Natural Oscillations

Natural Oscillations

 

Mechanical systems can produce natural (free) oscillatory responses (or, free vibrations) because they can possess two types of energy (kinetic and potential).

 

When one type of stored energy is converted into the other type, repeatedly back and forth, the resulting response is oscillatory.

 

 Of course, some of the energy will dissipate (through the dissipative mechanism of a damper) and the free natural oscillations will decay as a result.

 

 Similarly, electrical circuits and fluid systems can exhibit free, natural oscillatory responses due to the presence of two types of energy storage mechanism, where energy can “flow” back and forth repeatedly between the two types of elements.

But, thermal systems have only one type of energy storage element (A-type) with only one type of energy (thermal energy). Hence, purely thermal systems cannot naturally produce oscillatory responses unless forced by external means, or integrated with other types of systems (e.g., fluid systems).

 

DynamicAnalogies

 

The procedure of model development will be facilitated if we understand the similarities of the characteristics of different types of components.

 

This issue is addressed in the present section. Analogies exist among mechanical, electrical, hydraulic, and thermal systems.

 The basic system elements can be divided into two groups: energy-storage elements and energy dissipation elements gives the linear relationships, which describe the behavior of translator-mechanical, electrical, thermal, and fluid elements.

 

These relationships are known as constitutive relations.

 In particular, Newton’s second law is considered the constitutive relation for a mass element. The analogy between mechanical and electrical elements is known as the force-current analogy.

 

This analogy appears more logical than a force-voltage analogy, this follows from the fact that both force and current are through variables, which are analogous to fluid flow through a pipe, and furthermore, both velocity and voltage are across variables, which vary across the flow direction, as in the case of fluid pressure along a pipe.