Pre-Stress Modal analysis
Modal analysis determine the vibration characteristic such as natural frequency and more shape structure it often serve as starting point for several linear dynamic analysis such as transient dynamic, harmonic analysis or spectrum analysis. The mode frequency and shape depend on distribution of mass and stiffness in the structure when a structure is in a stress state. Its stiffness changes due to stress stiffening therefore presence of stress in a structure can alter its vibrational characteristic and this structure frequency and compressive stress decrease the frequency few examples where can see pre stress affecting mode of frequency are tuning of guitar strings where tension in the string is adjusted to change its frequency, slack lining where rope is stretch and its tension prevents from wobbling while walking and rotor spinning fast as it deforms under centrifugal forces and therefore in a stressed state. So performing modal analysis on pre-stressed structure.
A linear static analysis equation stated as :
[K] {x}= {F}
([K][M]) {??} = {0}
For pre-stressed modal analysis equation stated as:
([K+S][M]) {??} = {0}
?For applying pre-stress modal analysis we first perfer base stress analysis, where this analysis can either be static or transient analysis or linear or non-linear analysis. Computing the stress defining matrix during linear analysis and for non-linear analysis we also take any changes in stiffness and mass matrix. Where mass of the body may not change but center of gravity of the system changes due to rigid body motion or very large deformation this changes are taken in consideration during pre stressed modal analysis.
From base stress analysis and use the linear perturbation technique to perform pre stress analysis following points to remember during this:
For example bar with square cross section constrained on both ends and kept room tempreture of 22 degree centrigrade. This bar is subjected to thermal load which will generate thermal stresses in bar. Studying mode frequencies of the bar change with thermal load at five different value.
Running parametric analysis to run series of simulations and study simulation at each study point.??Stresses reported by modal analysis are relative and do not hold physical meaning. This connection implies thay solution from static analysis is used as setup for modal analysis.
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Inserting various boundary condition for applying displacements and thermal loads. As tensile stresses are generated in the bar, stresses in axial direction which is global x direction and you can see base stress result from which it extracts pre stress information as boundary conditions are already defined in static structure analysis.
Under modal analysis where mod frequencies for this system selecting 1st mode and by plotting mode shape evaluating result.
paramterising 3 quanitites: thermal load, avg normal stress and frequency of mode where thermal load is input paramter.
Other design points?by changing input parameter,?
Creating parametric chart conditions to evaluate the results:
Solving all this parameter results in
As thermal load increases beyond reference tempreture, the stress state in bar changes from tension to ccompression. As compressive stress increases mode frequency decreases, conversely tensile stress inreases mode frequency increases.
Therefore, it?can be said that non-zero stress in part changes its characteristics.