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Scale tests of a multi-seat airbag
Journal of Somld attd Vibration (1977) 51(1), 117-122
S C A L E TESTS O F A M U L T I - S E A T A I R B A G C. W. STAMMERS
School of Engineerhlg, University of Bath, Bath BA2 7A Y, England (Received 28 September 1976, and ht revisedform 5 November 1976) The natural frequency and damping of symmetrical and asymmetrical modes of a six seat airbag have been measured by using an approximately half-scale model. Pressure relief by venting of air is also examined, and the effect of changes in scale and geometry are discussed. 1. INTRODUCTION The transport helicopter is required to carry freight or passengers. Conventional seating presents a payload penalty and takes up cargo space even when stowed. A proposed solution [1] is to seat occupants on an air bag; this approach offers light-weight seating which can be deflated and stowed in a relatively small volume when not required. Airbags have been employed in a variety of roles: a rescue mat for arresting the fall of occupants jumping from burning buildings, a pneumatic jack to aid the movement of immobilized aircraft, and as a crash protection device for motor vehicle occupants, the bag being inflated explosively on impact. Considerable attention has been paid to this latter application; the only work which appears at all related to seating is that of Nefske [2] who measured the pressure and deflection of a cylindrical bag indented by a rectangular box representing the human torso.
2. THEORY
Given a bag of depth H, supporting a number of indenters of mass M, the effective support area for each is S = Mg]Ap, where/Ip is the gauge pressure, and S' is related to the indenter area SI. If for a collective (heave) mode X is the downward vertical co-ordinate for each mass and the volume V is given by V o / V = f ( X [ H ) = f ( r ) , where Vo is the equilibrium volume and f(0) = 1, the pressure during an oscillation (assuming no venting of air) is p =pof~(r), where Po is the static load pressure and ~ the ratio of specific heats for air. The upward force on each mass is S(p -Pa) - Mg wherepo is atmospheric pressure. The frequency, f2,, of free vertical oscillations satisfies f2] = (I/M) [Sypo f*-a(r) ( d f / d ) f ) + (dS/dX) {Po f ' ( r ) -Pa}],=o-
(1)
A system scaled by a factor of). will have indenter area 22S, and effective support area s= 22S; for the same gauge pressure, and hence the same Po, the mass of each indenter must be ).2M. I f x is the downward co-ordinate for the scaled system,
d f / d X = ). df/dx,
dS/dX = (1[2) ds/dx,
so that the natural frequency to, satisfies I2~ = ).092. The analysis for an asymmetrical mode follows similarly;f (r) is the volume function corresponding to the mode chosen. t17
118
r w. STAMMERS 3. SCALE MODEL
A general view of the model can be seen in Figure 1. The airbag, representing a six sea module when inflated and laden, was 0.85 m in length, 0.25 m deep and 0.65 m in width A plan view of the bag and load is given in Figure 2(a). The mass representing each occupant was bolted on to an indenter representing thq buttocks. The indenter shape was based on that proposed by the Occupant Protectio t Sub-Committee of the SAE (Society of Automotive Engineers): namely (full scale), a 76 mr( deep section of a sphere of radius 245 mm [3]. For ease of manufacture in chipboard, th~ shape used was somewhat different; the scale dimensions are compared in Figure 2(b). Each load was prevented from toppling by means of an " H " sub-frame which carried sleeve through which the load rod passed. (This precluded a study of the rocking ofindividua~ occupants.) A nut at the top of the rod enabled the load to be lifted clear of the bag whe~ the sub-frame was hoisted. The weight of the sub-frame was normally carried by the cross~ member of the main frame (Figure 1) via a bolt pushed through the central column of thl sub-frame. Five valves, three in one side and two in the other, were fitted to provide pressure relie~ when desired. The valves consisted of a spring loaded cap sealing an orifice of diameteI 30 mm. For natural frequency tests the valves were sealed, although leakage of air occurredq both from the valves and from the seams. A compensating supply of air was fed into the bag to provide equilibrium in the static load case. The vertical response of each mass was measured with an accelerometer, fixed by mea~ of a magnetic base to the top of the load rod and its hoist nut. Only two accelerometers wert used at any one time; the output signal was filtered to remove noise, and recorded on~ double-trace storage oscilloscope. The bag did not quite have the dimensions intended; to obtain at least 0.515 m (full scalel per occupant [4] a scale factor of 0.55 was chosen, giving a full scale length of 1.55 m but depth of 0.45 m, rather greater than the value of 0.4 m recommended [4]. However, thI results of modifications to the geometry can be deduced, and are discussed in the concludin~
Figure 1. Scale model test rig.
SCALE
TESTS OF A MULTI-SEAT
I A I \~ ,//
\
X I D \
/ IE~' \
,-
I \
/
C
/
I
310 mm \ /
I
\ /
|
119
AIRBAG
650 mn
/ I \
,~ F I /
< 310 m m >
8 5 0 mm
(o)
i 15 mm
~
36 mm
.-"
m
~
Ib)
Figure 2. (a) Plan of bag and indenters; (b) side view of]ndenter used (solid line) and SAE model (dashed line). Scale factor 0-55. section. The width of the full scale bag (1-18 m) may appear generous but it makes allowance for the volume of a backrest. On the assumption of a full scale height for this of I m [4]--if the head is to be supported also--and a width of 0.1 m, for a base of depth of 0.45 m the backrest volume can be expressed as an increase in width of 0.22 m in the base. The actual width of the bag represented would then be 0.96 m Which, on subtracting 0.1 m for the backrest thickness, gives each row a front to back distance of 0-43 m. It may be objected that the gometry is different in the two cases, and hence the effective support areas may not be the same, but the appreciable increase in volume (23 Yo) needs to be allowed for, albeit crudely. The scaled mass was 17 kg, which corresponds to a 75 kg occupant if 75 ~o of the weight is taken by the seat [3] or a 70 kg occupant if 80 Yo is supported [4].
4. RESULTS The collective or heave mode was excited by dropping the sub-frame and suspended loads on to the bag (the sub-frame was arrested after impact of the indenters so that it did not strike them). The response of mass B (see Figure 2(a) for indenter locations) is shown i n Figure 3(a) for the case of 17 kg masses. Mass E was in phase with B and repeated drops with the accelerometers at other stations confirmed that this was in fact the heave mode. A natural frequency of 5 Hz (full scale 3.7 Hz) is evident. Tests with masses of 14.5 kg and 19 kg (representing occupants of total mass 64 kg and 84 kg, respectively, if only 75 ~o of the weight is carried by the bag) gave a similar result.
120
C. W. STAMMERS I
-0~ .~-
-0.5 I0
I
2
Time (s)
Figure 3. Response of B, 25 mm drop. (a) Valves sealed; (b) with venting.
The tests indicated a damping ratio of between 0.05 and 0.10, except when obvious nai~ alignment of an indenter occurred, the damping ratio being as high as 0.2 in these cases: The deduction was that the bag itself produced a damping of about 5 ~o critical, and thai the remainder was due to friction between the rod and its guide sleeve. Some drops produced a response having an apparent subharmonic content. This wa~ identified as rocking about the axes of symmetry of the bag, the natural frequency of bot[ being about one half that of heave. Rocking is clearly shown in Figure 4 which depicts thl response of masses C and D following a disturbance in which one was depressed and tht other raised. Damping is again between 5 and 10~o critical. No other vertical modes were identified, although six are to be expected (and in practice with rocking of individual occupants admitted, and possibly lateral motion also, a cor~ siderable number more). The alleviation achieved by venting of air can be seen in Figure 3 in which the response o~ B is compared for a 25 mm drop with (a) no venting and (b) all five valves venting. Thl first peak is reduced, but the dominant effect is an increase in damping. Tests were also performed with loads at A, C, D and F only and with loads at B and i only, to simulate the empty seat situation. The natural heave frequencies were found to b~ approximately 4 Hz (full scale 3 Hz) and 5 Hz (full scale 3.7 Hz), respectively. A reductio in natural frequency was expected, but in the case oftwo occupants there was a compensatin effect, presumably due to the appreciable bag indentation the concentrated load produce( Fabric tension would then increase the effective support area.
"K
o
"~= - 0 . 2
0
I
Time (s) Figure 4. Rocking response: C (top) and D (bottom).
SCALE TESTS OF A MULTI-SEAT AlP,BAG
121
5. CONCLUSIONS The predicted frequency of heave oscillations for a module 1.55 m x 1.18 m x 0"45 m (laden) is about 3.7 Hz for loads typical of seated adults, the frequency of asymmetrical motion (rocking) being about one-half of this. Damping due to bag fabric is not more than 5 Yo critical. An idea of the influence of scale can be obtained by varying the scale factor 2. With 2 = 0.5 (making the indenters slightly oversize) a bag 1-7 m x 1-3 m x 0-5 m would have a predicted heave frequency of 3-5 Hz for total masses of between 77 kg and 101 kg (only 75 Yosupported by the seat), while with ). = 0.6 (the indenters slightly undersize) the predicted value for a bag 1.42 m x 1.08 m x 0.42 m is 3.9 Hz for masses between 54 kg and 70 kg. The latter case allows each occupant no more than 0.47 m shoulder width and represents a minimum length for a six seat module. Examination of equation (I) indicates that the natural frequency On depends on depth to the --~ power. Hence reducing depth from 0-45 m to 0.4 m should, on the assumption that the support area S does not change appreciably, increase f2~ by about 6 ~o; the predicted value for a bag 1.55 m x 1.18 m x 0.4 m would then be approximately 3.9 Hz. Tests on a single seat bag [5], 0-4 m • 0.4 m x 0.115 m laden, indicated a natural frequency of about 8 Hz for a 500 N load. If the heave mode for a six seat module is viewed somewhat crudely as six single bags oscillating independently, a bag 1-2 m x 0.8 m x 0.115 m would have a heave frequency of this value (8 Hz). With the height adjusted to 0.4 m, a predicted value of 4.3 Hz is obtained. Since the plan dimensions are smaller than would occur in practice, the value of 4.3 Hz can be offered as an upper bound for heave frequency of a bag of depth 0.4 m if the constraints of the backrest and seat belt are neglected. The effect of these factors needs to be studied since constraints might modify the results considerably. The frequency range to be expected for unconstrained heave is 3.5 Hz to 4 Hz for loads typical of seated adults, which would be undesirable for road vehicle operation, but for a helicopter with n blades the lowest frequency of vertical excitation is n/rev [6], which is not less than 10 Hz for a two bladed helicopter and at least 15 Hz for a typical transport helicopter which has four or more blades. However, the constraints of seat belts and backrest need to be considered before one can be sure that vibration isolation is assured. The asymmetrical mode could be excited by I/rev (3 Hz to 5 Hz) forces in the plane of the rotor; 1/rev velocity levels may in service be of the same order as those at n/rev as the vibration tolerance criterion appears to be a velocity one [7]. Since a frequency of I/rev is closer to the natural frequency of the bag's asymmetrical mode than n/rev is to that of the symmetrical mode, 1/rev vibration may be the more troublesome. As an increase of only 1 Hz in the asymmetrical natural frequency would produce a transmission ratio exceeding unity, the effect of constraints seems a necessary area of study. To summarize, even with the study restricted to vertical oscillations (precluding lateral motion and rocking of individuals) the possibility of undesirable vibration response, particularly at l/rev, cannot be ruled out. For this reason, a study of the effect of vertical constraints is proceeding.
ACKNOWLEDGMENTS The author would like to thank the referee for his helpful comments, Mr P. Davies of Avon Industrial Polymers Limited for his advice on bag construction and Mr J. Butt for his diligence in the design and construction of the rig.
122
c . w . STAblMERS REFERENCES
1. WESTLANDAIRCRAFTLIMITED1973 Patent Application 31477173. 2. D.J. NEFSKE 1972 2nd hlternational Conference on Passice Restraints SAE 720445. A basic airba~ model. 3. L. F. STIKELEATHER1973 National Conlbined Farm, Construction and Industrial d~lachinery an~ Fuels and Lubricants ,~Ieetingx, ~lilwaukee, Wisconsin--September 1973, S,4E 730823. Evaluatin~ the vibration and shock isolation qualities of operator seats for construction machinery. 4. D. C. READER 1975,4irscrew Equipment Group Report No. 365. Helicopter crew seat design. 5. C. W. STAMMERSTO be published, Automotire Engineer. Venting airbags for seat applications. 6. A. GEssow and G. MYERS 1952.4erodynamicx of the Helicopter. New York: Ungar. 7. C. E. P. JACKSONand W. F. GRIStSTER1972 Journal of SouJldand Vibration 20, 343-351. Hurnat aspects of vibration and noise in helicopters.
S C A L E TESTS O F A M U L T I - S E A T A I R B A G C. W. STAMMERS
School of Engineerhlg, University of Bath, Bath BA2 7A Y, England (Received 28 September 1976, and ht revisedform 5 November 1976) The natural frequency and damping of symmetrical and asymmetrical modes of a six seat airbag have been measured by using an approximately half-scale model. Pressure relief by venting of air is also examined, and the effect of changes in scale and geometry are discussed. 1. INTRODUCTION The transport helicopter is required to carry freight or passengers. Conventional seating presents a payload penalty and takes up cargo space even when stowed. A proposed solution [1] is to seat occupants on an air bag; this approach offers light-weight seating which can be deflated and stowed in a relatively small volume when not required. Airbags have been employed in a variety of roles: a rescue mat for arresting the fall of occupants jumping from burning buildings, a pneumatic jack to aid the movement of immobilized aircraft, and as a crash protection device for motor vehicle occupants, the bag being inflated explosively on impact. Considerable attention has been paid to this latter application; the only work which appears at all related to seating is that of Nefske [2] who measured the pressure and deflection of a cylindrical bag indented by a rectangular box representing the human torso.
2. THEORY
Given a bag of depth H, supporting a number of indenters of mass M, the effective support area for each is S = Mg]Ap, where/Ip is the gauge pressure, and S' is related to the indenter area SI. If for a collective (heave) mode X is the downward vertical co-ordinate for each mass and the volume V is given by V o / V = f ( X [ H ) = f ( r ) , where Vo is the equilibrium volume and f(0) = 1, the pressure during an oscillation (assuming no venting of air) is p =pof~(r), where Po is the static load pressure and ~ the ratio of specific heats for air. The upward force on each mass is S(p -Pa) - Mg wherepo is atmospheric pressure. The frequency, f2,, of free vertical oscillations satisfies f2] = (I/M) [Sypo f*-a(r) ( d f / d ) f ) + (dS/dX) {Po f ' ( r ) -Pa}],=o-
(1)
A system scaled by a factor of). will have indenter area 22S, and effective support area s= 22S; for the same gauge pressure, and hence the same Po, the mass of each indenter must be ).2M. I f x is the downward co-ordinate for the scaled system,
d f / d X = ). df/dx,
dS/dX = (1[2) ds/dx,
so that the natural frequency to, satisfies I2~ = ).092. The analysis for an asymmetrical mode follows similarly;f (r) is the volume function corresponding to the mode chosen. t17
118
r w. STAMMERS 3. SCALE MODEL
A general view of the model can be seen in Figure 1. The airbag, representing a six sea module when inflated and laden, was 0.85 m in length, 0.25 m deep and 0.65 m in width A plan view of the bag and load is given in Figure 2(a). The mass representing each occupant was bolted on to an indenter representing thq buttocks. The indenter shape was based on that proposed by the Occupant Protectio t Sub-Committee of the SAE (Society of Automotive Engineers): namely (full scale), a 76 mr( deep section of a sphere of radius 245 mm [3]. For ease of manufacture in chipboard, th~ shape used was somewhat different; the scale dimensions are compared in Figure 2(b). Each load was prevented from toppling by means of an " H " sub-frame which carried sleeve through which the load rod passed. (This precluded a study of the rocking ofindividua~ occupants.) A nut at the top of the rod enabled the load to be lifted clear of the bag whe~ the sub-frame was hoisted. The weight of the sub-frame was normally carried by the cross~ member of the main frame (Figure 1) via a bolt pushed through the central column of thl sub-frame. Five valves, three in one side and two in the other, were fitted to provide pressure relie~ when desired. The valves consisted of a spring loaded cap sealing an orifice of diameteI 30 mm. For natural frequency tests the valves were sealed, although leakage of air occurredq both from the valves and from the seams. A compensating supply of air was fed into the bag to provide equilibrium in the static load case. The vertical response of each mass was measured with an accelerometer, fixed by mea~ of a magnetic base to the top of the load rod and its hoist nut. Only two accelerometers wert used at any one time; the output signal was filtered to remove noise, and recorded on~ double-trace storage oscilloscope. The bag did not quite have the dimensions intended; to obtain at least 0.515 m (full scalel per occupant [4] a scale factor of 0.55 was chosen, giving a full scale length of 1.55 m but depth of 0.45 m, rather greater than the value of 0.4 m recommended [4]. However, thI results of modifications to the geometry can be deduced, and are discussed in the concludin~
Figure 1. Scale model test rig.
SCALE
TESTS OF A MULTI-SEAT
I A I \~ ,//
\
X I D \
/ IE~' \
,-
I \
/
C
/
I
310 mm \ /
I
\ /
|
119
AIRBAG
650 mn
/ I \
,~ F I /
< 310 m m >
8 5 0 mm
(o)
i 15 mm
~
36 mm
.-"
m
~
Ib)
Figure 2. (a) Plan of bag and indenters; (b) side view of]ndenter used (solid line) and SAE model (dashed line). Scale factor 0-55. section. The width of the full scale bag (1-18 m) may appear generous but it makes allowance for the volume of a backrest. On the assumption of a full scale height for this of I m [4]--if the head is to be supported also--and a width of 0.1 m, for a base of depth of 0.45 m the backrest volume can be expressed as an increase in width of 0.22 m in the base. The actual width of the bag represented would then be 0.96 m Which, on subtracting 0.1 m for the backrest thickness, gives each row a front to back distance of 0-43 m. It may be objected that the gometry is different in the two cases, and hence the effective support areas may not be the same, but the appreciable increase in volume (23 Yo) needs to be allowed for, albeit crudely. The scaled mass was 17 kg, which corresponds to a 75 kg occupant if 75 ~o of the weight is taken by the seat [3] or a 70 kg occupant if 80 Yo is supported [4].
4. RESULTS The collective or heave mode was excited by dropping the sub-frame and suspended loads on to the bag (the sub-frame was arrested after impact of the indenters so that it did not strike them). The response of mass B (see Figure 2(a) for indenter locations) is shown i n Figure 3(a) for the case of 17 kg masses. Mass E was in phase with B and repeated drops with the accelerometers at other stations confirmed that this was in fact the heave mode. A natural frequency of 5 Hz (full scale 3.7 Hz) is evident. Tests with masses of 14.5 kg and 19 kg (representing occupants of total mass 64 kg and 84 kg, respectively, if only 75 ~o of the weight is carried by the bag) gave a similar result.
120
C. W. STAMMERS I
-0~ .~-
-0.5 I0
I
2
Time (s)
Figure 3. Response of B, 25 mm drop. (a) Valves sealed; (b) with venting.
The tests indicated a damping ratio of between 0.05 and 0.10, except when obvious nai~ alignment of an indenter occurred, the damping ratio being as high as 0.2 in these cases: The deduction was that the bag itself produced a damping of about 5 ~o critical, and thai the remainder was due to friction between the rod and its guide sleeve. Some drops produced a response having an apparent subharmonic content. This wa~ identified as rocking about the axes of symmetry of the bag, the natural frequency of bot[ being about one half that of heave. Rocking is clearly shown in Figure 4 which depicts thl response of masses C and D following a disturbance in which one was depressed and tht other raised. Damping is again between 5 and 10~o critical. No other vertical modes were identified, although six are to be expected (and in practice with rocking of individual occupants admitted, and possibly lateral motion also, a cor~ siderable number more). The alleviation achieved by venting of air can be seen in Figure 3 in which the response o~ B is compared for a 25 mm drop with (a) no venting and (b) all five valves venting. Thl first peak is reduced, but the dominant effect is an increase in damping. Tests were also performed with loads at A, C, D and F only and with loads at B and i only, to simulate the empty seat situation. The natural heave frequencies were found to b~ approximately 4 Hz (full scale 3 Hz) and 5 Hz (full scale 3.7 Hz), respectively. A reductio in natural frequency was expected, but in the case oftwo occupants there was a compensatin effect, presumably due to the appreciable bag indentation the concentrated load produce( Fabric tension would then increase the effective support area.
"K
o
"~= - 0 . 2
0
I
Time (s) Figure 4. Rocking response: C (top) and D (bottom).
SCALE TESTS OF A MULTI-SEAT AlP,BAG
121
5. CONCLUSIONS The predicted frequency of heave oscillations for a module 1.55 m x 1.18 m x 0"45 m (laden) is about 3.7 Hz for loads typical of seated adults, the frequency of asymmetrical motion (rocking) being about one-half of this. Damping due to bag fabric is not more than 5 Yo critical. An idea of the influence of scale can be obtained by varying the scale factor 2. With 2 = 0.5 (making the indenters slightly oversize) a bag 1-7 m x 1-3 m x 0-5 m would have a predicted heave frequency of 3-5 Hz for total masses of between 77 kg and 101 kg (only 75 Yosupported by the seat), while with ). = 0.6 (the indenters slightly undersize) the predicted value for a bag 1.42 m x 1.08 m x 0.42 m is 3.9 Hz for masses between 54 kg and 70 kg. The latter case allows each occupant no more than 0.47 m shoulder width and represents a minimum length for a six seat module. Examination of equation (I) indicates that the natural frequency On depends on depth to the --~ power. Hence reducing depth from 0-45 m to 0.4 m should, on the assumption that the support area S does not change appreciably, increase f2~ by about 6 ~o; the predicted value for a bag 1.55 m x 1.18 m x 0.4 m would then be approximately 3.9 Hz. Tests on a single seat bag [5], 0-4 m • 0.4 m x 0.115 m laden, indicated a natural frequency of about 8 Hz for a 500 N load. If the heave mode for a six seat module is viewed somewhat crudely as six single bags oscillating independently, a bag 1-2 m x 0.8 m x 0.115 m would have a heave frequency of this value (8 Hz). With the height adjusted to 0.4 m, a predicted value of 4.3 Hz is obtained. Since the plan dimensions are smaller than would occur in practice, the value of 4.3 Hz can be offered as an upper bound for heave frequency of a bag of depth 0.4 m if the constraints of the backrest and seat belt are neglected. The effect of these factors needs to be studied since constraints might modify the results considerably. The frequency range to be expected for unconstrained heave is 3.5 Hz to 4 Hz for loads typical of seated adults, which would be undesirable for road vehicle operation, but for a helicopter with n blades the lowest frequency of vertical excitation is n/rev [6], which is not less than 10 Hz for a two bladed helicopter and at least 15 Hz for a typical transport helicopter which has four or more blades. However, the constraints of seat belts and backrest need to be considered before one can be sure that vibration isolation is assured. The asymmetrical mode could be excited by I/rev (3 Hz to 5 Hz) forces in the plane of the rotor; 1/rev velocity levels may in service be of the same order as those at n/rev as the vibration tolerance criterion appears to be a velocity one [7]. Since a frequency of I/rev is closer to the natural frequency of the bag's asymmetrical mode than n/rev is to that of the symmetrical mode, 1/rev vibration may be the more troublesome. As an increase of only 1 Hz in the asymmetrical natural frequency would produce a transmission ratio exceeding unity, the effect of constraints seems a necessary area of study. To summarize, even with the study restricted to vertical oscillations (precluding lateral motion and rocking of individuals) the possibility of undesirable vibration response, particularly at l/rev, cannot be ruled out. For this reason, a study of the effect of vertical constraints is proceeding.
ACKNOWLEDGMENTS The author would like to thank the referee for his helpful comments, Mr P. Davies of Avon Industrial Polymers Limited for his advice on bag construction and Mr J. Butt for his diligence in the design and construction of the rig.
122
c . w . STAblMERS REFERENCES
1. WESTLANDAIRCRAFTLIMITED1973 Patent Application 31477173. 2. D.J. NEFSKE 1972 2nd hlternational Conference on Passice Restraints SAE 720445. A basic airba~ model. 3. L. F. STIKELEATHER1973 National Conlbined Farm, Construction and Industrial d~lachinery an~ Fuels and Lubricants ,~Ieetingx, ~lilwaukee, Wisconsin--September 1973, S,4E 730823. Evaluatin~ the vibration and shock isolation qualities of operator seats for construction machinery. 4. D. C. READER 1975,4irscrew Equipment Group Report No. 365. Helicopter crew seat design. 5. C. W. STAMMERSTO be published, Automotire Engineer. Venting airbags for seat applications. 6. A. GEssow and G. MYERS 1952.4erodynamicx of the Helicopter. New York: Ungar. 7. C. E. P. JACKSONand W. F. GRIStSTER1972 Journal of SouJldand Vibration 20, 343-351. Hurnat aspects of vibration and noise in helicopters.