11.10:
Stability of Equilibrium Configuration
A system in equilibrium can be neutral, stable, or unstable.
In neutral equilibrium, if the system is slightly displaced, it remains in equilibrium at its new position. Its potential energy remains constant at this point.
In stable equilibrium, as the system is displaced slightly, it returns to its original position. Such a system is at its minimum potential energy.
In unstable equilibrium, after a small displacement, the system moves farther away from its original equilibrium position, and its potential energy is maximum.
Consider a schematic truss in a laboratory loaded with a small weight that deforms it slightly. Upon removing the weight, the truss returns to its original position. This system is in stable equilibrium.
If the truss is equally loaded on both sides, it displaces slightly and remains in its new position. So, it is in neutral equilibrium.
If the load and support at one end are removed, the system moves away from its original position and is in unstable equilibrium.
Determination of stability at equilibrium is essential for designing stable structures.
11.10:
Stability of Equilibrium Configuration
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight is centered directly below the free end, the beam will be in a position of stable equilibrium. The potential energy of the system is at its minimum, and any small displacement of the weight will cause the beam to oscillate. However, whenever the weight is moved away from the center, the beam will experience a restoring force due to the internal stresses within the beam, which brings it back to its original position.
In a neutral equilibrium, the system remains in balance even after being given a small displacement from its original position, and the potential energy stays constant. An example of neutral equilibrium is a ball placed on a flat and level surface. If the ball is given a slight displacement to one side, it will still remain in the state of equilibrium, and the potential energy of the system will stay constant.
An unstable equilibrium happens when the system tends to move further away from its original state when given a small displacement. At this point, the potential energy of the system is at its maximum. A cantilever beam deflected beyond its elastic limit is an example of this phenomenon; once it exceeds the elastic limit, further deflection leads to instability and eventual collapse.
Overall, understanding these three types of equilibria is essential in mechanical engineering for predicting how systems will respond under different conditions or disturbances. By understanding their properties and limitations, engineers can plan for safe operation and ensure the effective functioning of their designs.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics: Statics. Fourteenth Edition, New Jersey: Pearson. Pp. 601.
- Meriam, J.L., Kraige, L.G. and Bolten, J.N.(2016). Engineering Mechanics: Statics and Dynamics. Eighth Edition, Singapore: John Wiley & Sons. Pp. 415.