A theory of sound transmission through a clamped curved piezoelectric membrane connected to a negative capacitor

An analytical calculation of the acoustic transmission loss of sound propagating through a thin cylindrically curved piezoelectric membrane, which is rigidly clamped at its straight ends, is presented. The membrane is placed inside an acoustic tube and connected to an active electric shunt circuit that behaves as a negative capacitor. A properly adjusted shunt circuit has a significant impact on the effective elastic stiffness of the piezoelectric membrane and, hence, influences the membrane acoustic reflectivity and transmission loss of sound. Such a setup represents a noise control system based on the principles of the active elasticity control of piezoelectric materials. The non-uniform radial motion of the clamped membrane and its interaction with the acoustic field and the electric shunt circuit are analyzed. The main objective of the calculations, which are based on Donnell’s theory, is the determination of the effects of the membrane clamps on the flexural motion of the membrane and, therefore, effects on the acoustic transmission loss of sound. Approximative formulae for the amplitude of the membrane displacement and the acoustic transmission loss of sound are expressed as well as the resonant frequencies of the uniform mode and flexural vibration modes.     

Analytical modeling of fluid loaded orthogonally rib-stiffened sandwich structures: Sound transmission

An analytic model is developed to investigate the wave propagation and sound transmission characteristics of an infinite sandwich structure reinforced by two sets of orthogonal rib-stiffeners when subjected to convective fluid-loaded pressure. The rib-stiffeners are assumed to be identical and uniformly spaced, which can exert not only tensional forces and bending moments but also torsional moments on the facesheets. Inertial terms of the tensional forces, bending moments and torsional moments are introduced to account for inertial effects arising from the mass of the rib-stiffeners. With the surrounding acoustic fluids restricted by the acoustic wave equation, fluid-structure coupling is considered by imposing velocity continuity condition at fluid-panel interfaces. By applying the Bloch theorem for periodic structures, the structural and acoustic responses are expressed in a superposition form of space harmonics for a given wavenumber. The application of the virtual work principle for one periodic element yields two infinite sets of simultaneous algebraic coupled equations, which are numerically solved by truncating them in a finite range insofar as the solution converges. The validity and feasibility of the analytic model is qualified by comparing model predictions with existing results, in which the necessity and advantage of the exact modeling of rib-stiffener motions are also demonstrated. Specifically, the influences of inertial effects arising from rib-stiffener mass, the periodicity spacing of rib-stiffeners, and the airborne as well as structure-borne paths on the transmission of sound across the sandwich structure are quantified and conclusions of significant practical implications are drawn.     

Theoretical model for sound transmission through finite sandwich structures with corrugated core

Due to the promising applications of lightweight double-leaf structures in noise control engineering, numerous investigations have been performed to study the vibroacoustic properties of these structures. However, no attention has been focused on the vibroacoustic properties of finite double-leaf structures with corrugated core used extensively in constructing the hulls of bullet passenger trains. In the present paper, a theoretical model is developed to predict the sound transmission loss (STL) characteristics of simply supported double-leaf partitions with corrugated core. The boundary conditions are accounted for by writing the displacements of the face plates in a series form of modal functions. The model predictions are validated by comparing with existing experimental measurements. The vibroacoustic properties of the sandwich construction are examined and the physical mechanisms for sound transmission through the structure explored, including the phenomena of ‘coincidence resonance’ and ‘standing wave resonances’. The effects of structural links, structural dimensions, inclination angle of the corrugated core, as well as the thickness of face plates and core layer on the STL are systematically investigated.     

Modeling the sound transmission through complex structures with attached noise control materials

This paper discusses three extensions of the Transfer Matrix Method (TMM). The first deals with the modeling of the transmission loss of sandwich–composite panels. A wave based model is recalled and used to derive a simpler model based on identifying effective properties of an equivalent orthotropic panel. An experimental case study is presented to show the accuracy of these models when used to predict practical sound transmission problems involving single wall sandwich–honeycomb panels and double wall sandwich–honeycomb with an absorbing material filling the cavity between the two panels. In the second extension, the use of the TMM to predict the response of panels under various types of excitations is discussed. A wave based method is presented and compared with Finite Element Method (FEM) predictions for two types of excitations: Turbulent Boundary Layer (TBL) and point source. The comparison shows that the method allows for accurate predictions of the frequency averaged Transmission Loss (TL). Finally, the use of the TMM to model double wall systems with mechanical links is presented and numerically validated using FEM. It is found that the method captures well the decrease of the TL due to the insertion of the links and the effect of the excitation nature on this decrease.     

Dynamic response of clamped sandwich beams: analytical modeling

An improved analytical model is developed to predict the dynamic response of clamped lightweight sandwich beams with cellular cores subjected to shock loading over the entire span.The clamped face sheets are simplified as a single-degree-of-freedom(SDOF) system, and the core is idealized using the rigid-perfectly-plastic-locking(RPPL) model. Reflection of incident shock wave is considered by incorporating the bending/stretching resistance of the front face sheet and compaction of the core. The model is validated with existing analytical predictions and FE simulation results, with good agreement achieved. Compared with existing analytical models, the proposed model exhibits superiority in two aspects: the deformation resistance of front face sheet during shock wave reflection is taken into account; the effect of pulse shape is considered. The practical application range of the proposed model is therefore wider.     

Exact solution of sound reflection on infinite laminated plate and transmission through it

An exact solution is proposed in this paper based on the elasticity theory for sound reflection from an infinite laminated plate and transmission through it, and some phenomena of sound propagation in an isotropic media are also discussed. Some examples given here could be used to test approximate models of laminated plates.     

Reciprocity and antireciprocity in sound transmission through layered materials including elastic and porous media

Sound transmission through elastic solids and porous media having an elastic frame involves longitudinal and transverse waves. A modelling of sound propagation through layers of these media by transfer matrices, which is equivalent to a representation by analogous multi-port circuits was performed previously. The different ports of the circuits are related to the normal and the tangential strains and velocities on the two faces of the layers. The use of impedance matrices instead of transfer matrices shows that the coupling between the normal and the tangential conjugate variables is antireciprocal, and is reciprocal for conjugate variables having the same nature. Moreover, it can be proven that the transmission loss through strafied materials in contact with the same fluid on the and the rear face is the same in opposite directions of propagation.     

Analytical modeling of constricted channel flow

Analytical flow models are frequently applied when describing constricted channel flow at low and moderate Reynolds numbers. A common assumption underlying such flow models is two-dimensional or axi-symmetrical flow. In this work, two analytical model approaches are formulated in order to overcome this assumption in the case of naturally occurring channel flows for which the assumption might be critiqued. Advantages and flaws of both model approaches are discussed and their outcome is compared with experimental data.     

Characterization and modeling of air muscles

Two flexible pneumatic actuators, McKibben and straight fiber, were analyzed. The muscles were modeled by finite element method. The numerical models take into account the non-linearity of the expanding rubber inner tube, and of the mechanism for transferring load to the braided cords surrounding the tube. Because of its own fabrication, McKibben muscle model may capture the initial backslash between rubber tube and cords.Despite of the McKibben specimen, a straight fiber muscle prototype was fabricated on purpose in the laboratory. In order to validate the numerical models, numerous experimental tests were carried out. The numerical results showed a good agreement with the data measured experimentally in terms of muscle pull force and of its deformed shape. Finally, the models of two muscles similar in terms of input energy allow their performances to be compared.     

Interferometric study of natural convection in rectangular air cavities of various orientations

The results of an experimental investigation into the temperature profiles and heat transfer associated with natural convection in rectangular air cavities are presented, the angle of inclination varying from 0 (heating at the bottom) to 180° (heating at the top). The range of Rayleigh numbers was R=2.68·10³–2.57·10⁵, and n=H/d=5.06–18.3. The investigation was carried out by an optical method, using an IZK-454 interferometer. For a horizontal orientation of the cavity the heat-transfer data satisfy the relation N=0.216 R^0.25, for a vertical orientation N=0.144 R^0.3h^–0.129, where N is the Nusselt number. In the region of an inclination of 30° the heat transfer passes through a maximum under all conditions studied.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 89–93, July–August, 1972.     

Comparative assessment of SAS and DES turbulence modeling for massively separated flows

Numerical studies of the flow past a circular cylinder at Reynolds number 1.4 × 10~5 and NACA0021airfoil at the angle of attack 60?have been carried out by scale-adaptive simulation (SAS) and detached eddy simulation (DES), in comparison with the existing experimental data. The new version of the model developed by Egorov and Menter is assessed, and advantages and disadvantages of the SAS simulation are analyzed in detail to provide guidance for industrial application in the future. Moreover, the mechanism of the scale-adaptive characteristics in separated regions is discussed, which is obscure in previous analyses. It is concluded that: the mean flow properties satisfactorily agree with the experimental results for the SAS simulation, although the prediction of the second order turbulent statistics in the near wake region is just reasonable. The SAS model can produce a larger magnitude of the turbulent kinetic energy in the recirculation bubble, and, consequently, a smaller recirculation region and a more rapid recovery of the mean velocity outside the recirculation region than the DES approach with the same grid resolution. The vortex shedding is slightly less irregular with the SAS model than with the DES approach,probably due to the higher dissipation of the SAS simulation under the condition of the coarse mesh.     

Control of a separated boundary layer: reduced-order modeling using global modes revisited

The possibility of model reduction using global modes is readdressed, aiming at the controlling of a globally unstable separation bubble induced by a bump geometry. A combined oblique and orthogonal projection approach is proposed to design an estimator and controller in a Riccati-type feedback setting. An input?Coutput criterion is used to appropriately select the modes of the projection basis. The full-state linear instability dynamics is shown to be successfully controlled by the feedback coupling with controllers of moderate degrees of freedom.     

Numerical modeling of a viscous incompressible unsteady separated flow past a rotating cylinder

For studying unsteady flow past a rotating circular cylinder the Navier-Stokes equations are used. The numerical algorithm is based on an artificial-compressibility method, an implicit three-layer second-order scheme with subiterations with respect to time, a third-order scheme with splitting of the flux vectors for the convective terms, and a central-difference scheme for integrating the viscous terms. The calculated velocity profiles, the vorticity fields, the Strouhal numbers, the distribution of the pressure and friction coefficients over the cylinder surface, and the coefficients of the drag and lift forces for the laminar flow regime are analyzed.     

The jump phenomenon effect on the sound absorption of a nonlinear panel absorber and sound transmission loss of a nonlinear panel backed by a cavity

Theoretical analysis of the nonlinear vibration effects on the sound absorption of a panel absorber and sound transmission loss of a panel backed by a rectangular cavity is herein presented. The harmonic balance method is employed to derive a structural acoustic formulation from two-coupled partial differential equations representing the nonlinear structural forced vibration and induced acoustic pressure; one is the well-known von Karman??s plate equation and the other is the homogeneous wave equation. This method has been used in a previous study of nonlinear structural vibration, in which its results agreed well with the elliptic solution. To date, very few classical solutions for this nonlinear structural-acoustic problem have been developed, although there are many for nonlinear plate or linear structural-acoustic problems. Thus, for verification purposes, an approach based on the numerical integration method is also developed to solve the nonlinear structural-acoustic problem. The solutions obtained with the two methods agree well with each other. In the parametric study, the panel displacement amplitude converges with increases in the number of harmonic terms and acoustic and structural modes. The effects of excitation level, cavity depth, boundary condition, and damping factor are also examined. The main findings include the following: (1)?the well-known ??jump phenomenon?? in nonlinear vibration is seen in the sound absorption and transmission loss curves; (2)?the absorption peak and transmission loss dip due to the nonlinear resonance are significantly wider than those in the linear case because of the wider resonant bandwidth; and (3)?nonlinear vibration has the positive effect of widening the absorption bandwidth, but it also degrades the transmission loss at the resonant frequency.     

Numerical modeling of the disturbances of the separated flow in a rounded compression corner

Numerical modeling of the time-dependent supersonic flow over a compression corner with different roundness radii is performed on the basis of the solution of the two-dimensional Navier-Stokes equations in the regimes corresponding to local boundary layer separation. The development of unstable disturbances generated by local periodic injection/suction in the preseparated boundary layer is calculated. The results are compared with those of similar calculations for a flat plate. It is shown that the natural oscillations of the boundary-layer second mode stabilize in the separation zone and grow intensely downstream of the reattachment point. The acoustic modes excited within a separation bubble are studied using numerical calculations and an asymptotic analysis.     

Thermal convection heat transfer of air/water layers enclosed in horizontal annuli with mixed boundary conditions

This paper presents a numerical study for thermal convection of air/water layers enclosed in a horizontal concentric/eccentric cylindrical annulus with the inner wall subjected to a constant heat flux and an isothermal condition at the outer wall. Results are generated for an annulus of radius ratio of 2.6 with three different vertically eccentric positions of the inner cylinder, the modified Rayleigh number up to 10⁷, and the modified Marangoni number varying from 0.0 to 10⁴. The heat transfer characteristics and fluid flow patterns driven by buoyancy and/or thermocapillary effects in air/water-filled annulus are illustrated by means of contour maps of healtline and streamline respectively. Under the mixed thermal boundary conditions considered, significant heat exchange across the air-water interface is found and appears to be unaffected by the thermocapillary convection.Es wird eine numerische Untersuchung der thermischen Konvektion von Luft/Wasser-Schichten, die von horizontalen konzentrischen/exzentrischen zylindrischen Ringkanälen umschlossen sind, deren innere Wand einer konstanten Wärmestromdichte und deren äußere Wand isothermen Bedingungen ausgesetzt sind, dargestellt. Ergebnisse werden für einen Ringkanal mit einem Radiusverhältnis von 2,6 mit drei verschiedenen senkrechten exzentrischen Positionen des inneren Zylinders, für die modifizierte Rayleigh-Zahl bis 10⁷ und für die modifizierte Marangoni-Zahl zwischen 0,0 und 10⁴ erhalten. Die Charakteristiken der Wärmeübertragung und des Fluid-Stromlinienbildes, hervorgerufen durch Auftriebskräfte und/oder thermokapillare Effekte in mit Luft/Wasser gefüllten Ringkanälen wurden mittels Schichtlinienplänen der Isothermen und der Stromlinien dargestellt. Bei den untersuchten gemischten thermischen Randbedingungen wurde ein signifikanter Wärmeaustausch über der Luft/Wasser-Grenzfläche gefunden, der scheinbar nicht durch die thermokapillare Konvektion gestört wird.