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 use Simulation to change the Frequencies of a Design:  

  • 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.   

How to Evaluate Rigid-Body Modes in a Modal Analysis:

  • If rigid-body modes are unexpected and undesired in a model, it indicates lack of constraint.
  • Rigid-body modes are expected in free-free modal analysis where a model is unconstrained on purpose.
  • Rigid-body modes are expected for Grounding Check process. Rigid-body modes with non-zero frequencies indicate there are artificial internal constraints in the system, which should be eliminated.
  • When analyzing the system for presence of any grounding, it is usually expected to have rigid body modes when constraints are temporarily suppressed. If rigid-body modes are not present in such scenarios, it’s usually suggested to verify the model along with respective contact definitions.
  • For cases where rigid-body modes are not desired, it is best to ensure sufficient boundary conditions and appropriate contact settings are included in the system.