Insights through Modal Minimal Models for Analysis of Linear and Nonlinear Dynamic Problems

Table 1

References, comparison of analytical solutions using modal and lumped mass equations, and illustrations of the examined cases.

Self-excited modes	Equation/lumped mass	Equation/modal	Sketch
Fixed point stability-critical slope [17]⟶ [13]
Fixed point stability-critical modal damping [17]⟶ [13]
Amplitude [1]⟶ [12]
Damping
Friction inertia damper [7]⟶ [14]
Fluid inertia damper [6]
Tuned-mass inertia damper [9,10]⟶ [15]
Friction stiffness damper [8]⟶ [14]	(firmly clamped on one side)

Principle sources are marked with