Analytical and experimental evaluations of space shuttle TPS tile vibration response

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  • Journal of Sound and Vibration (1982) 83(1), 37-51




    Boh Beranek and Newman Inc., Canoga Park, California 91303, U.S.A.

    (Received 8 June 1981, and in revised form 10 October 1981)

    Analytical studies and laboratory experiments have been performed to evaluate the vibration response of the Space Shuttle Thermal Protection System (TPS) tiles due to the intense rocket generated acoustic noise during lift-off. The TPS tiles are mounted over the exterior of the Space Shuttle orbiter structure through Strain Isolation Pads (SIP) which protect the tiles from thermal induced shear loads at their interface. The analytical predictions indicate that the response of a typical tile is governed by the structural vibration inputs through the SIP under the tile at frequencies below 250 Hz, and by the direct acoustic excitation over the exterior surface of the tile at frequencies above 250 Hz. An evaluation of the laboratory test data for this same tile, in which conditioned (partial) coherent output spectral analysis procedures were used, leads to exactly the same.conclusion. The results demonstrate the power of conditioned spectral analysis procedures in identifying vibration response mechanisms when two or more of the inputs are highly correlated.


    The Space Shuttle orbiter vehicle is protected from the heat of re-entry by a Thermal Protection System (TPS) consisting of a collection of small tiles attached through an interface material to the exterior of the aluminum skin, The TPS tiles, which are fabricated from a silica material, have spectacular thermodynamic properties, but are physically fragile and must be protected from the shear loads that would arise if they were directly attached to the aluminum skin because of the widely different coefficients of thermal expansion of the tile and skin materials, This alleviation of shear loads is accomplished by a Strain Isolation Pad (SIP) as illustrated in Figure I, The shear and extensional moduli of the SIP material are very low relative to the tile material, Figure 2 shows the non-linear behavior of the SIP in tension and compression, Various experiments have been performed on sample TPS tiles mounted through the SIP to simulated skin structure with both acoustic excitation in a traveling wave acoustic facility and aerodynamic boundary layer excitation in a wind tunnel, This paper is concerned with an evaluation of the results from acoustic tests in which the dynamic loads on the tiles due to rocket noise excitation during lift-off were simulated, Of specific interest is the mechanism causing the tile response: i,e,, is the tile motion caused by a resonant response to the panel vibration under the tile or by a direct response to the acoustic pressures over the exterior surface of the tile? To answer this question, the response of a selected tile is first predicted by using an analytical model with experimentally measured input para- meters, The experimental data are then evaluated by using (conditioned) coherent output spectral analysis procedures, for comparison with the analytical results,

    37 0022--460X/82/130037.+ 15502.00/0 O 1982 Academic Press Inc. (London) Limited

  • 38 A. G . PIERSOL AND L. D . POPE

    ~ ~Adjocent tiles

    Propagating ~ / ~ ~ ~.v.~ AdJacent tiles

    ~ ~ Adjacent tiles

    VlV x


    Tile ~ , , / - - Tile occelerometer 9 -- -T- ~ / ~ Tile density = y 0"0,57 m , /m 3 144 kg

    4 mm 1 ~ , - ~ |

    Panel "~' ~ Panel ~ Strain Isolation accelerometer Pod (SIP)

    z Figure 1. Experimental set-up for tile vibro-acoustic tests.

    105 I i

    5 X 104 L

    A g- o v


    -5 x 10 4

    -105-0~4 -1~-2 O l:

    i i / 0~2 0"14 0"5

    Figure 2. Typical stress--strain relationship for strain isolation pad (SIP).


    The experiment (referred to as the Peelable SIP Test) was designed by personnel of the Rockwell International Space Systems Division in Downey, California, and carried out by personnel in the Rockwell International B-1 Division in Los Angeles, California. The basic data reduction to auto- and cross-spectral density estimates was also performed by the Rockwell International B-1 Division.


    A total of 20 TPS tiles were mounted on a ribbed aluminum panel simulating a typical orbiter skin section. The tiles and the panel were instrumented at various locations with accelerometers. The entire assembly was placed in a traveling wave acoustic test facility and microphones were located over selected tiles. The data of interest here are from a single tile representing a typical installation, as shown in Figure 1. The tile had a density of 144.2 kg/m 3 (9 lb/ft 3) and was attached to the panel through a layer of SIP material


    with a thickness of 4.06 mm (0.160 in). The tile side of the panel assembly was exposed to a propagating acoustic wave with grazing incidence to the tile surface, simulating the rocket noise during lift-off.

    2.2. DATA ANALYSIS PROCEDURES The basic data analysis was accomplished by using a GenRad two channel FFT signal

    processor. Auto- and cross-spectral density functions were computed by conventional FFT procedures [1]. Specifically, given two time history signals, a (t) and p (t), representing acceleration and acoustic data, the one-sided auto- and cross-spectra (defined for f>~ 0) were estimated with

    2 -d 2 G~ =-----j,~l la'(f)l~' OP(f) = n---~,=l ~ IP'(f)l~'

    2 nd G~p(jO = ~aT ,~1 a* (JOP,(~, (1)

    where the asterisk (*) denotes the complex conjugate, T is the length of individual records, and na is the number of disjoint (statistically independent) records used in the averaging operation. The Fourier transforms of the individual records in equation (1) are given by

    T I , T

    a,(]') = Io ai(t) e -i2~'f' dt, Pi(j0 = Jo pi(t) e -i2"*f' dt. (2)

    The coherence function between two signals a (t) and p(t) was estimated with

    -- ( f)6p(f)-- I ao.(f)l=/ o (f)Gp(f), (3) where the spectral density estimates are as defined in equation (1). The individual record lengths for the analysis were T = 0.5 s giving a basic frequency resolution of f = 2 Hz in the spectral estimates. However, the spectral results were frequency averaged over 10 contiguous components to provide a final resolution of Be = 20 Hz in the results. The equivalent number of disjoint averages was na = 1800. This means that the random error (coefficient of variation) is e =0.024 in the auto-spectra estimates and e = 0.024/1~,(f)1 in the cross-spectra magnitude estimates [1]. The random error in the coherence estimates is given by e = 0.03311 -

    i05 I I I I I I I I I __-_

    N " l -


    '0 4

    10 3


    i0 2 0 lO0 200 300 400 500 600 "tO0 800 900 I000

    Frequency (Hz)

    F igure 3. Auto -spect rum of acoust ic p ressure immediate ly above ti le. Be = 20 Hz , na -- 1800 averages .

  • 40 A. G. P IERSOL AND L. D. POPE

    2.3. EXCITATION AND RESPONSE SPECTRA The auto-spectrum of the acoustic excitation applied to the tile is shown in Figure 3.

    The auto-spectra of the acceleration response levels of the panel and tile are shown in Figure 4. Note that the response spectral levels of the panel and tile are similar at

    A N I0


    g - - I -0 o


    0 -1

    I I I I I I I I


    E I I I I I I I I I J0O. 20o 30o 400 .500 600 too 8oo 9oo fO00

    Frequency (Hz)

    Figure 4. Vibration response of panel and tile due to acoustic excitation. Be = 20 Hz, na = 1800 averages. , Tile; - - - , panel.

    frequencies below 300 Hz, suggesting that the tile rides on the panel as a fixed rigid body at these lower frequencies. Above 300 Hz, however, the panel and tile response levels are qu!te different. It is known that the first resonance frequency of the tile body is well above 100 Hz. Hence, the difference in the panel and tile response between 300 and 1000 Hz must involve strain in the SIP material. The issue of interest is as follows: how much of the tile response below 1000 Hz is due to the mechanical excitation from the panel through the SIP material and how much is due to the direct acoustic excitation on the exterior surface of the tile?


    For the basic tile response model that is developed here it is assumed that the tile is driven by a fluctuating pressure over its exterior surface and a fluctuating panel motion from below, the panel itself responding to the excitation fluctuating pressure. The excitation pressure is due to an acoustic field passing diagonally across the tile as shown in Figure 1. The static pressure is allowed to increase across the tile to simulate a pressure gradient. At the leading edge, the static pressure is taken to be pl and at the trailing edge p2. The pressure beneath the tile can range between pl and P2. This pressure appears in the void of the SIP which has 90% porosity. Thus the model allows for a net "lift" on the tile. In the case of no pressure gradient, pl = pz and there is no net lift.


    If the static pressure is not uniform over the tile, since the SIP has a non-linear stress-strain curve, each elemental area of the SIP has a different stiffness due to the rotation imposed on the tile. To account for this effect, the tile is considered to rest on a number of different springs, each located a distance yi away from the x axis, which is defined to be perpendicular to the direction of propagation of the acoustic wave. For simplicity in the present case, only two degrees of freedom are considered: namely, (1) vertical translation, and (2) rocking about the transverse (x) axis. The tile itself is considered rigid and broken down into N elements. Each ith element has area At. Acting


    on top of each tile element is a force F~ given by

    F~ (pi -i i = +p )Ai =p Ai, (4)

    where pi is the static pressure on top of the ith element (pl> l, where l is the maximum dimension across the tile. Thus,

    Ft -- SAt tan {( zr/ 2L )(zt - zp)}. (11)

    Since all elements A~ are the same, say A, and since the tile is assumed rigid, the equations of motion become

    N 77" N m .. -S ~, tan-~-s ~, (pt--p~b)=-7-Z, (12)

    iffil i=l Y-t

    7r - -Zp) y i+ 1 1 -S ~ tan~(z+yt0 ~ (pi-pib)yi=--~O. (13) i=1

    Suppose now that the equilibrium position for an assumed static pressure distribution is desired. Then k" = 0" = 0, and with Zp = 0, pi = pJ, and p/b = P~, it follows that

    N 7r N ~[ ~. ] N S E tan~--~(z+y,0)= F. (Pi-Pib), S tan~-~(z+y,O) yt = E (Pi--Pib)Yi.

    i=1 iffil iffil t=l (14, 15)

    The solutions of equations (14) and (15) are z =Zo and 0 = 0o.

  • 42 A .G . P IERSOL AND L. D. POPE

    One can now reconsider equations (12) and (13). Let z = Zo+5 and 0 = 0o+ 0. Also pt=pJ+pi andp~ i -i =Pb +pb. Then equation (12) becomes (upon noting that 3o = 0)

    DI .. -S ~ tan ~-~ (Zo+2+y, Oo+y,O-zp)+~. (Pi -P/b) +X (P i -P~) =XS.

    " i i

    But since by equation (14)


    Z (P i -P~) = rr S ~ tan m (Zo + y~Oo), t 2L

    it follows that equation (16) reduces to

    , [ 2L 2L (z~176 -S~ tan--(zo+y~Oo+5+y~O-zp)-tan~Tr - 7r (P-i-Pb)=-~z m ._.

    Upon using the identity

    tan x - tan y = tan (x -y ) [1 +tan x tan y],

    this becomes




    ~- - [ ~r - ~- ] - S ~ tan ~zz. (2 + y~O - z~) 1 + tan ~ (Zo + Ydo + 5 + y~O - z~) tan ~ (Zo + y~Oo)

    +Z (P~-P~,) m .. =~-2.

    ] (20)

    Now one can let 5, O, and zp represent small oscillations such that tan{(~r/2L) (2 + y f i - zp)} = (~/2L)(5 + y i0 - zp). Then equation (20) reduces to

    m._. }] " Xz+~-s ~--s Oo) (~+yd-z~)= Z (P~-P~).

    i~ l I= l (21)

    Similarly, the moment equation becomes

    -~O+-~ Lfxy, sec 2 ~-~(zo+y, Oo) (2+yf i -zp)= Y. (/~i-P~)Yi. (22) /= l

    It is convenient to define ki = (Sz'/2L) sec2{(~r/2L)(zo+ yi0o)}. Then, in matrix notation, the dynamic equations reduce to


    The fluctuating pressure on the underside of the tile ff~, could be due to the presence of a contained volume of air in the SIP (acting as an airspring) in which case, one might model it as p~ = kcA V = k,.A(z - zp), where ft, = NA, kc = pc2~ V, p is the density of air in the contained volume, c is the speed of sound in the air, and V is the enclosed air volume in the SIP in some deformed state. Here, however, it is assumed that ,O~ is much less then pi, and thus can be neglected. Then, with the definitions

    m/A = Mz, I /A = Mo, ~ ki = k11, ~ kiy~ = k12 = k2b Z kiy~ = k22,


    equation (23) becomes


    The resonance frequencies are given by

    Mzk22+Mok,1+l M~k22+Mokll 2 1/'~11 22-- '2~1 (27rf)'= ~ ~[( ~ !) -4 " " k k2"" /2 ~ M---~ )J '

    where/ '=fa and f2, with f~

  • 44 A .G . P IERSOL AND L. D. POPE

    Zpr (13 are Fourier transforms of the fluctuating (random) pressure and panel displacement observed over time T, and E denotes the expected value of the quantity in the brackets, determined in practice by an ensemble average over independent records of ar(]') as detailed in equation (1). Also

    N(0I )2 + N(0~)2 [ (0'.)2kH + 010~k,2 (0~)2k,, + 0~020k,2]

    g,(D Yl(f) Y2(13' g2(D = t ~'~-~ q -~2(~ .!" (32)

    Then ar(D=(27r13~gl(13pr(D+g2(13C~r(13, where ar(13=(2~rD2zpT(D is the Fourier transform of the acceleration of the panel below the tile. This gives

    G.(D = (2~r1341gl]2Gp(13+lg2]2G~(D+(2~r132[g,g*G~p(D+g~g2G*p(D], (33)

    where G~(f) is the spectral density of the pressure on top of the tile, G,,(D is the spectral density of the acceleration of the panel below the tile, and G,~p(D is the cross-spectral density of the exciting pressure on top of the tile and the panel acceleration below the tile.

    With 3~p(D the coherence function for the exciting pressure and the panel acceleration, and q~,,p the associated phase, then

    Go~ (1314G (I3 O~ (13 = ,/-~r~. (D e-J~~ Therefore

    Ga(D = (27rD41gd2G,(D+lg21~O.(13+(2~rD2O~.(13[g,g * +g'g2 ei2~ (34)

    Now, to obtain preliminary estimates of the tile response, the cross terms in equation (34) can be ignored, and this simplified prediction model gives

    G~ (D = (27rf)4lg,12G, (13 + Ig 12 o,, (13. (35) By using equation (35), the tile acceleration spectral density can be estimated from a

    measured pressure spectral density above the tile and a measured 15anel acceleration spectral density below the tile. Except in rare circumstances, one or another of the two terms on the right-hand side of equation (35) will dominate and yield the estimate for the left-hand side. Of course G~(13, the panel acceleration spectral density, is ultimately dependent on Gp(13 and this dependence must be considered in a final prediction of the tile response.

    3.3. DETERMINAT ION OF DOMINANT SOURCE The tile acceleration spectral density level in dB re 1 g can be defined as

    ALr = 10 log [G~(13/g2]. (36)

    Similarly the panel acceleration spectral density level in dB re 1 g can be defined by

    ALp = 10 log [O.(13/g2], (37)

    and the excitation pressure spectral density level in dB re 20/zPa by

    SPL = 10 log [Gp(DIp...


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