The purpose of this work has been to evaluate the possibility of using modified lower order methods - such as the Bernoulli-Euler or Timoshenko beam theories with frequency dependent parameters - to calculate the response of sandwich beams subject to different end conditions. The models have been verified by measurements on a freely suspended asymmetric sandwich beam with aluminium laminates and a plastic foam core, indicating good agreement.
The flexural vibration of an asymmetric sandwich beam is modelled using Timoshenko theory with frequency dependent parameters. The advantage of this approach, as compared to using modified Bernoulli-Euler theory, is the independence of the frequency dependent parameters on the boundary conditions of the beam. Using Bernoulli-Euler theory, the apparent bending stiffness would have to depend on the particular end conditions of the beam configuration in order to achieve the best possible accuracy. Using instead Timoshenko theory, with frequency dependent bending stiffness and shear modulus parameters, this problem is avoided. The results are compared to measurements and to the results obtained from a previously derived 6th order sandwich beam theory, which takes into account the effects of pure bending of the entire beam, core shear and its coupling to the bending of the laminates, and rotational inertia. The possibility of implementing the approach in existing Timoshenko beam elements in commercial FEM programs is discussed.
The energy flow corresponding to the propagation of flexural waves in sandwich beam structures is investigated. A previously derived 6th order theory describing the bending of sandwich beams is utilized and important properties such as group velocity and energy transmission through joints are analyzed and compared to those expected from classical beam theory. The results could be applied in the method of statistical energy analysis (SEA) in order to predict the vibration level of different members of composite structures composing sandwich beam elements.
Various types of sandwich beams with foam or honeycomb cores are currently used in the industry, indicating the need for simple methods describing the dynamics of these complex structures. By implementing frequency-dependent parameters, the vibration of sandwich composite beams can be approximated using simple fourth-order beam theory. A higher-order sandwich beam model is utilized in order to obtain estimates of the frequency-dependent bending stiffness and shear modulus of the equivalent Bernoulli-Euler and Timoshenko models. The resulting predicted eigenfrequencies and transfer accellerance functions are compared to the data obtained from the higher-order model and from measurements.
The dynamic response of the vibrating structures are studied with the standard finite element method against the more computationally efficient spectral finite element method. First a simple beam structure is modelled with the standard method and newly developed spectral elements; which has the advantage that dispersion relations for all beam structures may be developed. Some numerical examples are given to illustrate and validate the developed method and studies of the measured responses of structures that may be used for vehicle panels are compared.
Road traffic noise is nowadays a major environmental pollutant. In the near future traffic noise will increase even further, especially due to the expected increase of heavy traffic. Noise radiated from tyres of the vehicles is a dominating source. The acoustic field inside the tyre has previously been modelled. The first acoustic mode for a standard stationary passenger car tyre is at 225 Hz. The tyre becomes stiffer at these tyre air cavity resonances and radiates comparatively high tonal noise to the exterior at this frequency range. In order to reduce this tonal noise at low frequencies a set of new modified wheels are developed implementing some sound absorbing material inside the tyre. Preliminary sound intensity measurements have been carried out on a static tyre. The influence of the tyre air cavity resonances on the radiated noise is reduced adding sound absorbing material inside the tyre.
A great deal of recent research related to the aeronautic industry has been devoted to the theoretical study of sound transmission through fuselage structures. However, the literature records few test data with reference to the influence of overpressure on sound transmission. In this article, the airborne sound transmission through curved panels under the condition of overpressure at the concave side has been investigated experimentally and it is shown that experimental results agree well with a theoretical prediction due to an infinite cylindrical shell model at relatively high frequencies. Discrepancies, which occur at lower frequencies, can be explained, inter alia, by the influence of the finite size and attached stiffeners of the panel.At frequencies higher than the corresponding ring frequency for the curved panel, both experimental and theoretical predictions reveal that the overpressure at the concave side tends to reduce the sound transmission loss at the rate of about 0.5dB/10000Pa. While at lower frequencies, say well below the ring frequency, the overpressure may increase or reduce sound transmission loss of a finite panel depending on the shift of resonant frequencies resulting from the overpressure.
he purpose of this paper is to investigate the pressurization effects on sound transmission through airplane panels. The airborne sound transmission through airplane panels under the condition of overpressure at one side has been investigated by measurement. The test results agree well with the theoretic prediction of infinite cylindrical shell model at high frequencies, but have considerable discrepancies at low frequencies, which, however, are ready to be explained by the influence of finiteness and stiffeners of the panel. When the frequency is higher than the ring frequency of curved panel, both test and theoretic prediction reveal that the overpressure under laboratory conditions tends to reduce the sound transmission loss at the rate of about 0.5dB/10000 Pa. while at low frequencies, say below around the ring frequency, the overpressure may increase the sound transmission loss of ring-stiffened panel, the reason of this behavior is resulted from the shift of the resonant frequencies led by the increased in-plane tension.
A numerical approach based on a receptance method has been developed to evaluate the airborne sound insulation of aircraft panels with stringer and ring frame attachments. Theoretical predictions have been compared with laboratory measurements conducted on both model structures and aircraft panels. Certain parameters were varied in this study to gauge stiffener effects on sound transmission through the panel. For large curved aircraft panels studied here, it was found that the ring frames have little influence on sound transmission loss in the frequency range of interest. However, the stringers may have considerable influence on the sound transmission loss. The stringer improves the sound transmission loss for a curved panel in the vicinity of the ring frequency, but may result in a potential deterioration above this frequency. In addition it was found that the sound transmission loss for the composite skin attached with composite stringers was lower than that of the metallic panel attached with metallic stringers. The results suggest that acoustical optimization design for the stringers is necessary to achieve improved airborne sound insulation for aircraft panels
A model has been developed for the prediction of velocity levels of ships hull plates which are excited by turbulent boundary layers. The model is based on the theory developed by Corcos. It is found that the velocity of the hull plates strongly depends on the speed of the ship. The acoustic power induced in the hull can be reduced if the thickness of the hull plates is increased. Other parameters like frame distance and height of hull plate are of secondary importance. The effect of turbulent boundary layer excitation is most efficiently reduced by changing the hull shape or by changing the transmission path from the hull plates to the accommodation decks.
Some basic parameters used in a traditional SEA calculation are coupling loss factors, modal densities, mobility and energy flow. For calculating the coupling loss factor the group velocity as well as the transmission coefficient for the energy flow from one structure to another must be known. These parameters are derived and discussed for some simple sandwich structures and are compared to the corresponding parameters for homogeneous structure.
A sixth-order differential equation governing the flexural vibration of sandwich plates is derived. The sandwich plates considered consist of laminates bonded to honeycomb or foam cores. The structures are assumed to be symmetric. Shear and rotation in core are included in the model. The effect on the bending stiffness of rotation and shear in the core is discussed. Shear effects are of great importance, whereas rotation of the core has only a marginal effect on the bending stiffness of lightweight sandwich plates. The bending stiffness of a sandwich plate is found to strongly depend on frequency. The bending stiffness of a structure determines its acoustical coupling to any surrounding fluid and thus its sound transmission loss and sound radiation ratio. Loss factors of sandwich plates are discussed. Boundary conditions are formulated for rectangular plates having simply supported, clamped, or free edges. There are five boundary conditions to be satisfied at each edge of the plate. The bending stiffness of simply supported and infinite plates is presented as a function of frequency. Expressions for the point mobility for infinite or simply supported finite panels are given.
This three-volume book gives a thorough and comprehensive presentation of vibration and acoustic theories. Different from traditional textbooks which typically deal with some aspects of either acoustic or vibration problems, it is unique of this book to combine those two correlated subjects together. Moreover, it provides fundamental analysis and mathematical descriptions for several crucial phenomena of Vibro-Acoustics which are quite useful in noise reduction, including how structures are excited, energy flows from an excitation point to a sound radiating surface, and finally how a structure radiates noise to a surrounding fluid. Many measurement results included in the text make the reading interesting and informative. Problems/questions are listed at the end of each chapter and the solutions are provided. This will help the readers to understand the topics of Vibro-Acoustics more deeply. The book should be of interest to anyone interested in sound and vibration, vehicle acoustics, ship acoustics and interior aircraft noise. This is the first volume, and covers the following topics: Mechanical systems with one degree of freedom, Frequency domain, Waves in solids, Interaction between longitudinal and transverse waves, General wave equation, Wave attenuation due to losses and transmission across junctions, Longitudinal vibrations of finite beams, Flexural vibrations of finite beams, Flexural vibrations of finite plates.
Anders Nilsson holds MSc in Engineering Physics from University of Lund, Sweden and Dr.Tech. in Sound and Vibration from Chalmers University. Anders Nilsson has worked on problems relating to the propagation of sonic booms at Boeing Co., Seattle, USA. At Det Norske Veritas he became head of the Acoustics Department at the Research Division. At Veritas Anders Nilsson worked on the propagation of structure borne sound in large built up structures and on the excitation of plates from flow and cavitation. Anders Nilsson was head of the Danish Acoustical Institute for four years. His main activities in Denmark were building acoustics. In 1987 Anders Nilsson was appointed professor of Applied Acoustics at KTH in Stockholm, Sweden. He was also the head of the Department of Vehicle Engineering and the founder and head, until 2002, of the Marcus Wallenberg Laboratory of Sound and Vibration Research (MWL).Anders Nilsson is since 2008 professor emeritus at MWL, KTH. His main interests are problems relating to composite structures as well as vehicle acoustics. Bilong Liu received his PhD in acoustics at the Institute of Acoustics, Chinese Academy of Sciences in 2002. He was thereafter supported financially by an EU-project- Friendly Aircraft Cabin Environment- and worked on noise transmission through aircraft structures at MWL, KTH till 2006. Bilong Liu also holds a PhD in applied acoustics from MWL. During the period Aug. 2004 to Jan. 2005 he also worked on pipe/pumpnoise at the University of western Australia in Perth. From 2007 he is working as a research professor at the Institute of Acoustics, Chinese Academy of Sciences. His main interests include vibro-acoustics, fluid induced noise, duct acoustics, active noise control, smart acoustic materials and structures.
Sandwich and honeycomb materials are increasingly used by the vehicle and building industries. Consequently, the prediction of the acoustic properties and in particular the sound transmission loss of sandwich structures is of importance. The dynamic and acoustic properties of a composite sandwich beam or plate depend on the geometry of the structure as well as on the material properties of core and laminates. The method of bonding laminates to core can also influence the dynamic properties of sandwich constructions. For example a bonding substance can increase the spacing between the laminates. In general, the construction of a sandwich plate is often symmetric with respect to the centerline. The thickness of the lightweight core is typically of the order 5 to 75 mm whereas the thickness of the laminates could vary between 0.5 and 8 mm. The E-modulus for a laminate is typically high and much higher than the corresponding modulus for the core. Some of the basic parameters of a sandwich structure can be determined by means of some simple tests on a beam element of the structure. For the test the beam is suspended by strings to simulate free-free boundary conditions. By exciting the beam by an impedance hammer the first ten or more natural frequencies of the beam can be determined. Based on these measurements of natural frequencies and the weight and dimensions of the beam, the static bending stiffness, shear modulus of the core and bending stiffness of the laminates are determined. The data is used to calculate the sound transmission loss of a plate structure being constructed in the same way as the beam. The model can also be used for parameter studies of the influence on the sound transmission loss due to changes of dimensions of laminates, core etc.
Twenty listeners with hearing impairment evaluated three noise-reduction algorithms using paired comparisons of speech clarity, noise loudness, and preference. The subjective test produces results in terms of physical signal-to-noise ratios that correspond to equal subjective performance with and without the noise-reduction algorithms. This facilitates a direct test of how well a number of objective performance measures correspond with the subjective test results.
In the framework of the EU-project FACE, sound transmission measurements have been performed by NLR and KTH on a curved and stiffened composite fuselage panel and an aluminium panel with the same structure. Both panels consist of a part with axial stiffeners and a part, suitable for mounting windows, without these stiffeners. The main goals of the measurements are to provide experimental data for validation of numerical models, and experimental determination of the effect of a.o. panel material on the sound transmission. At NLR the panels have been suspended on springs, implementing well defined (free-free) boundary conditions, suppressing flanking noise adequately by a special designed panel support structure. At KTH, the panels have been clamped. In spite of the different boundary conditions, the TL data measured by KTH and NLR TL data show a good agreement for 200 Hz and higher frequencies. Due to the curvature and stiffening, the transmission loss of the panels is much lower than the mass law prediction. For frequencies above about 600 Hz, the transmission loss of the composite panel is significantly lower than that of the metal panel, despite its 6% larger mass. For the frequency band of 250 - 2000 Hz, the transmission loss of the window area of the composite panel is much (up to 5 dB) larger than for the stringer area. It seems that the stringers of the composite panel have some bad influence on the sound transmission loss and should be further investigated.