**Mechanical Vibrations** plays an important role in the field of Automobile Engineering and Structural Engineering. When any sudden disturbance takes place then the structure should be in a position to tackle with that. Else, the structure fails. Therefore, In this article, I am providing all the concepts of Vibrations like Condition Monitoring, its effects, classification, remedies, Damped Forced Vibrations, Damped Forced Vibrations etc.along with various aspects were furnished below in the form of Table.

**Tabular Column:**

## Mechanical Vibrations-All Concepts:

All the concepts which are presented above in the tabular column are furnished below in a detailed manner.

**1. What is Damped Forced Vibrations?**

**Damped Forced Vibrations:** If the external force (i.e mass)is acted upon the system, then the system undergoes vibratory motion and thus called as Forced Vibration on the System. In this article, I will be explaining about Damped Forced Vibrations in a detailed manner.

**Damped Forced Vibrations-Explanation:**

- If the damper is induced within the construction along with the external force acting on the system, then the system is called Damped Forced Vibrations.
- If the damper is induced within the construction with no applied force on the system, then the system is called Damped Free Vibrations.
- The forced vibration is represented as
**F**coswt or**F**sinwt. - The equation of motion is represented in the video which is shown below.
- As soon as the harmonic force is applied there will be a transient response coupled with the forced response. The transient part is the one which dies out after some time.
- Hence neglecting the transient response, we have

**x = Asinwt +Bcoswt**

It can also be written as **x=Xsin(wt-(fi))**

Watch Below video for further explanation:

**2. What is Damped Free Vibrations?**

As the name suggests that the system is Damped, It means a Damper is present in the system which is used to absorb the vibrations. But the system doesn’t undergo any external force which means the system is under natural vibrations also called free vibrations. The entire system with all these specifications is called Damped free vibratory system. In this article, I will be explaining about the Damped Free Vibrations in an effective manner.

**Explanation of Damped Free Vibrations:**

**Free vibrations**are oscillations where the total energy stays the same over time.- This means that the amplitude of the vibration stays the same.
- This is a theoretical idea because in real systems the energy is dissipated to the surroundings over time and the amplitude decays away to zero, this dissipation of energy is called
**damping**.

Thus called a system under “Damped Free Vibrations”.

The equation of motion and the formulas to calculate the problems related to damped free vibrations are presented in the video which is shown below.

*Watch Below video for further explanation:*

**3. What is Vibration Monitoring and its benefits?**

**Vibration Monitoring and its benefits:** Monitoring the system when it is under vibrations is called vibration monitoring. Vibrations in the system take place for many reasons and some are discussed below. In this article, I am going to explain Vibration Monitoring and its benefits in a detailed manner.

**Other details of Vibration Monitoring and its benefits:**

How the typical machine problems are detected in a machine when it is under vibration was shown below.

**Detect Typical Machine Problems:**

- Imbalance
- Misalignment
- Looseness
- Rolling element bearing defects
- Gear defects
- Pump cavitation etc.

**Advantages of Vibration Monitoring:**

- Vibration magnitude is proportional to the magnitude of the problem.
- Vibration can help to find the location of the fault.
- Vibration can help to find the cause of the fault.
- Vibration measurement is non-invasive.
- Most faults show increased vibrations in an early stage of the deterioration sequence.
- Vibration can be measured instantaneously.
- Vibration can indicate severity and deterioration rate of a fault.

- An advance indication of developing problems
- Keep people out of hazardous areas
- Protect health, safety, and environment
- Monitor inaccessible equipment
- Complement portable monitoring programs.

The remaining explanation of Vibration monitoring is presented in the video which was shown below.

**Other Information:**

**4. What are the Methods to Analyze Nonlinear Vibratory Systems?**

**Methods to analyze nonlinear vibratory systems:** In this article, I will be explaining the methods to analyze nonlinear vibratory systems in a detailed manner.

**Methods:**

The methods to analyze Non-Linear vibratory systems are as follows. They are

- EXACT Method
- Approximate Analytical Methods

The Approximate analytical methods are further classified into four types and are as follows:

- Poincore method
- Lindsted’s perturbation
- Iterative method
- Phase-plane method

The above methods consist’s of numerical part i.e.formulas and calculations which are difficult to write here. Therefore they are furnished below in the form of video.

Watch Video:

**5. What is the theory of Non-linear and Random Vibrations?**

**Non-linear and Random Vibrations:** Vibration phenomena that might be modeled well using linear vibration theory include small amplitude vibrations of long slender objects like long bridges, airplane, wings, helicopter blades, etc. In this article, I will be explaining about theory of Non-linear and Random Vibrations in a detailed manner.

**Applications of Non-linear and Random Vibrations:**

- Small rocking motions of ships in calm waters
- The simplest whirling motions of flexible shafts
- Interactions between bridges and foundations
- Interactions between wings/blades and air
- Interactions between ships and waves
- Interactions between shafts and bearings and so on are all nonlinear.

__Nonlinear systems can display behaviors that linear systems cannot. These include:__

- Multiple steady state solutions in which some are stable and some are unstable in response to the same inputs.
- Jump phenomena, involving discontinuous and significant changes in the response of the system as some forcing parameter is slowly varied.
- Response at frequencies other than the forcing frequency.
- Internal resonances, involving different parts of the system vibrating at different frequencies, all with steady amplitudes (the frequencies are usually in rational ratios, such as 1:2, 1:3, 3:5, etc.)
- Self-sustained oscillations in the absence of explicit external periodic forcing.
- Complex, irregular motions that are extremely sensitive to initial conditions.

**Mechanical Vibrations-Random Vibrations:**

- In Mechanical Engineering
**random vibration is**a motion which is non-deterministic, meaning that future behavior cannot be precisely predicted. - The randomness is a characteristic of the excitation or input, not the mode shapes or natural frequencies.
- Some common examples include an automobile riding on a rough road, wave height on the water or the load induced on an airplane wing during flight.
- Structural response to random vibration is usually treated using statistical or probabilistic approaches.
- In mathematical terms, random vibration is characterized as a stationary process.

**6. What is the Theory of Vibrations due to Unbalance?**

Rotating Unbalance is the uneven distribution of mass around an axis of rotation. A rotating mass or rotor is said to be out of balance when its center of mass is out of alignment with the center of rotation (geometric axis).In this article, I am going to explain What is the theory of vibrations due to unbalance in a detailed manner.

__Explanation:__

Unbalance causes a moment which gives the rotor a wobbling movement characteristic of vibration of rotating structures.

**This article mainly focuses on**

- Inherent unbalance in the systems
- Vibrations due to Reciprocating mass of engines
- Critical or whirling speeds of an eccentric rotor mounted on the shaft.

The formulas related to the above contents are described briefly in the PPT shown below.

**Watch the Video: **

__Effects of unbalance:__

- Vibrations
- Unsafe work conditions
- Decreased life of bearings
- Increased maintenance
- Reduced machine life
- Noise

**Other Concepts of Mechanical Vibrations Include:**

- Condition Monitoring: Structure, Uses, Issues, and Types of maintenance
- What is Machine Fault Signature and its Detection Techniques?
- What is the theory of vibration Isolation and Transmissibility?