CONSISTENT AND LUMPED MASS MATRICES IN DYNAMICS AND THEIR IMPACT ON FINITE ELEMENT ANALYSIS RESULTS

There are two strategies in the finite element analysis of dynamic problems related to natural frequency determination viz. the consistent / coupled mass matrix and the lumped mass matrix. Correct determination of natural frequencies is extremely important and forms the basis of any further NVH (Noise vibration and harshness) calculations and Impact or crash analysis. It has been thought by the finite element community that the consistent mass matrix should not be used as it leads to a higher computational cost and this opinion has been prevalent since 1970. We are of the opinion that in today’s age where computers have become so fast we can use the consistent mass matrix on relatively coarse meshes with an advantage for better accuracy rather than going for finer meshes and lumped mass matrix . We also find that recently in MEMS simulations involving nano- technologies such as photostrictive materials have higher frequencies and here the consistent mass matrix formulation is much more beneficial FEA has been applied successfully to almost all kinds of problems, which range from statics to dynamics. Although we find lot of literature on static analysis with respect to verification and validation of result, this is not always the case with respect to dynamic problems in frequency and time domain due to complexity of physics and numerics.