Two-sided bounds on some output-related quantities in linear stochastically excited vibration systems with application of the differential calculus of norms

Figures & data

Figure 1. Multi-mass vibration model.

Figure 2. Curve $y=\Vert P_{x_S}(t)-P_S{\Vert }_2,0\le t\le 5,\mathrm{\Delta }t=0.01$.

Figure 3. Right norm derivative $y=D_{+}{\Vert P_{x_S}(t)-P_S\Vert }_2,0\le t\le 5,\mathrm{\Delta }t=0.01$.

Figure 4. Second right norm derivative $y=D_{+}^2{\Vert P_{x_S}(t)-P_S\Vert }_2,0\le t\le 5,\mathrm{\Delta }t=0.01$.

Figure 5. $y=\Vert P_{x_S}(t)-P_S{\Vert }_2$ along with the best upper and lower bounds on range [0;5].

Figure 6. $y=\Vert P_{x_S}(t)-P_S{\Vert }_2$ along with the best upper and lower bounds on range [5;25].