acoustic scattering by submerged cylindrical shell stiffened by an internal lengthwise rib

Acoustic scattering by submerged cylindrical shell stiffened by an internal lengthwise rib

Aleksander Klauson and G&rard Maze LAUE URA CNRS 1373 Universit• du Havre, Place Robert Schuman, 76610 Le Havre, France

Jaan Metsaveer

Tallinn Technical University, Ehitajate tee 5, Tallinn EE 0026, Estonia

(Received 20 July 1993; revised 15 February 1994; accepted 2 May 1994)

An experimental study of sound scattering by a thin-walled cylindrical shell stiflened by an internal lengthwise rib is presented. The results show that, in the explored frequency band, the positions of the resonance frequencies of the wave S o are not affected much by the presence of a stiffener. Measurements made during the transient state after the quasiharmonic excitation of the stiflened shell have shown that, at the S O wave resonance frequencies, backscattering is at its maximum when the rib is located at the vibration node of the shell. On the other hand, when in the total backscattered pressure, forced vibration is also taken into account, the maxima are detected when the rib is located at the vibration antinodes. In the stiflened shell other additional resonances appear which are not excited in the case of an unstiffened shell. These resonances are attributed to the propagation of the flexural type waves which are not detected in an unstiffened shell. In a stiflened shell these resonances appear as a result of the interaction of the rib and the shell at their structural joint. These additional resonances are better observed when the rib is located at the "illuminated" part of the shell which indicates that most of the energy is scattered by the rib and shell joint. In the case of a short-pulse excitation, specular reflections from a joint can be observed. The experimental results correlate very well with the theoretical models.

PACS numbers: 43.40.Ey, 43.20.Fn

INTRODUCTION

To obtain experimental resonance spectra from a submerged target, the method of isolation and identification of resonances (MIIR) can be used. •'2 Up to now correlation between theoretical and experimental results obtained by MIIR has been verified for various solid and thin-walled

scatterers. In technical applications thin-walled shells are of- ten stiflened by internal ribs and walls which cause considerable changes to the dynamic characteristics of the structure. Some experimental studies of acoustic scattering have been realized from internally loaded finite cylindrical shells or finite cylindrical shell with internal structures and excited in axial incidence. 3'4 Theoretical studies of the lengthwise reinforced cylindrical shells 5'6 have shown the influence of the stiffeners on the scattered sound pressure field. The ap- proach used in these studies is based on a separate study of the contributions of the shell and of the stiffeners in the

scattering. In the special case of stiffeners placed along the diameter of the shell, the solution to the problem can be simplified as the contributions of symmetrical and antisymmetrical vibrations of the shell, with respect to the rib, can be found separately. The analysis of the numerical results have shown that the contribution of the rib in the pressure field mainly consists in the generation of the flexural-type waves from very low frequencies, whereas in an unstiffened shell with the same parameters only So (membrane-type wave) wave is generated. The aim of this paper is to present an experimental verification of the theoretical results of sound

scattering by the axially reinforced shell as well as the inves- tigation of the sound generation mechanism caused by the shell and the rib interaction.

I. THEORETICAL STATEMENT OF THE PROBLEM

Let us consider an infinitely long thin-walled elastic cir- cular cylindrical shell of medium radius R and thickness h with a vacuum inside, immersed in an unbound fluid medium. The shell is supported from inside by a lengthwise stiffener-stringer of radial dimension l s and thickness h s. The stringer is attached to the shell along the line. The Timoshenko-Mindlin theory of plates and shells is used to describe the vibrations of the shell and the stiffener. The shell

is insonified by a plane acoustic pressure wave at normal incidence to its axis. We have to determine the scattered

sound pressure field p generated by the incident wave. This 2-D problem is described in the polar coordinates associated with the cylindrical shell. The expressions of the displacements of the shell and the internal plate at their junction caused by unit coupling forces are first found. Then the coupling forces are determined from the conditions of the con- tinuity of displacements of the two substructures at their junction. Finally the coupling forces add their contribution to the resulting pressure p scattered from the shell stiflened by axial rib. The total pressure can be written

P = P shell q-prib, sm q- P rib,asm ,

where P shell is the contribution of the shell, P rib is the contribution of the rib, P-rib,sin is the contribution of the normal coupling force, and P rib, asm is the contribution of the trans-

1575 J. Acoust. Soc. Am. 96 (3), September 1994 0001-4966/94/96(3)/1575/7/$6.00 ¸ 1994 Acoustical Society of America 1575

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transmitter/ receiver

FIG. 1. Scheme for monostatic setup.

versal coupling force and the bending moment. The normal coupling force or the normal reaction of the rib to the motions of the shell generates symmetrical vibrations of the shell with respect to the rib. Two other coupling forces or antisymmetrical components of the reaction of the rib to the motions of the shell generate antisymmetrical vibrations with respect to the rib. The form functions of the scattered pressure field can be calculated separately for every contribution. According to the Fourier transform, time signals can be determined for a given spectral function and the central frequency of the incident pulse. Details of the theoretical ap- proach used can be found in Ref. 6.

In order to obtain the resonance spectrum of the shell, the influence of the specularly reflected wave (nonresonant background component) must be eliminated. Generally, the type of background chosen corresponds to that of the per- fectly rigid target for the thick shell or of a soft target for the thin shell. In the case of an intermediate thickness, the liquid shell, obtained from the elastic one for ct-•0, where c t is the transverse velocity in the elasticity theory, can be used as backgr0und. 7 This resonance spectrum corresponds to the free vibration state of the shell after forced excitation by an incident pressure wave.

II. EXPERIMENTAL DETAILS

The insonified targets are 200-mm-long stainless-steel cylindrical shells of the internal radius b=25 mm and the internal-to-external radius ratio b/a=0.98 [R=(a+b)/2]. The' steel plate of the same thickness is soldered, inside one of the shells, at one edge diametrically along the generatrix of the cylinder. The radial dimension of the plate is /s=49 mm. The targets are placed vertically and immersed in water. The transducers emitter-receiver have a broad passband and a central frequency of 200 and 500 kHz, respectively. Ex- perimental results are obtained for two types of excitations of the target. (a) The incident signal is a burst. composed of a number of cycles sufficient to obtain a quasiharmonic vibration of the target; the scattered field is measured either during or after the forced vibration. (b) The incident signal is a pulse of short duration; the scattered sound field is measured by the same transducer working in the receiver regime. The monostatic setup used is shown in Fig. 1.

50 100 1•0 . ).._•

260 250 300 kHz

5O

(b)

i

300 kHz

FIG. 2. Measured spectra of resonances. (a) Unstiffened shell, (b) shell stiffened by the axial rib.

III. EXPERIMENTAL AND THEORETICAL RESULTS AND THEIR DISCUSSION

A. Resonance spectrum

The resonance spectrum of the unstiffened shell is presented in Fig. 2(a). This spectrum is recorded by a transducer with a central frequency of 200 kHz in the quasiharmonic regime, which is obtained by exciting the shell with a suffi- ciently long burst. The scattered signal is measured 25 /as after the end of the forced vibration. The explored frequency band is between 50 and 300 kHz which corresponds to the dimensionless frequency band 5.40<kR<32.38 (5.45<ka <32.71). Only the resonances of the So wave are present in this spectrum, as the flexural-type wave does not radiate at such low frequencies. The same resonances can also be seen in the calculated resonant component of the form function in Fig. 3(a) and their positions are in good agreement with the measurements. It must be noted that all the theoretical curves

are corrected with respect to the real passband of the transducer and to the real measurement time after the forced ex-

citation. The first factor affects the amplitude distribution over the spectrum with respect to the central frequency and the second affects the overall magnitude of the resonance contribution of the shell.

1576 J. Acoust. Soc. Am., Vol. 96, No. 3, September 1994 Klauson et aL: Scattering by a cylindrical shell 1576


IPI

0.5

50 100 150 200

(a)

250 300

0.5

10 15 20 25 30

140

0.5

5O

160 180 200 220

100 150

kHz

kHz 14 16 18 20 22 24

kR

200 250 300

[ I i i i i J

10 15 20 25 30

FIG. 3. Calculated spectra of resonances. (a) Unstiffened shell, (b) shell stiflened by the axial rib.

The spectrum in Fig. 2(b) is measured under the same conditions but for a shell stiflened by an axial stiffener. The angle between the incident wave and the stiffener is Os=O ø when the shell and the stiffener joint is in front of the transducer. At this angle, only symmetrical vibrations of the shell generate symmetrical vibrations in the rib. The presence of the stiffener changes the resonance spectrum drastically, many additional resonances appear. These resonances are closer in frequency than in an unstiffened shell and form groups separated by large minima. The same spectrum char- acter can also be seen in Fig. 3(b), where the calculated resonant component of the form function of the stiflened shell is presented. The main part of the resonant component is due to the symmetrical contribution P rib, sm in the pressure field. The resonances of the So wave are present although they are attenuated. The agreement of the curves in Fig. 2(b)

FIG. 4. Measured (thick line) and calculated (thin line) spectra of resonances for shell stiflened by the axial rib.

and Fig. 3(b) in the vicinity of the central frequency is rather good: Most of the theoretical resonances can also be found in the measured resonance spectra, although their amplitudes are not always of the same magnitude. The zoomed part of the spectrum from 125 to 225 kHz, where the experimental (thick line) and theoretical (thin line) results are superim- posed, is shown in Fig. 4. Additional resonances appearing in the reinforced shell correspond to the flexural-type wave resonances which do not appear when the shell is not reinforced. These resonances are shifted with respect to the corresponding eigenfrequencies of the "dry" unstiffened shell and will only appear in a submerged shell as a result of the interaction between the shell and the stiffener. The total num-

ber of eigenfrequencies of the stiflened shell in a given frequency band increases with respect to that of the unstiffened shell by the number of eigenfrequencies of the rib. All the resonances in Figs. 2(b) and 3(b) form groups separated by rather large minima observed at frequencies 56, 110, 165, 219, and 272 kHz which correspond to the radial resonances of the rib and can be approximately calculated as the longi- tudinal resonances of the plate with the free edges? At these frequencies the normal reactions at the plate edges are null and the rib has no influence on the shell. The position of the flexural wave resonances in the stiflened shell spectrum can be compared to that of the A 0 Lamb-type wave resonances of the unstiffened "dry" shell. It can be shown that in the vicinity of the rib radial resonance frequency, flexural wave resonances are generally shifted toward the radial resonance of the stiffener.

B. Monostatic angular diagrams

The monostatic (the emitter-receiver transducer turns around the target) angular diagrams are presented. The diagram in Fig. 5(a) shows the results obtained by measuring the amplitude of the backscattered signal in quasiharmonic regime, 25 /as after the end of the forced excitation at the frequency 200 kHz (kR=21.58) which corresponds to the

1577 J. Acoust. Soc. Am., Vol. 96, No. 3, September 1994 Klauson et al.' Scattering by a cylindrical shell 1577


kR=21.58 f--200 kHz 0.4

,0. O

1BO ' 0'

(a)

0.3

0.2

0.1

-0.1

-0.2

kR=21.59 •200 kHz -0.3 0.6

.......... ; (b)

0.4 'i -0.4

'" ß 0.4

0 ..... ß , 0.3 : .

0.2

-0.2 ....... "....•' .:.' .,...

0.1 -0.4

..-'

.... •' '• 0 -0.6

-0.!

FIG. 5. Monostatic angular diagrams of the resonant part of backscattered pressure. (a) Measured at kR--21.58, (b) calculated at kR=21.59.

-0.2

resonance of the S O wave in an unstiffened shell with six -0.3 wavelengths included in the circumference (n-6). The resonances of this surface wave are known to be insensitive to

the changes in the thickness of the shell and apparently they are not influenced much by the presence of the rib either. The corresponding theoretical pattern at the frequency kR--21.59 in Fig. 5(b) is calculated taking into account the real recording time after the end of the forced excitation. To help inter- pret the results, the contributions of the symmetrical and antisymmetrical forms of vibration are presented, respectively, in Fig. 6(a) and (b). The maxima in Fig. 6(a) correspond to the position of the rib and shell junction in the vibration antinode and the maxima in Fig. 6(b) to position of the junction in the vibration node.

The angular plot in Fig. 7(a) is measured at the same frequency but during the forced excitation and that in Fig. 7(b) is calculated as the total backscattered pressure in the far field. The specularly reflected pulse changes the positions of the maxima and minima in the monostatic pattern so that maximum backscattering occurs when the rib is positioned in the vibration antinode. The agreement of the measured and calculated patterns is very good as, in this case, the pressure can be calculated exactly without removing the nonresonant

FIG. 6. Contributions in the monostatic angular diagram calculated at kR =21.59. (a) Symmetric with respect to the rib vibrations of the shell, (b) antisymmetric with respect to the rib vibrations of the shell.

background and without taking into account the recording time.

The mechanism analogous to that depicted in Figs. 5-7 can be observed at the frequency 165 kHz (kR=17.81) which corresponds to the previous resonance of the wave So (n=5) with five wavelengths included in the circumference of the shell. The measured pattern in Fig. 8(a) and the calculated pattern (166 kHz, kR = 17.90) in Fig. 8(b) are made in the same conditions as in Fig. 5. Ten maxima corresponding to the positions of vibration nodes of the shell in the rib and shell joint can be seen in the circumference.

The monostatic pattern in Fig. 9(a) is measured at the frequency 208 kHz (kR =22.45) corresponding to high resonance peak in Fig. 2(b). It can be seen that at this resonance frequency, which is outside the So wave resonance, the rib



kR=21.58 f=200 id-lz kR=17.81 f=165 kHz

9.0' O 9

180' )o" 180' 1.5

o. O

•J x, (a) -.:" kR=17.9 f=166 kHz

0.t5

. ...:.-. ., ..... (b)

0.5

ß . /." 0.2 0

-0.2

ß

./.

.o., " i: ......... ...... '..'"' .....' -15' ...... ..'" / '-

FIG. 7. Monostatic angular diagrams of the total backscattered pressure at kR--21.58. (a) Measured, (b) calculated.

has an effect in the backscattered field mainly when situated in the "illuminated" part of the shell. Being out of spatial resonance, flexural-type waves can only be transmitted in the surrounding fluid through the rib and shell junction. The lobes of the calculated pattern in Fig. 9(b) are larger than the measured ones. Theoretically the rib is considered to be point attached, its monopolelike contribution tends to be more important than detected experimentally.

From the angular diagrams it can be stated that in the explored frequency band, generally, the contribution due to the rib in the backscattered acoustical pressure is considerable when the rib is in the "illuminated" part of the shell. The major part of the pressure is radiated symmetrically with respect to the vibration of the rib and is monopolelike. The lateral lobes are due to the antisymmetrical vibration with respect to the rib. At the So wave resonance frequencies the contribution of the rib in resonant backscattering is considerable in all directions when the rib is situated in the vibra-

tion nodes. The spatial resonance of the membrane-type wave So provides an uniform distribution of vibration energy over the circumference of the shell. In terms of propagation, membrane-type waves circumnavigating around the shell are weakly attenuated and carry over the stiffener-born sound energy in the shadow zone. The contribution of the antisymmetrical motion of the rib at these resonance frequencies is very important. The influence of the forced vibration consid-

-0.6

FIG. 8. Monostatic angular diagrams of the resonant part of backscattered pressure. (a) Measured at kR = 17.81, (b) calculated at kR--17.90.

erably changes the importance of the different contributions in such a way that maximal total backscattering is observed when the rib is situated in the directions of the vibration

lobes.

C. Excitation by a short pulse

The calculated and measured echoes are presented in Fig. 10(a) and (b), respectively, and they are related to the excitation of the stiflened shell by a short Gaussian pulse of duration equal to 5 /as emitted by a broadband transducer with a central frequency of 500 kHz. This frequency band includes the frequency range where a flexural-type wave in the unstiffened shell is generated. The angle between the direction of the incident wave and the stiffener is Os =65 ø.

The first detected signal is the specularly reflected one marked I. This pulse is not in contact with the rib and it is exactly the same as in case of an unstiffened shell. The eikonals of this pulse, as well as the next pulses, are depicted in Fig. 11. Pulse II is the one reflected from the junction of the shell and the rib and for this reason it is closely related to the position of the joint. Pulse III is the one propagating in the rib and reflected from the free edge of the rib. Its velocity in the rib is that of the membrane-type wave in "dry" plate and its amplitude has not much decreased, compared to the



kR=22.45 f=-208 kHz

90'

180'

(9

• (a)

kR=22.34 f=-207 kHz

0.8

= -: ..... (b) .

....

0.2 •i• ..............

-0.4 •,:'" '--.¾

........ ........... , ............ .............. :. .... -o.6 ..... ':: ..111• .......... .

............ / ........ i ......... • ............. -0.8

FIG. 9. Monostatic angular diagrams of the resonant part of backscattered pressure. (a) Measured at kR =22.45, (b) calculated at kR=22.34.

amplitude of Pulse II because during its propagation in the rib it is not in contact with a fluid. It is not the case for pulse III' which is propagating twice in the rib, its amplitude is considerably smaller. Pulse IV corresponds to the flexural- type wave in the shell. Its position in the echo structures is the same as in the unstiffened shell but its amplitude is slightly different owing to the reradiation at the joint. Pulses II-III' are connected to the rib and the time of their arrival is

changing when the position of the rib with respect to the incident wave changes. The times of arrival of pulses I and IV are not affected by the position of the stringer as they are caused by the main structure. After the arrival of pulse IV the interference of the individual pulses tends to be very important and their sum, after a considerable time after excitation, is practically unpredictable because of the accumulation of little differences. For example, the second measured flexural- type pulse is much bigger than the calculated one which could be explained by the reciprocal shift of two consequent pulses at a few microsecond interval.

IV. CONCLUSIONS

Experimental results correlate well with the theoretical predictions made for the acoustical scattering by the cylindrical lengthwise-reinforced shell. The best agreement is

0.1

-0.1

I II 111 IV

(a)

o 50 lOO 150

•s

(b)

200

FIG. 10. Echo signals from the stiflened shell after short-pulse excitation (angle between the rib and direction of incidence is Os =65 ø. (a) Calculated echo, (b) measured echo.

achieved in the vicinity of the central frequency of the transducer where the excitation of the shell is more efficient. Nev-

ertheless most of the predicted resonances can be found in the measured resonance spectrum as well as the minima corresponding to the radial resonances of the rib.

As for the backscattering at an arbitrary angle between the rib and the excitation, in the explored frequency band, the rib and shell joint radiates generally as a "sparkling point" and its major contribution occurs when the rib is in the "illuminated" part of the shell. Outside the spatial reso-

FIG. 11. Eikonals of the different echo-signal components.



nance this is the only wave generation mechanism which contributes to the scattered pressure field.

The resonances of the So wave are of particular interest as reference marks, because their position in the resonance spectra is relatively stable and is not much affected by the variation of the thickness of the shell. Membrane-type vibrations of the shell are influenced by the rib via transversal reactive forces which are at a maximum when the rib is in

the vibration node. This type of interaction of the rib and shell is also efficient when the rib is situated in the "illumi-

nated" part of the shell or in the shadow region because of the spatial resonance of the shell in the fluid. This statement is also confirmed by results obtained in Ref. 9, where the shadow region of the stiflened shell is mentioned as the com- pressional wave interaction region. In the resonant part of the backscattering, the maxima are obtained when the rib is situated in the vibration node, whereas in total backscattered pressure, taking into account the forced vibration of the shell, the maxima are detected when the rib is in the vibration

antinode.

In short-pulse excitation echoes from the joint of rib and shell can be clearly seen. Their positions in pulse structure are related to the position and the length of the rib. Eventu- ally in the later detection phase the interference of the individual pulses tends to be very important and their sum is practically unpredictable because of the accumulation of little differences.

Additional resonances in acoustical scattering correspond to the flexural-type wave in the stiflened shell. Being latent in the unstiffened shell with the same parameters, these resonances are displayed due to the very efficient excitation

of the shell by the rib. In order to predict the exact position of the flexural wave resonances in a stiflened shell, the vi- brational characteristics of the combined structure consisting of two subsystems (which are the shell and rib) must be determined.

ACKNOWLEDGMENT

This work was done at the University of Le Havre (France) and was supported by a grant of "Minist•re de la Recherche et de l'Espace" (MRE).

I G. Maze and J. Ripoche, "M6thode d'Isolement et d'Identification des R6sonances (MIIR) de cylindres et de tubes soumis h une onde acoustique plane dans l'eau," Rev. Phys. Appl. 18, 319-326 (1983).

2A. G6rard, J. L. Rousselot, J. L. Izbicki, G. Maze, and J. Ripoche, "R6so- nances d'ondes d'interface de coques cylindriques minces immerg6es: d6- termination et interpr6tation," Rev. Phys. Appl. 23, 289-299 (1988).

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4M. Conti and I. Dyer, "The influence of internal structures on bistatic scatter from finite cylindrical shells near axial incidence," J. Acoust. Soc. Am. 94, 1878 (1993).

5A. Klauson and J. Metsaveer, "Sound scattering by a lengthwise reinforced cylindrical shell," Sov. Phys.-Acoust. 35(1), 42-47 (1989).

6A. Klauson and J. Metsaveer, "Sound scattering by a cylindrical shell reinforced by lengthwise ribs and walls," J. Acoust. Soc. Am. 91, 1834- 1843 (1992).

7 N. Veksler, "Intermediate background in problems of sound waves scattering by elastic shells," Acustica 76, 1-9 (1992).

8A. Klauson and J. Metsaveer, "Sound radiation by a submerged axially reinforced shell," European Conference on Underwater Acoustics, edited by M. Weydert (Elsevier Applied Science, London, 1992), pp. 381-384.

9y. p. Guo, "Sound scattering from cylindrical shells with internal elastic plates," J. Acoust. Soc. Am. 94, 1936-1946 (1993).



acoustic scattering by submerged cylindrical shell stiffened by an internal lengthwise rib

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