Summary — Lesson 4

In this course, we introduced how to perform one of the most fundamental linear dynamics analysis types, modal analysis.  We discussed prestress effects and also how to use simulation to gain more insight into a design based on modal analysis results.    

 Let’s summarize the key points:  

 How to perform modal analysis:  

  • The participation factor shows the most prominent modes in certain directions that will be excited by forces in that direction. 
  • The effective mass can be useful for confirming that enough modes have been extracted for further analysis such as harmonic, response spectrum or random vibration.    

  

How to perform prestressed modal analysis:  

  • Stresses developed in a part change its overall stiffness due to stress stiffening. Due to this, the stress developed in a part changes its mode frequencies.  
  • A pre-stressed modal analysis is used to calculate the modal characteristics of a structure with inherent stress.  
  • A base static or transient analysis is performed to calculate stresses.  
  • A modal analysis is performed based on this analysis using the linear perturbation technique.  
  • The base analysis can either be linear or nonlinear, but the modal analysis is linear in nature.  

  

How to change frequencies using modal analysis:  

  • The strain energy density output helps to provide insight regarding the structural behavior and design, i.e., where to add material to increase the stiffness or where to remove material to reduce the mass.  
  • Thus, the modal analysis results, though being relative, give us information regarding the dynamic response of the system well before we perform more computationally expensive downstream dynamic simulations.  
  • The modal analysis can be used as a quick way to improve the design at early stages of the product development process.