Unit of Vibration

Dhristi JEE 2022-24

Vibration

The word vibration is derived from the Latin word “vibrationem” which means "shaking or brandishing".

 

Vibration is the back and forth periodic motion of an elastic material. Such an oscillation is a mechanical phenomenon that occurs in an  equilibrium position. 

 

In many places, you may find real-life applications of vibration, such as the motion of a pendulum, the motion of a tuning fork, etc.

 

In this article, you will learn vibration definition Physics, the SI unit of vibration, and vibration measurement units in detail. 

 

Vibration Definition Physics 

Vibration means the act of vibrating or the condition/instance of being vibrated. In Physics, vibration has the following properties:

  • It is a rapid linear motion of a particle or an elastic medium about an equilibrium position.

  • A single cycle of vibrating motion.

  • A periodic motion/process about an equilibrium position, such as the periodic displacement of air and the propagation of  sound from the microphone.

 

Sound and Vibration

The properties of sound and vibration are nearly similar. Sound is the pressure waves that are generated by vibrating structures such as vocal cords; these pressure waves can also induce the vibration of structures, such as an eardrum. Hence, attempts to reduce noise are mostly related to the issues of vibration.

 

Damping Free Vibration 

To proceed with the investigation for the mass-spring-damper, consider the damping is negligible and no external force is applied to the mass that means it is a free vibration. 

 

Now, the force applied to the mass by the spring is proportional to the amount with which the spring is stretched by "x" (presuming that the spring is already compressed because of the weight of the mass). 

 

The proportionality constant, k, is the hardness of the spring and has units of force/distance, a.k.a lbf/in or N/m. The negative sign indicates that the force always opposes the motion of the mass attached to it, so the equation for this statement is given by:

F = - kx

 

According to Newton’s second law of motion, the force generated by the mass is proportional to the  acceleration of the mass as provided in the following equation:

 

\[\sum F = ma = mx = m\frac{d^{2}x}{dt^{2}}\]

 

The sum of the forces on the mass generates an ordinary differential equation as;

 ma + kx = 0

 

For a simple mass-spring system, the undamped natural frequency fn is given by:          

\[f_{n} = \frac{1}{2}\pi \sqrt{\frac{k}{m}}\]

 

Types of Vibration

1. Free Vibration

It occurs when a mechanical device is set in motion with a starting input and allowed to vibrate./oscillate freely. 

 

Examples of this type of vibration are:

  1. Pulling a child back on a swing and letting it to-and-fro.

  2. Hitting a tuning fork and letting it oscillate. 

  3. The mechanical device vibrates at high natural frequencies and damps to motionlessness.


2. Forced Vibration

When time-varying distortions like load, displacement or  velocity are applied to a mechanical system, the disturbance can be periodic, a steady-state input, a transient input, or a random input. 

 

The periodic input can either be a harmonic or a non-harmonic disturbance. 

 

Examples of these types of vibrations involve:

  1. A washing machine shaking because of an imbalance.

  2. Vibration caused in vehicles by an engine or uneven road.

  3. The vibration of a building during an earthquake. 


Point To Note:

For linear systems, the frequency of the slow vibrations results from the application of a periodic, harmonic input and is equal to the frequency of the applied force or motion. The response magnitude is always dependent on the actual mechanical system.

 

3. Damped Vibration 

When the energy of a vibrating system gradually dissipates by friction or other resistances, the vibrations are considered damped. The vibrations reduce gradually or may vary in frequency or intensity or reduce and the system rests in its equilibrium position. 

 

A well-known example of damped vibration is the vehicular suspension dampened/lessened by the shock absorber.

 

SI Unit of Vibration

The SI unit of vibration or the vibration unit is Watts per meter square. 

 

Vibration Measurement Units

Talking about the vibration measurement units or the vibration amplitude measurement, vibration is generally expressed by the units of Frequency, Velocity, Acceleration, and Displacement which are denoted by English alphabets, F, V, A, and D. 

 

If we look at it practically, vibration is most often an intricate summation of various frequencies at different amplitudes.

 

Applications of Vibrations

Vibrations have a host of applications in the medical and industrial fields. Some of these applications are listed below:

  1. Most bodies have natural vibrations that are often left unused. However, utilizing these vibrations and harnessing the resultant energy could be a potential breakthrough in the form of self-powered electronics. 

  2. Vibrations are greatly used in the medical field for a plethora of purposes such as to measure bone mineral density, in health monitoring machines, ultrasound analysis, medical implants, etc.

  3. Vibrations play the most important role in creating sound, music and rhythm. Sound vibrations are used to produce acoustic properties central to the process of music synthesis. All musical instruments have one or the other component in their structural build that utilizes vibrations to produce harmonics or overtones. 

  4. Vibration analysis is used in the industrial maintenance environment specifically for those that aim to reduce faulty vibrations. 

  5. Resonance is another key phenomenon arising from vibrations. Acoustic resonance is of key use in musical instruments. Clocks such as the crystal quartz, pendulum and balance wheel work on the property of mechanical resonance. 

 

Disadvantages of Vibrations

  1. One major demerit of vibrations is the unintended absorption of vibrations from the surrounding environment by the mechanical body causing it to heat up and or swing/move undesirably. This mechanical resonance can cause catastrophic failure if not corrected timely by the engineers.

  2. Resonance Disaster has been a frequent outcome of faulty designs in bridges. One such disaster was the collapse of the Broughton suspension bridge (caused by soldiers walking in forceful rhythmic steps). Another disaster related to the resonating/ oscillating vibrations was the collapse of the Tacoma Narrows Bridge in 1940 (it was the first bridge to collapse owing to vibrations). It occurred due to the vertical movement of the bridge under high wind conditions.

  3. Vibrations also have damage-causing properties to the human body. Long term exposure to vibrations has been known to cause back pain, neck pain, elevated blood pressure levels among other occupational health hazards.

 

Do You Know?

Vibration can be desirable for the motion of a tuning fork, the reed in a woodwind instrument/harmonica, a mobile phone, or the knob of a loudspeaker.

 

However, in many cases, vibration is undesirable because it wastes energy and creates unwanted sound. 

 

For example, the vibrational motions of mechanical devices like heavy-duty vehicle engines, electric motors, or any device in function are unwanted. Such vibrations may be caused by the imbalance or irregularity in the rotating parts of machines, uneven friction, or the meshing of gear teeth (contact with adjacent gearwheel). 

 

Careful designing of these devices can minimize unwanted vibrations.

FAQs on Unit of Vibration

1. Describe an Oscillatory System.

One of the simplest and finest mechanical oscillating systems is a weight attached to a linear spring offered to the weight and tension. A system may be placed on an air table or ice surface. The system is said to be in an equilibrium state when the spring is static. However, when the system is displaced from the equilibrium, there is a net restoring force on the mass, which tries to bring it back to its equilibrium position. 


However, in moving the mass back to the equilibrium position, it acquires a momentum that keeps it moving beyond that position, and therefore, establishing a new restoring force on the opposite side. 


If a constant force, viz: gravity gets added to the system, the position of equilibrium shifts. The time taken for an oscillation to occur is often conferred the oscillatory period.

2. What is the Importance of Studying Mechanical Vibrations?

Vibrations are a rhythmic transmission of sound waves through objects. There are several practical examples such as vibration through a stretched string, vibrations in musical instruments and loudspeakers, etc. However, vibrations are not always desirable. Vibrations can help study bone density but the same vibrations in various mechanical parts of a system can cause noise, wear and tear and other undesirable outcomes (e.g. the Suspension bridges built in the early days of transport). Studying mechanical vibrations helps reduce these undesirable features while maximizing the efficiency of desirable vibrations.

3. What are sound waves?

Sound waves are a form of energy waves that transfer across a medium such as air, water or other liquid and solid objects, using adiabatic compression and decompression, when generated from a source of the sound. Sound waves differ from light (electromagnetic) and heatwaves in that, unlike the light waves, they require a medium to travel, as particle oscillation is a prerequisite, and unlike heat waves, they have higher frequencies, shorter wavelengths and travel as transverse waves.

4. What are the types of vibration in sound mechanics?

Vibrations in sound mechanics are classified into three broad types, namely

  • Free or Natural vibrations (further classified into transverse, longitudinal and torsional vibrations),

  • Damped vibrations and

  • Forced vibrations

 

Vibrations that are produced in the vibrating body (oscillating system) when no external force or stimulus acts on the body are called free or natural vibrations. Such vibration is said to be the natural vibration of the body. It is also known as Eigen frequency. When such vibrations get reduced after each oscillatory cycle, it is called Damped vibrations. Forced vibrations occur when an external stimulus/force is needed to vibrate a body.

5. What is the principle of a Vibration Sensor? Where is it used?

Vibrations in a system can be sensed by the use of various devices such as velocity sensors, accelerometers, strain gauges and gyroscopes. Its work is based on the principle of the use of optical and mechanical vibrational detecting systems. As stated above, vibrations can have an undesirable presence in certain mechanical systems. Detecting the source and limiting such vibrations becomes feasible with vibration sensors. Such sensors use the piezoelectric effects when sensing temperature, pressure and force changes in a closed system.

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