Coupling Vibration between Wind-Induced Internal Pressure ... · a single-degree-of-freedom roof dynamic system. Three factors, approaching wind velocities at the center of the dominant

KSCE Journal of Civil Engineering (2019) 23(9):4075-4084

Copyright ⓒ 2019 Korean Society of Civil Engineers

DOI 10.1007/s12205-019-2333-y pISSN 1226-7988, eISSN 1976-3808

www.springer.com/12205

Structural Engineering

TECHNICAL NOTE

Coupling Vibration between Wind-Induced Internal Pressure and a Flexible

Roof for Buildings with a Dominant Opening and Background Leakage

Xianfeng Yu*, Zhuangning Xie**, and Ming Gu***

Received December 9, 2018/Revised 1st: March 26, 2019, 2nd: May 27, 2019/Accepted July 10, 2019/Published Online August 6, 2019

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Abstract

After considering the combination of internal pressure and external pressure acting on the roof, the coupling dynamic equations to describe the relationship between wind-induced internal pressure and flexible roof are reviewed and further refined. The internal pressure responses and the first order modal response of a flexible roof can be evaluated by the coupling equations. Wind tunnel test was carried out on an aeroelastic roof model which was treated as a single-degree-of-freedom system. Three factors, approaching wind velocities at the center of the dominant opening, acceleration responses at dominant opening areas and background leakages, which have effects on roof acceleration responses were studied. On this basis, the effectiveness and calculation precision of the coupling equations were verified. Results show that the root-mean-square (RMS) value of roof acceleration increases with the increase of the approaching wind velocity and dominant opening area, and in background leakage decreases. Meanwhile, theoretical calculation values of RMS internal pressure and RMS acceleration response corresponding to the first order modal of flexible roof agree well with the wind tunnel experimental data.

Keywords: internal pressure, flexible roof, coupling vibration, wind tunnel experiment, dominant opening, background leakage

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1. Introduction

In severe windstorms, larger wind pressures and/or wind-borne

debris often result in sudden failures of doors or windows and

create openings in components & claddings of buildings (Moghim

et al., 2015). In the case of laminar flow, the sudden openings

created by wind drive airflow into the buildings within a short

period of time, consequently producing a transient initial internal

pressure that is typically higher than the external pressure at the

openings. The air-slug of internal pressure can attenuate vibrations

in the vicinity of these openings. Pressure balance is usually

achieved as soon as the internal pressure increases to balance the

external pressure. However, due to the turbulent nature of

approaching flow, the transient response to overshooting of

internal pressure induced by the sudden openings was not as high

as the subsequent steady-state peak fluctuations (Stathopoulos

and Luchian, 1989). Actually, the response of steady-state internal

pressure can be estimated by the Helmholtz resonator model.

And there will be a potential to excite resonant dynamic response

for internal pressure or even for flexible roof if the power energy

produced by external pressure at Helmholtz frequency is high

enough, leading to potential safety hazards.

The wind-induced internal pressure of rigid single-cell building

with a windward dominant opening has been widely studied and

the corresponding governing equation has been developed in the

past to estimate the internal pressure response. (Holmes, 1979;

Vickery and Bloxham, 1992; Sharma and Richards, 1997a).

More recently, the governing equation was improved and verified

by wind tunnel experiments when the background leakage was

considered (Guha et al., 2011a; Yu et al., 2008). However, in the

case of a building with flexible walls or roofs, the internal

volume of the building could be altered after the failure of

windows or doors, which affects the internal pressure to some

extent. For long-span or short-span lightweight industrial buildings,

the roofs are often much more flexible as compare with exterior

walls. For this reason, this study is concerned primarily with

flexible roof systems.

Assuming that the structure responds in a quasi-static manner

(i.e., the deformation of structure is in direct proportion to the

applied load), an equivalent volume method was adopted by

Vickery (1986) to simulate the influence of internal pressure

response as a result of structure flexibility and to improve the

governing equations of internal pressure.

For large span flexible roof systems, Novak and Kassem

*Lecturer, State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China (E-mail:

[email protected])

**Professor, State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China (E-mail:

[email protected])

***Professor, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China (Corresponding Author, E-mail:

[email protected])

− 4075 −

Xianfeng Yu, Zhuangning Xie, and Ming Gu

(1990) and Vickery and Georgiou (1991) regarded the internal

pressure and the roofs as linear systems, and utilized a simple

two degree-of-freedom model to describe the interaction between

flexible roofs and internal pressures. Novak and Kassem (1990)

validated their theoretical model in predicting resonance frequencies

and the damping ratios via scaled model experimental tests in still

air. Vickery and Georgiou (1991) showed that for large span

lightweight roof structures, the “added mass” was important in

the resultant response.

Sharma and Richards (1997b) conducted a study on low-rise

residential buildings and light industrial structures with flexible

roofs and evaluated the response of a flexible building to the

variation of internal pressure. If the structural frequency of a

building component (e.g., roof or wall) is much higher than the

Helmholtz frequency, the structure will respond in quasi-static

manner under the action of internal pressure. The structural

deflection is assumed to be in a linear relationship with the

loading. When a structure component (such as roof) responds in

a dynamic manner, it can be assumed as a single degree-of-

freedom system under the action of internal pressure. Unlike the

previous studies (Novak and Kassem, 1990; Vickery and Georgiou,

1991), Sharma and Richards (1997b) stated that the internal

pressure system was nonlinear and “the added mass” was

unimportant. However, the influence of roof external pressure

was not taken into account.

Sharma (2008) further developed a general governing equation

of internal pressure in any flexible buildings. The internal pressure

response equation was derived from the general governing

equation when the roof structure responded to the internal

pressure in a quasi-static manner and roof external pressure, but

it failed to take the influence of background leakage into account.

Following the work conducted by Sharma (2008), Guha et al.

(2011b, 2013) derived the governing equation of internal pressure in

a quasi-static flexible and leaky building. However, only the

impact of internal pressure was considered in establishing of the

motion equation of the flexible roof.

In this study, coupling equations governing internal pressure

response and dynamics response corresponding to the first order

modal of flexible roof are firstly reviewed and refined. Then the

simplified aeroelastic model wind tunnel test was carried out on

a single-degree-of-freedom roof dynamic system. Three factors,

approaching wind velocities at the center of the dominant

opening, dominant opening areas and background leakages,

which have effects on roof acceleration responses were investigated.

Finally, wind tunnel experiments results were used to evaluate

the effectiveness and calculation precision of the governing

equations.

2. Review of the Governing Equations

For a leaky building structure with a windward dominant

opening and flexible roof, it could be simplified to an approximate

linear dynamic model system by Guha et al. (2011b, 2013), as

shown in Fig. 1. The height of roof is H and the internal volume

is . CPW, CPL and CPi are the transient pressure coefficients at

windward wall opening, at the leeward wall lumped leakage

opening, and into the building, respectively. mr, Ar, kr, ζr and xr are

the mass, area, stiffness, damping ratio and displacement of the

roof, respectively. A0 and AL are the areas of windward wall

opening and lumped leakage opening, respectively. c is discharge

coefficient. Le is the effective length of the air slug. CL and

are energy loss coefficients of flow representing the energy

losses through the windward wall opening and lumped leakage

opening, respectively.

Furthermore, Guha et al. (2011b, 2013) derived coupling

equations governing internal pressure response and dynamics

response corresponding to the first order modal of flexible roof:

(1)

(2)

where

is the non-dimensional volume, is the natural

circular frequency of the roof. However, only the impact of

internal pressure was considered in establishing of the motion

equation of the flexible roof, which disaccord with the actual

situation.

Actually, flexible roof will vibrate under the combined action

of internal and external pressures (Sharma, 2008), so the differential

Eq. (2) should be written as follows:

(3)

where CPr is the area-average transient external pressure

coefficient of the roof.

0∀

CL′

( )

0 0 0

0

2

0

2

0 0

0 0

( )

2

2

2

ρ ρ ρυ υ

γ γ

γρ γυ

ργ

γ γυ

ρ

∀ ∀ ∀+ + +

′ −

⎛ ⎞−∀⎜ ⎟+ + + ⋅⎜ ⎟′∀⎝ ⎠

−+ + = −

′∀

�

��

� ��

�

�

�

�

a e a e e Pi a eL

Pi Pi

a o a o o oL Pi PL

L a Pi PLL a a

Pi

a La o

L a Pi PL a

Pi PW Pi

a L

L L L C LAC C

P cA P cA cA qcAU C C C

A P C CC q PC

qU CP cA

A P C C PC C C

qU C

2

2r

r r r

r 0

( 1) 2Pi

qAC

mυ ω υ ς ω υ= − − −

∀

��

r r r

0 r

( )1

+∀= = = +∀

A x H x

A H Hυ

r r r/= k mω

( )2

2r

Pr r r r

r 0

( 1) 2= − − − −∀

��

Pi

qAC C

mυ ω υ ς ω υ

Fig. 1. Building with Flexible Roof and Background Leakage

− 4076 − KSCE Journal of Civil Engineering

Coupling Vibration between Wind-Induced Internal Pressure and a Flexible Roof for Buildings with a Dominant Opening and Background Leakage

3. Wind Tunnel Experiment on Aeroelastic Model

3.1 Experimental Setup

The wind tunnel test model was made to simulate a low-rise

building with rectangular flat roof, as shown in Fig. 2(a). The

model was 800 mm long, 400 mm wide, and 200 mm high,

whose rigid walls were made of 5 mm thick plexiglass plate,

with elastic connection between the roof and rigid walls. The

influence of Reynolds number is neglected due to the planar-roof

structure with obvious edges in shape.

To correctly simulate the fluctuating internal pressure, as well

as to accurately obtain the Helmholtz resonance frequency, the

scaling (Holmes, 1979) requires that:

(4)

where L is the characteristic length, UH is the wind velocity at the

height of eave, is the internal volume, and the subscript m and

f stand for model and full-scale structures, respectively. To meet

the requirement of similarity, an additional volume-compensation

container of 800 mm × 400 mm × 1,200 mm was provided under

the model. A circular baffle with diameter of 2.4 m was placed

between the test model and compensation container and fixed to

a designed steel frame, to prevent the interference effect of

compensation container on flow field of the experimental model,

as shown in Fig. 2(b).

Roof was built by a 2 mm-thick aluminum alloy sheet with

great stiffness and its plane dimension was 700 mm × 300 mm. It

was fixed on a peripheral steel frame by 6 or 4 steel wires about

each 3 mm in diameter, which represented two different roof

stiffness (K1 or K2), respectively. Besides, 50 mm seam was set

around the roof and sealed with double-layer cling film, to make

sure that the roof can vibrate freely in vertical direction without

any leakage. Finally, the peripheral rigid frame was installed on

the plexiglass walls. The simplified model is shown in Fig. 3(a),

in which the micro-adjusting system consisted of screws, nuts

and steel sheet can adjust the steel wire to achieve uniform force.

Four piezoelectric accelerometers produced by piezotronics

incorporated company of USA were used to measure the acceleration

response of the roof. Arrangement of the four accelerometers is

presented in Fig. 3(b). Each accelerometer is about 5 g, which is

far lighter than the roof mass of 1.06 kg. Thus the mass of

acceleration sensor is negligible.

Ginger et al. (1997) pointed out the leakage of a typical

nominally sealed, engineered building envelope (defined as the

ratio of the effective leakage area to the building surface area)

ranged from 10−4 to 10−3. In current study, the surface area of the

building model is 800,000 mm2, so the maximum background

leakage area is 800 mm2 according to Ginger’s suggestion. The

background leakage was simulated by 112 small holes of 3 mm

in diameter, and all of them were uniformly arranged in the

leeward wall, as presented in Fig. 4. In wind tunnel test, different

proportions of small holes were blocked to simulate different

leakage levels.

To obtain the external pressure at the windward dominant

opening, the external pressure distribution of the roof and the

external pressure at the leeward wall, an additional rigid building

model with the same scale as the aeroelastic building model was

3

0, 0, 2

, ,

( / )

( / )∀ = ∀

m f

m f

H m H f

L L

U U

0∀

Fig. 2. Schematic Diagram of Wind Tunnel Test Model and Com-

pensation Empty Container: (a) Wind Tunnel Test Model,

(b) Volume Compensation Empty Container

Fig. 3. Simplified Flat Roof Model and Acceleration Sensor

Arrangement: (a) Simplified Flat Roof Model, (b) Acceleration

Sensor Arrangement

Vol. 23, No. 9 / September 2019 − 4077 −


designed and tested at the reference wind speed of 7.6 m/s, 8.4

m/s and 9.5 m/s before the aeroelastic wind tunnel tests. 45 taps

were arranged on the surface of the roof, 41 taps at the opening

region of windward wall, and 9 taps on the leeward wall, as also

shown in Fig. 4. Besides, 5 internal pressure taps were installed

inside the building model during aeroelastic wind tunnel test.

The wind tunnel tests was performed in the efflux section of

TJ-1 boundary layer wind tunnel laboratory located at Tongji

University, China (see Fig. 5). The exit of the contraction section

is a round one with a diameter of 2.4 m and the maximum wind

speed available is about 20 m/s (Gu et al., 2005). Fig. 6 shows

the variation of mean speeds at the center of exit section, in

which a strong linear relationship is indicated between them.

Fig. 7 presents the distribution of the mean wind speed at the

section I which is 1.0 meter away from the exit section. Wind

Fig. 4. Layout Diagram of Wind Pressure Taps and Background

Leakage (unit: mm) (Note: In the figure, the hollow circles

represent external pressure taps, solid circles represent

the internal pressure taps, and small solid circles represent

background leakages.)

Fig. 5. Photo of Aeroelastic Model Wind Tunnel Test

Fig. 6. Variation of Mean Speeds at the Center of Exit Section

with the Mean Inflow Speeds

Fig. 7. Distribution of the Mean Wind Speed at Section I (unit: m/s)

Table 1. Test Conditions of Simplified Aeroelastic Flat Roof

CasesRoof

stiffnessOpening area(mm × mm)

Wind speed at the opening

(m/s)

Total leakage area AL (mm2)

1

K = K1

A1 = 0

7.6 0

2 8.4 0

3 9.5 0

4 10.2 0

5

A2 = 30 × 30

6.6 0

6 7.6 0

7 8.4 0

8 9.5 0

9

A3 = 60 × 60

6.6 0

10 7.6 0

11 8.4 0

12

8.4

198.07

13 395.64

14 593.46

15 791.28

16 A4 = 100 × 100 7.6 0

17

K = K2 A3 = 60 × 60

6.6 0

18 7.1 0

19 7.6 0

20 8.0 0



tunnel experiments were conducted at five different wind speeds,

when the wind speed at the dominant opening reached 9.5 m/s,

the corresponding turbulence intensity was 8.5%. The sample

frequency of acceleration sensor is 1,000 Hz and the sampling

time is 60 second, so the total sampling data on each tap is

60,000. Wind tunnel test cases are shown in Table 1.

3.2 Parameter Analyses on Roof Acceleration Response

3.2.1 Wind Speed at the Center of Opening

When the roof stiffness are K = K1 and K = K2 and background

leakage is 0, the variation of RMS (root-mean-square) roof

acceleration with the wind speed at the center of opening is

presented in Fig. 8. It can be seen that the RMS value of the roof

acceleration increases as the wind speed at the center of the

opening of different opening areas increases.

3.2.2 Windward Dominant Opening Area

When the roof stiffness is K = K1, the wind speed at the centre

of opening is 7.6 m/s and background leakage is 0, the variation

of RMS roof acceleration with windward dominant opening area

is plotted in Fig 9. It indicates that the RMS roof acceleration

also increases with the increase of windward dominant opening

area.

3.2.3 Background Leakage

When the roof stiffness is K = K1, windward opening dimension is

Fig. 8. RMS Roof Acceleration Varies with Wind Speed at the Center of Opening: (a) Nominally Sealed, K = K1 (b) Opening 30 mm × 30 mm,

K = K1, (c) Opening 60 mm × 60 mm, K = K1, (d) Opening 60 mm × 60 mm, K =K2

Fig. 9. RMS Roof Acceleration Varies with Windward Dominant

Opening Area

Vol. 23, No. 9 / September 2019 − 4079 −


60 mm × 60 mm, and wind speed at center of opening is 8.4 m/s,

the variation of RMS roof acceleration with background leakage

(AL/Ao) is shown in Fig. 10. It is illustrated that the RMS roof

acceleration decreases with the increase of background leakage.

4. Comparison with the Theoretical Calculation

In previous section, parameter analyses on roof acceleration

responses were conducted by a series of aeroelastic wind tunnel

experiments, and the variations of RMS roof acceleration with

different influence factors were obtained. The influence

factors included wind speed at the center of opening, windward

dominant opening area and background leakage. To further

verify the availability and precision of the coupled dynamic

equations shown in section 2, comparisons of roof acceleration

and internal pressure between wind tunnel experiment results

Fig. 10. RMS Roof Acceleration Varies with Background Leakage

Table 2. Calculation Cases

CasesRoof

stiffnessOpening area (mm × mm)

Wind speed at the opening

(m/s)

Total leakage area

(mm2)

6 K = K1 A2 = 30 × 30 7.6 0

7 K = K1 A2 = 30 × 30 8.4 0

8 K = K1 A2 = 30 × 30 9.5 0

10 K = K1 A3 = 60 × 60 7.6 0

11 K = K1 A3 = 60 × 60 8.4 0

12 K = K1 A3 = 60 × 60 8.4 198.07

13 K = K1 A3 = 60 × 60 8.4 395.64

14 K = K1 A3 = 60 × 60 8.4 593.46

15 K = K1 A3 = 60 × 60 8.4 791.28

16 K = K1 A4 = 100 × 100 7.6 0

19 K = K2 A3 = 60 × 60 7.6 0

Fig. 11. Power Spectrum Density of Acceleration Response when the Roof Freely Vibrates (K = K1, A2 = 30 × 30 mm2): (a) Tap 1, (b) Tap 2,

(c) Tap 3, (d) Tap 4



and theoretical results calculated from the coupling equations

were made.

Before making comparative analyses between experimental

results and theoretical calculation results, it is necessary to

identify the natural frequency and damping ratio of the elastic

roof. The calculation cases are shown in Table 2.

4.1 Power Spectrum Density of Roof Acceleration

Dynamic characteristics of the elastic roof can be understood

by conducting power spectrum density analyses. When the roof

stiffness is K= K1 and windward opening area is A2 = 30 mm ×

30 mm, the power spectrum densities of acceleration responses

are presented in Fig. 11 as the roof freely vibrates vertically. It is

shown that the power at the first order frequency is dominant

when the roof freely vibrates. Fig. 12 shows the power spectrum

densities of acceleration responses when roof vibrates under the

action of internal pressure and external pressure (see case 6 in

Table 2). It is indicated that the powers for taps 3 and 4 which are

located at the front edge of roof are remarkably larger than those

for taps 1 and 2 which are located at the middle and end of the

roof. Moreover, the powers are dominant at the first-order

frequency for taps 3 and 4, which is because the external

pressures are larger in the upstream region of the roof. While the

powers at higher frequencies are also remarkable compared with

those at the first-order frequency for taps 1 and 2, which is

because the external pressures are relatively smaller in downstream

regions and the vibrations of taps 1 and 2 are also affected by

those of taps 3 and 4.

4.2 Identification of the First-Order Modal Parameters

It is assumed that the flexible roof behaves linearly when

establishing its motion equation. However, high-order mode of

vibration occurs on partial of the roof due to the disproportion of

external pressure on the roof surface. So the first order mode of

damping ratio must be investigated first.

The identification steps are as follows:

1. First, the acceleration signal of each taps is decomposed into

a finite number of intrinsic mode functions (IMFs) through

Hilbert-Huang transform (HHT) (Huang et al., 1998). Then

the corresponding frequency of each IMF is obtained by

power spectrum density analysis to determine which IMF is

corresponding to the first mode.

2. After determining the IMF corresponding to the first mode,

random decrement technique (RDT) (Ibrahim, 1998) is used

to identify the first mode of damping ratio.

To clarify this matters, take the tap 1 of case 6 as an example to

make the identification method above clear. All the components

of intrinsic mode function are shown in Fig. 13. The identified

Fig. 12. Power Spectrum Density of Acceleration Response when the Roof Forced Vibrates (Case 6): (a) Tap 1, (b) Tap 2, (c) Tap 3, (d) Tap 4

Vol. 23, No. 9 / September 2019 − 4081 −


− 40

Fig. 13. Components of Intrinsic Mode Decomposition of Tap 1 (Case 6): The separate indicators are shown in y-axis, respectively

Fig. 14. Identified Process to Obtain the First Order Modal Damping

Ratio of Tap 1 (Case 6)

Table 3. The First Order Frequency an

Case number

Tap 1 Tap 2

Frequency(Hz)

Damping ratio

Frequency (Hz)

Dam r

6 9.58 5.19% 10.67 3.

7 9.31 4.87% 11.33 3.

8 9.50 6.12% 11.98 5.

10 9.65 5.59% 10.84 3.

11 9.63 5.85% 11.32 4.

12 9.64 8.43% 11.34 6.

13 9.83 6.13% 11.30 7.

14 9.95 8.65% 11.29 4.

15 9.81 7.16% 11.11 4.

16 9.97 4.81% 11.08 6.

19 9.63 10.23% 10.60 3.

first order modal damping ratio is presented in Fig. 14.

By following the steps above, the damping ratios of first order

mode of acceleration responses in all cases are identified. The

first order frequency and damping ratio identification results are

presented in Table 3.

4.3 Comparison with the Theoretical Calculation Results

The fundamental calculation parameters are as follows: γ = 1.4,

ρa = 1.22 kg/m3, Pa = 101,300 Pa, c = 0.6, ,

, , Ar = 0.32 m2, H = 0.2 m, mr = 1.1 kg, ωr =

2πfr. The first-order natural frequency and damping ratio of the

roof. can be obtained by arithmetically mean over all the taps for

each calculation case as follows: When , the natural

Le πAo 4⁄=

CL 1.2= CL′ 2.68=

1K K=

82 − KSCE Journal of Civil Engineering

d Damping Ratio Identification Results

Tap 3 Tap 4

pingatio

Frequency (Hz)

Damping ratio

Frequency(Hz)

Damping ratio

20% 10.64 3.66% 10.50 4.38%

81% 11.36 2.65% 11.35 2.84%

30% 12.01 3.48% 12.00 3.18%

30% 10.77 4.03% 10.64 4.45%

27% 11.23 4.07% 11.17 5.67%

23% 11.11 5.44% 10.96 8.06%

03% 10.92 6.79% 10.83 8.39%

14% 11.02 4.60% 11.04 5.10%

02% 9.83 11.10% 10.82 5.14%

07% 10.34 5.31% 10.18 4.30%

42% 10.28 5.17% 10.48 1.78%


frequency and damping ratio of the roof are and

, respectively. When , the two values are

and , respectively. In addition, the

mean external pressure coefficients within the range of windward

opening and roof surface are taken as CPW and , respectively.

The mean external pressure coefficient on the leeward wall is

taken as .

Substitute the parameters above into the governing equations

(Eqs. (1) and (3)) and taking the internal volume

which contains compensated volume, then the internal pressure

response can be solved. Similarly, substitute the parameters

above into the governing equations (Eqs. (1) and (3)) and taking

the internal volume which doesn’t contain

compensated volume, then the roof displacement response are

solved, and the acceleration response of the roof can be further

obtained by second order differential calculation.

Theoretical and experimental RMS values of internal pressure

responses and acceleration responses corresponding to the first

order modal of flexible roof are presented in Figs. 15 and 16,

respectively. The theoretical and experimental results are basically

consistent, so the validity and accuracy of the coupled governing

equation are verified. However, It is noted that the governing

equations shown in Eqs. (1) and (3) are established based on the

assumption that roof behaves linearly (i.e., only the first order

modal acceleration response is considered).

5. Conclusions

A simplified and computationally efficient coupling equations

governing the internal pressure response and roof acceleration

response of a building with a dominant opening and background

leakage were presented based on certain rational assumptions.

The assumptions involved in the development of the governing

equations included lumping the distribution leakage into a single

equivalent leakage opening on the leeward wall and neglecting

the inertia effect of the air-slug at the lumped leakage in

comparison with its damping effect. Neglecting the leeward external

pressure fluctuation compare with internal pressure fluctuation, and

the same average external pressure coefficient was introduced to

calculate the leeward external pressure coefficient. Besides, the

flexible roof was assumed to behave linearly.

Wind tunnel experiments on a building model with aeroelastic

roof but rigid walls were conducted to investigate three factors,

namely, approaching wind velocity at the center of the opening,

windward dominant opening area and background leakage,

which have effects on roof acceleration responses. As a result,

RMS roof acceleration responses increase with the increase of

the approaching wind speed at the center of opening and

windward dominant opening area, while decrease with increased

background leakage ratios.

Finally, the experimental RMS values of internal pressure

fluctuations and acceleration fluctuations corresponding to the first

order modal of the roof were used to validate the two predicted RMS

values calculated from the coupling governing equations. It is shown

that the predictions of RMS internal pressure fluctuations and

acceleration fluctuations corresponding to the first order modal of

the roof are found to be in close agreement with the corresponding

wind tunnel experimental results, which verify the availability and

calculation precision of the coupling governing equations. However,

it must be pointed out that only the first order modal acceleration

response is considered in the coupling equations, more studies on the

accurate prediction model should be conducted in future.

Acknowledgements

The work described in this paper is supported by the National

Natural Science Foundation of China (No. 51778243), and the

State Key Laboratory of Subtropical Building Science, South

China University of Technology (No. 2019ZB28). The financial

supports are gratefully acknowledged.

ORCID

Xianfeng Yu https://orcid.org/0000-0002-3047-4886

Zhuangning Xie https://orcid.org/0000-0002-9014-503X

fr1 10.66Hz=

ζr1 5.32%= K K2=

fr2 10.25Hz= ζr2 5.15%=

PrC

PLC

0∀ 0.448 m3

=

0∀ 0.064 m

3

=

Fig. 15. Theoretical and Experimental RMS Internal Pressure

Responses

Fig. 16. Theoretical and Experimental RMS Acceleration Responses

Corresponding to the First Order Modal of Roof

Vol. 23, No. 9 / September 2019 − 4083 −

https://orcid.org/0000-0002-3047-4886https://orcid.org/0000-0002-9014-503X


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Coupling Vibration between Wind-Induced Internal Pressure and a Flexible Roof for Buildings with a Dominant Opening and Background LeakageAbstract1. Introduction2. Review of the Governing Equations3. Wind Tunnel Experiment on Aeroelastic Model3.1 Experimental Setup3.2 Parameter Analyses on Roof Acceleration Response3.2.1 Wind Speed at the Center of Opening3.2.2 Windward Dominant Opening Area3.2.3 Background Leakage

4. Comparison with the Theoretical Calculation4.1 Power Spectrum Density of Roof Acceleration4.2 Identification of the First-Order Modal Parameters4.3 Comparison with the Theoretical Calculation Results

5. ConclusionsAcknowledgementsORCIDReferences

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Coupling Vibration between Wind-Induced Internal Pressure ... · a single-degree-of-freedom roof dynamic system. Three factors, approaching wind velocities at the center of the dominant