Vibrations

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Module 2: Excitation reduction at source and factors affecting vibration level Lecture 4: Control of Vibration due to forced excitation and other causes

The Lecture Contains:

Control of Vibration due to Forced Excitation

Control of a Self Excited Vibration

Control of Flow Induced Vibration

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Vibration Reduction at Source

In a large number of practical situations, the vibration can be controlled by reducing the excitation levelat the source. This reduction in excitation is possible only after the source has been identified and thenature of excitation clearly understood. In this module, we shall discuss some examples of forced, self, and parametric excitations where thevibration level can be controlled at the source.

Example 1: Forced Excitation

Let us consider the vibration of an aircraft due to jet noise. The fuselage and other structures of theaircraft are subjected to intense pressure fluctuations present in the jet noise (which contains of theorder of 1% of the total jet energy). This results in the so-called acoustic fatigue of the aircraftstructures. Also, due to the fuselage vibration, noise is transmitted within the aircraft cabin. An effectivesolution to this vibration problem can be obtained by reducing the jet-noise excitation.

Figure 4.1 : Vibration in aircraft due to jet noise

An analysis of the jet flow (Fig.4.1) brings out the following:

i. High shear rate exists in the flow-mixing region in the vicinity of the jet exit. The region is full ofsmall eddies oscillating at high frequencies.

ii. Large eddies of low frequencies are present in the region away from the jet exit.iii. The larger the jet diameter, the larger the eddies, implying more of low-frequency noise.

Likewise, the high-frequency content in the jet noise is more if the jet diameter is small.

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How do we Control?

It is known that atmospheric attenuation of noise is higher for high frequencies than that for lowfrequencies.

Figure 4.2: Jet noise reduction through modified jet exit

By using multiple number of smaller jets (Fig.4.2a) instead of a big one, the noise at the jet exit can bemade to contain predominantly high frequencies. The noise (excitation) impinging on the aircraftstructure would then be considerably reduced due to high atmospheric attenuation. Another method of reducing the jet noise is to provide a serrated jet exit (Fig.4.2b), which improves themixing of flow in the exit region by making it more gradual. This, in turn, reduces the shear rate and theresulting large-scale turbulences.

Recently, a new technique of impinging microjet (as shown in Figure 4.2c) is being explored forcontrolling the jet noise. A spining disc containing microjet is introduced around the central nozzle. Byvarying the disc from 0 to 150 Hz it has been observed that the jet noise could be controlled effectively.

Similar Application

The flow-induced vibration of air duct can always be controlled by providing a tubular flow smoothenerat the exit of the fan feeding the duct. The flow smoothener reduces the turbulent pressure fluctuationsexciting the duct walls.

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Example 2 : Self-excited Vibration due to Dry Friction.

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Fig 4.3: Variation in friction force with relative velocity

Figure 4.3 shows the variation of the dry friction force (between two bodies in relative motion) with arelative velocity. The negative slope of this curve, as opposed to the positive slope for viscous damping,is important. It implies that the friction force does positive work in every cycle of oscillation of the drivenmember. This work manifests itself in the oscillatory instability of the driven member, i.e., the memberoscillates at its natural frequency with its amplitude increasing gradually. This type of oscillation,normally referred to as chatter, is frequently encountered in machining and similar situations. Suchfriction-induced oscillations in disc brakes of automobiles give rise to "brake-squeal", control of which isan important topic of current research. Providing a lubricant which essentially reduces the friction at thetool-job interface, sometimes controls the chatter of a cutting tool.

A machine can be made less susceptible to chatter by improving the

surface finish dimensional tolerance and lubrication standard of the machine elements (e.g., guideways) that are in contact but

move relative to each other.

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Let us look at an interesting example of a huge drawbridge that failed due to dry-friction.

Figure 4.4 : Schematic diagram of a Draw-bridge

Figure 4.4 schematically shows one-half of this drawbridge where the deck used to be positioned bymoving the four-bar parallelogram linkage O2ABO4. After about a year, one of the bridge towers failed

by fatigue. An experiment with the other half revealed that the whole bridge vibrated violently at a ratherlow frequency each time the deck was raised. The answer was found in the bearing at B. This bearingcarried the huge load of the counterweight. As a result, the grease originally present in the bearing gotsqueezed out and the bearing was running dry. This dry friction gave rise to chatter which was violentenough to ultimately cause the failure by fatigue. The simple remedy to this vibration problem consistedin providing proper grease cups at B and keeping them under regular inspection.

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Example 3: Karman Vortices

A very common source of oscillation found in many practical situations, like

power transmission cables heat-exchanger tubes chimneys end tower of a bridge or the bridge itself marine structures and cables, is the so-called Karman vortices.

The resulting vibrations are referred to as flow-induced vibrations. Any structure with a sufficiently blufftrailing edge, if placed in a moving fluid, sheds vortices. These vortices are quite similar irrespective ofthe shape of the tripping structure. The vortices, called the Karman Vortices are shed alternatelyclockwise and counter-clockwise in a regular manner from each side of the structure. As a result, thestructure is subjected to a periodic sidewise force having the same frequency as that of the vortexshedding.

Figure 4.5: Karman vortices in moving flow

Figure 4.5 schematically shows the Karman vortices in the wake of a cylinder. For such a body, thevortex- shedding frequency f(Hz) can be obtained from the relation

(4.1)

where D = diameter of the cylinder (m), and V = free stream velocity of the fluid (m/s), S =Strouhalnumber.The value of the Strouhal number is approximately 0.2 for a cylinder.

For a noncylindrical body, Eqn.(4.1) can still be used when D represents the maximum width of thecross-section normal to the free stream. The value of the Strouhal number for such a body varies from0.12 to 0.17, depending on the cross-sectional geometry. If the vortex-shedding frequency is close to anatural frequency of the structure, excessive vibration is generated.

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Module 2: Excitation reduction at source and factors affecting vibration level Lecture 4: Control of vibration due to forced excitation and other causes

To control the vortex-induced vibration, various methods have been suggested.

a. One obvious way of avoiding vortex shedding is to streamline the body, if possible. A streamlineconstruction of the marine pier has been met with moderate success. This method is effectiveonly if the flow angle relative to the structure is essentially constant.

Figure 4.6 : Streamline marine pier

b. The helical spoiler (Fig. 4.7) has been found to be successful in breaking the regular vortexpattern in the wake of a tall cylindrical stack (chimney), thus preventing a clearly definedexcitation.

Figure 4.7 : Helical spoiler

Shrouds and small rectangular plates fitted at intervals around a stack also introduce irregularitynear the wake of the cylinder and disrupt the process of regular vortex shedding. The use ofthese vortex-breaking devices, however, can increase the magnitude of the exciting force on thestructure.

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As compared to a stack, a marine cable requires a larger vortex-interfering device. This is because thedensity of water is much higher than that of air.

Figure 4.8 : Spoilers used in underwater cables

One such device is the plastic ribbon. If woven into a cable at close intervals (Fig. 4.8), the plasticribbons effectively prevent the vortex shedding. It has been suggested that the ribbons be one diameter(of the cable) wide, extending four diameters behind the cable and spaced no more than one diameterapart.

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