EXPERIMENT NO 5: VIBRATION OF PLATES

Objective: Measure the natural frequencies & mode shapes during the transverse vibration of a circular

plate. Verify results by FEM

Procedure:

1) Experiment

Clamp the plate on vibration exciter. Start exciting the plate starting from 0 Hz to 150 Hz

slowly and observe the amplification in vibration of the plate at increasing frequencies. The

frequency at which plate vibrates violently is the resonant frequency. Observe this plate with

Stroboscope & determine the resonant frequency with the help of Stroboscope.

Stroboscope

A stroboscope also known as a strobe, is an instrument used to make a cyclically moving object

appear to be slow-moving, or stationary. It consists of either a rotating disk with slots or holes or a

lamp such as a flashtube which produces brief repetitive flashes of light. Usually the rate of the

stroboscope is adjustable to different frequencies. When a rotating or vibrating object is observed

with the stroboscope at its vibration frequency (or a submultiple of it), it appears stationary. Thus

stroboscopes are also used to measure frequency. The principle is used for the study

of rotating, reciprocating, oscillating or vibrating objects

Types of Stroboscope

Mechanical

In its simplest mechanical form, a rotating

cylinder (or bowl with a raised edge) with evenly-

spaced holes or slots placed in the line of sight

between the observer and the moving object.

The observer looks through the holes/slots on

the near and far side at the same time, with the

slots/holes moving in opposite directions. When the holes/slots are aligned on opposite sides, the

object is visible to the observer.

Alternately, a single moving hole or slot can be used with a fixed/stationary hole or slot. The

stationary hole or slot limits the light to a single viewing path and reduces glare from light passing

through other parts of the moving hole/slot.

Viewing through a single line of holes/slots does not work, since the holes/slots appear to just sweep

across the object without a strobe effect.

The rotational speed is adjusted so that it becomes synchronised with the movement of the

observed system, which seems to slow and stop. The illusion is caused by temporalaliasing,

commonly known as the stroboscopic effect.

Electronic

In electronic versions, the perforated disc is replaced by

a lamp capable of emitting brief and rapid flashes of light.

Typically a gas-discharge or solid-state lamp is used, because

they are capable of emitting light nearly instantly when power

is applied, and extinguishing just as fast when the power is

removed.

By comparison, incandescent lamps have a brief warm-up

when energized, followed by a cool-down period when power

is removed. These delays result in smearing and blurring of

detail of objects partially illuminated during the warm-up and

cool-down periods. For most applications, incandescent lamps

are too slow for clear stroboscopic effects. Yet when operated

from an AC source they are mostly fast enough to cause audible hum (at double mains frequency)

on optical audio playback such as on film projection.

The frequency of the flash is adjusted so that it is an equal to, or a unit fraction of the object's cyclic

speed, at which point the object is seen to be either stationary or moving slowly backward or

forward, depending on the flash frequency.

Neon lamps or light emitting diodes are commonly used for low-intensity strobe applications, Neon

lamps were more common before the development of solid-state electronics, but are being replaced

by LEDs in most low-intensity strobe applications.

Xenon flash lamps are used for medium- and high-intensity strobe applications. Sufficiently rapid or

bright flashing may require active cooling such as forced-air or water cooling to prevent the xenon

flash lamp from melting.

Vibration:

Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The

oscillations may be periodic such as the motion of a pendulum or random such as the movement of

a tire on a gravel road.

Vibration is occasionally "desirable". For example, the motion of a tuning fork, the reed in

a woodwind instrument or harmonica, ormobile phones or the cone of a loudspeaker is desirable

vibration, necessary for the correct functioning of the various devices.

More often, vibration is undesirable, wasting energy and creating unwanted sound – noise. For

example, the vibrational motions ofengines, electric motors, or any mechanical device in operation

are typically unwanted. Such vibrations can be caused byimbalances in the rotating parts,

uneven friction, the meshing of gear teeth, etc. Careful designs usually minimize unwanted

vibrations.

Types of vibration

Free vibration occurs when a mechanical system is set off with an initial input and then allowed to

vibrate freely. Examples of this type of vibration are pulling a child back on a swing and then letting

go or hitting a tuning fork and letting it ring. The mechanical system will then vibrate at one or more

of its "natural frequency" and damp down to zero.

Forced vibrations is when a time-varying disturbance (load, displacement or velocity) is applied to

a mechanical system. The disturbance can be a periodic, steady-state input, a transient input, or a

random input. The periodic input can be a harmonic or a non-harmonic disturbance. Examples of

these types of vibration include a shaking washing machine due to an imbalance, transportation

vibration (caused by truck engine, springs, road, etc.), or the vibration of a building during an

earthquake. For linear systems, the frequency of the steady-state vibration response resulting from

the application of a periodic, harmonic input is equal to the frequency of the applied force or motion,

with the response magnitude being dependent on the actual mechanical system.

Natural Frequency of Vibration

Natural frequency is the frequency at which a system tends to oscillate in the absence of any

driving or damping force.[1]

Free vibrations of any elastic body is called natural vibration and happens at a frequency called

natural frequency. Natural vibrations are different from forced vibration which happen at frequency of

applied force (forced frequency). If forced frequency is equal to the natural frequency, the amplitude

of vibration increases manyfold. This phenomenon is known as resonance.[2]

In electrical circuits, s1 is a natural frequency of variable x, if the zero-input response of x includes

the term   where   is a constant dependent on initial state of the circuit, network

topology, and element values.[3] In a network, sk is a natural frequency of the network if it is a natural

frequency of some voltage or current in the network.[4]Natural frequencies depend only on network

topology and element values but not the input.[5] It can be shown that the set of natural frequencies in

a network can be obtained by calculating the poles of all impedance and admittance functions of the

network.[6] All poles of the network transfer function are also natural frequencies of the corresponding

response variable, however there may exist some natural frequencies that are not a pole of the

network function, these frequencies happen at some special initial states.[7]

In LC and RLC circuits, natural frequency of circuit can be calculated as:[8]

Resonance

In physics, resonance is a phenomenon that occurs when a given system is driven by another

vibrating system or external force to oscillate with greater amplitude at a specific

preferential frequency.

Increase of amplitude as

damping decreases and

frequency approaches

resonant frequency of a

driven damped simple

harmonic oscillator.[1][2]

Frequencies at which the

response amplitude is a

relative maximum are

known as the system's

resonant frequencies,

or resonance frequencies.

At resonant frequencies,

small periodic driving forces

have the ability to produce large amplitude oscillations. This is because the system storesvibrational

energy.

Resonance occurs when a system is able to store and easily transfer energy between two or more

different storage modes (such as kinetic energy and potential energy in the case of a pendulum).

However, there are some losses from cycle to cycle, called damping. When damping is small, the

resonant frequency is approximately equal to the natural frequency of the system, which is a

frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies.

Resonance phenomena occur with all types of vibrations or waves: there is mechanical

resonance,acoustic resonance, electromagnetic resonance, nuclear magnetic

resonance (NMR), electron spin resonance (ESR) and resonance of quantum wave functions.

Resonant systems can be used to generate vibrations of a specific frequency (e.g., musical

instruments), or pick out specific frequencies from a complex vibration containing many frequencies

(e.g., filters).

The term Resonance (from Latin resonantia, 'echo', from resonare, 'resound') originates from the

field of acoustics, particularly observed in musical instruments, e.g. when strings started to vibrate

and to produce sound without direct excitation by the player.