Mechanical Vibration
Web Book
Mass, Spring & Damper Elements
Learning objectives
Determine the equivalent mass, equivalent stiffness and equivalent damping in a vibrating system
Sections
2.1 Vibration energy
2.2 Stiffness element
2.3 Mass element
2.4 Damper element
2.1 Vibration energy
Consider a block of rigid mass placed on a vertical spring. We can press the mass to suppress the spring and then let it go. The mass then bounces up and down around an equilibrium position. See Animation 2.1.1.
The motion of this system is simply an exchange between the kinetic energy (KE) and the potential energy (PE). The kinetic energy is released with the motion of the mass and stores the energy in the form of potential energy with the deflection of the spring.
If the spring is made of material where there are no frictions among its atoms or molecules during its suppression or extension, then the mass on that spring will bounce forever (undamped vibration). At any given time in Animation 2.1.1, the total energy is the same: KE + PE = constant.
However, the mass is eventually stop because there is a mechanism that drains out the energy from the system. The total energy is the same, but now the kinetic and the potential energy changes into another form of energy; in this case it changes into heat due to friction (damped vibration). It can also drains in the form of sound radiation, for example a vibrating plate.
Animation 2.1.1 Exchange of kinetic energy (KE) and potential energy (PE) of an undamped vibrating system. Maximum PE is when the spring is fully stretched or fully suppressed, while max KE is when the mass is its full speed (just before or after passing the equilibrium line).
As pointed out in Chapter 1, three important elements in a vibrating system are:
- Stiffness component which stores potential energy
- Mass component which stores kinetic energy
- Damping component which dissipates energy
When we analyse, design and solve a vibration problem, these three important physical parameters are those that we have to control. Either to increase or to reduce its value depends on certain conditions, for example the excitation frequency and the natural frequency of the system.
