The sound transmission loss of a stiffened window was investigated using a coupled finite element and boundary element method. This approach allowed the window to have arbitrary elastic boundary conditions and the stiffeners to be located at arbitrary positions inside the window. The in-plane deformation of the window was also taken into account. The natural frequencies predicted by the present approach showed good agreement with earlier published results. The prediction method was subsequently applied to parametric studies examining the effects of stiffeners on the sound transmission loss of a window. The results showed that the stiffeners (or their locations) notably influenced the window’s sound transmission loss values, thereby demonstrating the possibility of using stiffeners to improve the sound insulation of a practical window.
Practical applications: This study provides an approach that can be used to predict the sound insulation of a window with arbitrary elastic boundary conditions and with any-shape stiffeners lying anywhere inside the window. This approach can also be used to guide the design of windows (or other plate-like building structures) with better sound insulation.
WuJRLiuWH. Vibration of rectangular plates with edge restraints and intermediate stiffeners. J Sound Vibrat1988; 123(1): 103–113.
2.
LauraPAAGutierrezRH. A note on transverse vibrations of stiffened rectangular plates with edges elastically restrained against rotation. J Sound Vibrat1981; 78(1): 139–144.
3.
YunYMakCM. A study of coupled flexural-longitudinal wave motion in a periodic dual-beam structure with transverse connection. J Acoust Soc Am2009; 126(1): 114–121.
4.
LangleyRS. A dynamic stiffness technique for the vibration analysis of stiffened shell structures. J Sound Vibrat1992; 158(3): 521–540.
5.
MaceBR. Periodically stiffened fluid-loaded plates, II: response to line and point forces. J Sound Vibrat1980; 73(4): 487–504.
6.
MaceBR. Periodically stiffened fluid-loaded plates, I: response to convected harmonic pressure and free wave propagation. J Sound Vibrat1980; 73(4): 473–486.
MeadDJ. Plates with regular stiffening in acoustic media: vibration and radiation. J Acoust Soc Am1990; 88(1): 391–401.
9.
GinsbergJHMcDanielJG. An acoustic variational principle and component mode synthesis applied to the analysis of acoustic radiation from a concentrically stiffened plate. J Vibrat Acoust1991; 113(3): 401–408.
10.
PhotiadisDM. Anderson localization of one-dimensional wave propagation on a fluid-loaded plate. J Acoust Soc Am1992; 91(2): 771–781.
11.
LeeJHKimJ. Analysis of sound transmission through periodically stiffened panels by space-harmonic expansion method. J Sound Vibrat2002; 251(2): 349–366.
12.
InoueKYamanakaMKiharaM. Optimum stiffener layout for the reduction of vibration and noise of gearbox housing. J Mech Design2002; 124(3): 518–523.
13.
JoshiPMulaniSBGuravSP. Design optimization for minimum sound radiation from point-excited curvilinearly stiffened panel. J Aircraft2010; 47(4): 1100–1110.
14.
QuirtJD. Sound transmission through window I. Single and double glazing. J Acoust Soc Am1982; 73(3): 834–844.
15.
UtleyWAFletcherBL. The effect of edge conditions on the sound insulation of double windows. J Sound Vibrat1973; 26(1): 63–72.
16.
BerryALocqueteauC. Vibration and sound radiation of fluid-loaded stiffened plates with consideration of in-plane deformation. J Acoust Soc Am1996; 100(1): 312–319.
17.
MukhopadhyayM. Vibration and stability analysis of stiffened plates by semi-analytical finite difference method, part II: consideration of bending and axial displacements. J Sound Vibrat2011; 130(1): 41–53.
18.
BarikMRMukhopadhyayM. Free flexural vibration analysis of arbitrary plates with arbitrary stiffeners. J Vibrat Control1999; 5(5): 667–683.
19.
EwinsDJ. Modal testing: theory, practice and applications, 2nd edn. Baldock: Research Studies Press Ltd, 2000.
20.
KimWMKimJTKimJS. Development of a criterion for efficient numerical calculation of structural vibration responses. KSME Int J2003; 17(8): 1148–1155.
21.
HerrinDWMartinusFWuTW. An assessment of the high frequency boundary element and Rayleigh integral approximations. Appl Acoust2006; 67(8): 819–833.
22.
WuTW. Boundary element acoustics: fundamentals and computer codes, Boston, MA: WIT Press, 2000.
23.
BerryAGuyaderJLNicolasJ. A general formulation for the sound radiation from rectangular, baffled plates with arbitrary boundary conditions. J Acoust Soc Am1990; 88(6): 2792–2802.
24.
ChielloOSgardFCAtallaN. On the use of a component mode synthesis technique to investigate the effects of elastic boundary conditions on the transmission loss of baffled plates. Comput Struct2003; 81: 2645–2658.
25.
LiWL. Vibration analysis of rectangular plates with general elastic boundary supports. J Sound Vibrat2004; 273(3): 619–635.
26.
OuDYMakCM. The effects of elastic supports on the transient vibroacoustic response of a window caused by sonic booms. J Acoust Soc Am2011; 130(2): 783–790.
27.
RobertDCDavidSMMichaelEP. Concepts and applications of finite element analysis, 4th edn. New York, NY: Wiley, 2002.
28.
XinFXLuTJ. Analytical and experimental investigation on transmission loss of clamped double panels: implication of boundary effects. J Acoust Soc Am2009; 125(3): 1506–1517.
29.
NairPSRaoMS. On vibration of plates with varying stiffener length. J Sound Vibrat1984; 95(1): 19–29.
30.
SheikhAHMukhopadhyayM. Free vibration analysis of stiffened plates with arbitrary planform by the general spline finite strip method. J Sound Vibrat1993; 162(1): 147–164.
31.
AksuG. Free vibration analysis of stiffened plates by including the effect of inplane inertia. J Appl Mech Tech Phys1982; 49(1): 206–212.
32.
HarikIEGuoM. Finite element analysis of eccentrically stiffened plates in free vibration. Comput Struct1993; 49(6): 1007–1015.
33.
MukherjeeAMukhopadhyayM. Finite element free vibration of eccentrically stiffened plates. Comput Struct1988; 30(6): 1303–1317.
34.
LeventhallHG. Low frequency noise and annoyance. Noise Health2004; 6(23): 59–72.
35.
BerglundBHassmenP. Sources and effects of low frequency noise. J Acoust Soc Am1996; 99(5): 2985–3002.
36.
TakahashiYKanadaKYonekawaY. A study on the relationship between subjective unpleasantness and body surface vibrations induced by high-level low-frequency pure tones. Indust Health2005; 43(3): 580–587.
37.
Hodgdon KK, Atchley AA and Bernhard RJ. Low frequency noise study. The Partnership for AiR Transportation Noise and Emissions Reduction 2007; Report No. PARTNER-COE-2007-001: 16–17.
38.
OuDYMakCM. Experimental validation of the sound transmission of rectangular baffled plates with general elastic boundary conditions. J Acoust Soc Am2011; 126(9): EL274–EL279.
