Modal Analysis with Springs and Preload - Mass Participation Factors
I am running an idealized engine isolator assembly. There are 3 isolators used to support the engine with the front (flywheel) side of the engine having angled isolators and rear isolator being oriented vertically. The isolators are modeled as springs with extensional stiffness. I have my engine sub as a lumped mass with moments of inertia. There is an external belt pulley force applied as well. The belt force and lumped mass are connected via rigid links to one end of each spring. The other end of the spring is connected to a constraint with all 6 DOFs locked. I've run a static analysis to determine the axial force in the spring as well as a modal analysis and a prestress modal analysis. I have a couple questions that come from the results I am seeing.
1. My natural frequencies and mass participation factors do not change between a standard modal analysis and a pre-stress modal using my static analysis. I thought the effect of the belt load and gravity would change the stiffness of the system and I would get different frequencies? Is it because the only stiffness is provided by linear springs?
2. Mass participation factors. I don't fully understand how Simulate reports these. For some modes and and translational/rotational components I get negative participation factors and yet have positive effective mass. I also thought that for a particular mode if I added all 3 translational and all 3 rotational effective mass percentages, they would add to 100% but they actually sum to over 100%.
3. Is there a way to either report or determine from the effective mass the kinetic energy in the 3 translational and 3 rotational directions?
I've attached my model and have the 3 analyses setup.
1. Either the preload is not applied correclty or the modes you are looking (predicted) are not affected by the spring preload - don't knwo the model so can't say more than that
2. Mass is aslways positive ! (unless you use anti-mater!) and the fact the modal participation factor is squared to calcuatae the effective modal mass. This modal participation factor (which is a vector) can have negative terms) - Check the manual (or any manual/book for that matter). on the formula used to calculate Participation factor. sum = 100% only if you have exactly 3 modes. ie 3 DoFs
3. for a KE calc one needs speed (0.5*m*v^2) - where do you propose to ge the speed from - m can be m_effective.? Depending on the mode shape (and direction of excitation) a mode may not be exited and therefore will have no "speed"