Example No. 2 Mode Coupling

Consider the 2-DOF system shown in Fig. 4.12 studied by Hoffman and Gaul [76, 77]. This model consists of a point mass sliding on a conveyor. The mass is suspended using vertical and horizontal linear springs and dampers. An additional spring placed at 45° angle is also considered which acts as the coupling between vertical 

The equation of motion for this system can be written in matrix form as 

Shifting the equilibrium point (steady-sliding state) to the origin by setting x = X — Xeq and zi = z — Zeq, whcrc 

The symmetry-breaking role of friction is clearly shown by (4.38). Note that f(y, y) is nonzero only when yi Vb. In a small neighborhood of the origin, (4.38) simplifies to a linear homogeneous differential equation 

Neglecting damping, from (3.29) the characteristic equations is foxmd as 

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