Transmissibility
Explore how forces and motions are transmitted through vibrating systems.
System Parameters
kg
N/m
Ns/m
rad/s
N
System Information
Natural Frequency: 10.00 rad/s
Damping Ratio: 0.250
Frequency Ratio: 0.500
Transmissibility Ratio: 1.000
Key Frequency Ratios
Force Transmissibility Simulation
Transmissibility Curve
Governing Equation
Equation of motion for force or motion transmissibility
\[m\ddot{x} + c\dot{x} + kx = F(t) \text{ or } m\ddot{x} + c(\dot{x} - \dot{y}) + k(x - y) = 0\]
Force Transmissibility
Ratio of transmitted force to input force
\[TR = \left|\frac{F_{T}}{F_{0}}\right| = \frac{\sqrt{1 + (2\zeta r)^{2}}}{\sqrt{(1-r^{2})^{2} + (2\zeta r)^{2}}}\]
Force isolation occurs when frequency ratio exceeds √2
\[\text{ For } r > \sqrt{2}, TR < 1 \text{ (isolation region) }\]