4. Partitioning, modal densities, behavior laws

4.1 Partitioning into sub-systems

When dynamic systems are continuous, resonance modes appear. We will therefore characterize them around an analysis frequency band in order to evaluate the number of these resonances in the band. To evaluate these resonances, we must first define a partition into loosely coupled subsystems for which it will be relatively easy to define a constitutive law of vibratory behavior. This is based on discontinuity lines between parts of the system: thickness jumps, material changes, stiffness jumps, etc. This partition must result in subsystems with sufficient extent to contain resonance modes in the band concerned. Each subsystem is then assigned a behavioral law by assimilating it to a simple dynamic system, known according to its topology: bar, beam,...