’s natural frequencies and mode shapes
Vibration is a design concern in machinery and structures. A system undergoing vibration usually requires a dynamic analysis during the design process. The natural frequencies and free vibration modes serve as a fundamental basis for determining a system’s time-dependent deformations, inertial forces, and damping forces.
For a single degree of freedom system, most engineers would consider a dynamic analysis rather straightforward to handle because there is only a single natural frequency and mass under consideration. For multiple degrees of freedom system, dynamic analysis can become computationally demanding, and a solution with the aid of a computer is often required. For this reason, many rely on commercial finite element analysis software to calculate natural frequencies and mode shapes of machines and structures. For some, analysis software may be cost-prohibitive or inaccessible, and therefore, it is advantageous to have other tools available to use. Microsoft Excel offers the same computational capabilities for modal and dynamic analysis as commercial software packages, for a much lower price tag.
This course will dive into the generalized eigenvalue problem as it relates to the mass and stiffness of a system and then demonstrates a step-by-step detail of the eigenvalue and mode shape extraction process in Excel with the use of example problems. The intent of the example problems is to demonstrate a practical and efficient application of the eigenvalue/eigenvector problem in an office setting.
A background in matrix algebra and finite element analysis is helpful for this course. This course is intended for practicing mechanical, civil, and structural engineers.
Specific Knowledge or Skill Obtained
This course teaches the following specific knowledge and skills:
- Free vibration analysis of a single degree of the system (SDOF)
- Modal analysis of multiple degrees of freedom system (MDOF)
- The extraction process of eigenvalue-eigenvector pairs for an MDOF
- Natural frequency and mode shape solution verification
- The significance of mode shapes
Certificate of Completion
You will be able to immediately print a certificate of completion after passing a multiple-choice quiz consisting of 15 questions. PDH credits are not awarded until the course is completed and quiz is passed.
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