Assessment of sandwich models for the prediction of sound transmission loss in unidirectional sandwich panels

The consistent higher-order approach and the two-parameter foundation formulation are used for the derivation of sound transmission loss in symmetric unidirectional (infinitely wide) sandwich panels with isotropic face sheets. In both models, transmission loss is calculated using decoupled equations representing symmetric and anti-symmetric motions of a sandwich panel. The closed-form expressions for impedances and transmission coefficient of a symmetric sandwich panel with an isotropic core are derived for the two-parameter foundation model. A comparison between the numerical predictions based on the two sandwich models and available experimental data shows that the consistent higher-order formulation can be used to predict the transmission loss in symmetric sandwich panels with both honeycomb and isotropic cores. For prediction of transmission loss of symmetric sandwich panels with an isotropic core, the two-parameter foundation model is more convenient, while the consistent higher-order approach is more accurate.     

金属蜂窝夹芯结构抗水下冲击性能

为揭示高强度水下爆炸冲击载荷作用下金属夹芯结构的抗冲击性能,在实验室开展小尺寸水下爆炸加载技术对金属蜂窝夹芯结构性能影响的实验研究。基于实验结果,开展了全尺寸数值模拟金属蜂窝夹芯结构在水下冲击载荷作用下的动态响应和抗冲击性能研究。结果表明,数值模拟、实验和理论模型计算的结果具有良好的一致性。由于蜂窝芯材相对密度对夹芯结构能量耗散方式和载荷传递机制的影响,结构动态响应、失效模式以及抗冲击性能随着冲击强度的变化表现出较为明显的不同。通过抗冲击参数分析,建立了反映金属蜂窝夹芯结构抗冲击性能的结构横向变形、固支反力、透射脉冲和塑性能耗随冲击强度和芯材相对密度变化的结构-载荷-性能量化关系。     

Applications of electronic speckle interferometry (ESI) techniques for spacecraft structural components

Laser-based electronic speckle interferometry (ESI) techniques, viz., electronic speckle pattern interferometry (ESPI) and electronic speckle shearographic interferometry (ESSI) are used for testing of spacecraft structural components. The combined ESPI and ESSI system developed in house was successfully used for the non-destructive evaluation (NDE) of honeycomb sandwich panels and propellant tanks of Indian Space Research Organization (ISRO). Debonds between face sheet and the honeycomb core were identified using (i) thermal and (ii) dual vacuum stressing methods. On-line NDE of the propellant tanks under internal pressure loading for identification of the minute cracks and thickness reduction areas were successfully implemented by ESI.     

各向异性蜂窝夹芯材料的电磁传输性能分析算法研究

蜂窝夹芯结构作为天线罩最常用的透波材料, 其电各向异性特征对电磁传输性能具有不可忽略的影响. 本文基于各向异性蜂窝夹芯材料对电磁波水平极化和垂直极化分量的有效介电常数, 建立了多层蜂窝夹芯材料的等效传输线网络传输方程, 并给出了其传输系数的计算公式.该计算公式由于考虑了材料的三维各向异性特征, 不仅理论上可以计算多层各向异性介质板对任意方向入射电磁波的传输系数, 而且能够揭示出材料方向角对传输性能的影响规律.同时, 通过传输线网络等效, 其计算效率远高于有限元等方法.数值算例表明, 本方法能够有效地揭示蜂窝夹芯材料的各向异性对其传输性能的影响, 计算结果在入射角为0°–80° 时与有限元法符合很好. 关键词： 电磁传输性能 电各向异性介质 蜂窝夹芯材料     

Optimal design of acoustical sandwich panels with a genetic algorithm

An optimization study is performed to design a sandwich panel with a balance of acoustical and mechanical properties at minimal weight. An acoustical model based on higher-order sandwich beam theory is used with mechanical analysis of the maximum deflection at the center of the sandwich panel under a concentrated force. First, a parametric study is performed to determine the effects of individual design variables on the sound transmission loss of the sandwich panel. Next, by constraining the acoustical and mechanical behavior of the sandwich panel, the area mass density of the sandwich panel is minimized using a genetic algorithm. The sandwich panels are constructed from eight face-sheet and sixteen core materials, with varying thicknesses of the face sheets and the core. The resulting design is a light-weight, mechanically efficient sound insulator with strength and stiffness comparable to sandwich structures commonly used in structural applications.     

Sound transmission loss of foam-filled honeycomb sandwich panels using statistical energy analysis and theoretical and measured dynamic properties

Comparisons between the experimental and predicted sound transmission loss values obtained from statistical energy analysis are presented for two foam-filled honeycomb sandwich panels. Statistical energy analysis (SEA) is a modeling procedure which uses energy flow relationships for the theoretical estimation of the sound transmission through structures in resonant motion. The accuracy of the prediction of the sound transmission loss using SEA greatly depends on accurate estimates of: (1) the modal density, (2) the internal loss factor, and (3) the coupling loss factor parameters of the structures. A theoretical expression for the modal density of sandwich panels is developed from a sixth-order governing equation. Measured modal density estimates of the two foam-filled honeycomb sandwich panels are obtained by using a three-channel spectral method with a spectral mass correction to allow for the mass loading of the impedance head. The effect of mass loading of the accelerometer is corrected in the estimations of both the total loss factor and radiation loss factor of the sandwich panels.     

Low frequency sound insulation using stiffness control with honeycomb panels

A new honeycomb core design has been used to increase the stiffness of the panel and applied to improve the noise transmission loss at frequencies between 100 and 200 Hz. A model is presented to predict the transmission loss of the honeycomb panels based on the structural modal parameters. A new test specimen with fiber reinforced plastic cores and face sheets had been used to investigate the effect of stiffness and damping on noise transmission loss. The measurements of noise transmission loss have been compared with data for common structural panels. The results show that the new core fabrication techniques using moulding to improve the noise transmission are effective. In comparison to a cement panel of the same mass, the honeycomb panels have higher TL at low frequencies between 100 and 200 Hz due to higher stiffness and damping. The honeycomb panels have more significant vibration responses above 500 Hz but these are limited by damping.     

Finite element analysis of the dynamic behavior of a laminated windscreen with frequency dependent viscoelastic core

This paper presents numerical and experimental validation of results obtained by a shell finite element, which has been developed for modeling of the dynamic behavior of sandwich multilayered structures with a viscoelastic core. The proposed shell finite element is very easy to implement in existing finite element solvers, since it uses only the displacements as degrees of freedom at external faces and at inter-layer interfaces. The displacement field is linearly interpolated in the thickness direction of each layer, and analytical integration is made in the thickness direction in order to avoid meshing of each sandwich layer by solid elements. Only the two dimensional mid-surface of reference is meshed, facilitating the mesh generation task. A simplified modal approach using a real modal basis is also proposed to efficiently calculate the dynamic response of the sandwich structure. The proposed method reduces the memory size and computing time and takes into account the frequency-dependence of the polymer core mechanical properties. Results obtained by the proposed element in conjunction with the simplified modal method have been numerically and experimentally validated by comparison to results obtained by commercial software codes (MSC/nastran and ESI/rayon-vtm), and to measurements done on automobile windscreens.     

Analytical Study on the Rate of Sound Transmission Loss in Single Row Honeycomb Sandwich Panel Using a Numerical Method

Honeycomb structures have recently, replaced with conventional homogeneous materials. Given the fact that sandwich panels containing a honeycomb core are able to adjust geometric parameters, including internal angles, they are suitable for acoustic control applications. The main objective of this study was to obtain a transmission loss curve in a specific honeycomb frequency range along with same overall dimensions and weight. In this study, a finite element model (FEM) in ABAQUS software was used to simulate honeycomb panels, evaluate resonant frequencies, and for acoustic analysis. This model was used to obtain acoustic pressure and then to calculate the sound transmission loss (STL) in MATLAB software. Vibration and acoustic analysis of panels were performed in the frequency range of 1 to 1000 Hz. The models analyzed in this design includes 14-single row-honeycomb designs with angles of −45°, −30°, −15°, 0°, +15°, +30°, +45°. The results showed that a-single row and −45°cell angle honeycomb panel in the frequency range of 1 to 1000 Hz had the highest STL as well as the highest number of frequency modes (90 mods). Furthermore, the panel had the highest STL regarding the area under the STL curve (dB∙Hz). The panels containing more frequency mods, have a higher transmission loss. Moreover, the sound transmission loss is more sensitive to the cell angle variable (θ). In other studies, the STL was more sensitive to the number of honeycomb cells in the horizontal and vertical directions, as well as the angle of cells.     

Forced non-linear vibrations of a damped sandwich beam

Forced, damped, non-linear, low-frequency flexural motions of a clamped-clamped sandwich beam with thin face sheets and a soft viscoelastic core are examined experimentally and theoretically. The theory employed neglects the extensional rigidity of the core and treats the face sheets as membranes. The non-linearity stems from axial stretching of the face sheets. Damping is taken into account by modeling the core as a Kelvin solid, with the material parameters used being obtained experimentally as functions of frequency and temperature. Theoretical frequency-amplitude relations are obtained using Galerkin's procedure and the method of harmonic balance. Results on fundamental natural frequencies, mode shapes, and stability are also presented. In the experiment, mechanical contact with the specimen was avoided by employing electromagnetic forcing and using a proximeter to measure displacements. Also, special attention was given to the interface bonds and to the reproduction, as close as possible, of clamped-clamped conditions. Agreement between the theoretical and experimental results is, in general, quite good.     

Transmission loss of damped asymmetric sandwich panels with orthotropic cores

A theoretical model of the acoustic performance of asymmetric sandwich panels is developed and verified by comparison with experimental data. The panel models consist of unequal elastic isotropic skins sandwiching an elastic orthotropic core. Damping is incorporated in both the skins and the core. The roles of various structural and material properties are determined via a parametric study. The importance of phase wave speeds and panel impedances for physically symmetric panels is discussed, as are implications for transmission loss characterization. For asymmetric panels it is seen that a relatively thick skin on one side produces some change in the transmission loss.     

Sound transmission across lightweight all-metallic sandwich panels with corrugated cores

The transmission of sound through all-metallic sandwich panels with corrugated cores is investigated using the space-harmonic method. The sandwich panel is modeled as two parallel panels connected by uniformly distributed translational springs and rotational springs, with the mass of the core sheets taken as lumped mass. Based on the periodicity of the panel structure, a unit cell model is developed to provide the effective translational and rotational stiffness of the core. To check the validity of the model, it is used first to study the sound insulation properties of double-panel structures with air cavity, and the analytical predictions agree well with existing experimental data. The model is then employed to quantify the influence of sound incidence angle and the inclination angle between facesheet and core sheet on sound transmission loss （STL） across sandwich panels with corrugated cores. The results show that the inclination angle has a significant effect on STL and it is possible to avoid STL dips by altering the inclination angle. Moreover, it is found that sandwich panels with corrugated cores are more suitable for the insulation of sound waves having small incidence angles.     

Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels

This paper investigates free vibration and dynamic instability of functionally graded cylindrical panels subjected to combined static and periodic axial forces and in thermal environment. Theoretical formulations are based on Reddy's higher order shear deformation shell theory to account for rotary inertia and the parabolic distribution of the transverse shear strains through the panel thickness. Thermal effects due to steady temperature change are included in the analysis. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The panel under current consideration is clamped or simply supported on two straight edges and may be either free, simply supported or clamped on the curved edges. A semi-analytical approach, which takes the advantages of one-dimensional differential quadrature approximation, Galerkin technique and Bolotin's method, is employed to determine the natural frequencies and the unstable regions of the panel. Numerical results for silicon nitride/stainless-steel cylindrical panels are given in both dimensionless tabular and graphical forms. Effects of material composition, temperature rise, panel geometry parameters, and boundary conditions on free vibration and the parametric resonance are also studied.     

Vibration and dynamic stability of a traveling sandwich beam

The vibration and dynamic stability of a traveling sandwich beam are studied using the finite element method. The damping layer is assumed to be linear viscoelastic and almost incompressible. The extensional and shear moduli of the viscoelastic material are characterized by complex quantities. Complex-eigenvalue problems are solved by the state-space method, and the natural frequencies and modal loss factors of the composite beam are extracted. The effects of stiffness and thickness ratio of the viscoelastic and constrained layers on natural frequencies and modal loss factors are reported. Tension fluctuations are the dominant source of excitation in a traveling sandwich material, and the regions of dynamic instability are determined by modified Bolotin's method. Numerical results show that the constrained damping layer stabilizes the traveling sandwich beam.     

Non-destructive inspection of drilled holes in reinforced honeycomb sandwich panels using active thermography

The aerospace industry is in constant need of ever-more efficient inspection methods for quality control. Product inspection is also essential to maintain the safe operation of aircraft components designed to perform for decades. This paper proposes a method for non-destructive inspection of drilled holes in reinforced honeycomb sandwich panels. Honeycomb sandwich panels are extensively employed in the aerospace industry due to their high strength and stiffness to weight ratios. In order to attach additional structures to them, panels are reinforced by filling honeycomb cells and drilling holes into the reinforced areas. The proposed procedure is designed to detect the position of the holes within the reinforced area and to provide a robust measurement of the distance between each hole and the boundary of the reinforced area. The result is a fast, safe and clean inspection method for drilled holes in reinforced honeycomb sandwich panels that can be used to robustly assess a possible displacement of the hole from the center of the reinforced area, which could have serious consequences. The proposed method is based on active infrared thermography, and uses state of the art methods for infrared image processing, including signal-to-nose ratio enhancement, hole detection and segmentation. Tests and comparison with X-ray inspections indicate that the proposed system meets production needs.     

Free vibration of formed sandwich panel

In this paper, the free vibration of prefabricated architectural sandwich panels is studied. The core of the sandwich panel is approximated by finite prisms and the thin faces are modelled by finite strips. The finite prism-strip method is simple to program and saves considerable computing effort when compared with the finite element method. In this paper, only the dynamic characteristics of flat faced homogeneous sandwich panels are compared with results obtained by other methods, and also with the analytical solutions. Several examples are also presented for the free vibration of prefabricated architectural sandwich panels.     

Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation

Free vibration analysis of functionally graded curved panels is carried out using a higher-order formulation. A C⁰ finite element formulation is used to carry out the analysis. The element consists of nine degrees of freedom per node with higher-order terms in the Taylor's-series expansion, which represents the higher-order transverse cross-sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effects of rotary inertia and transverse shear. A realistic parabolic distribution of transverse shear strains through the shell thickness is assumed and the use of shear correction factor is avoided. Material properties are assumed to be temperature independent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Heat conduction between ceramic and metal constituents is neglected. The accuracy of the formulation is validated by comparing the results with those available in the literature. Effects of panel geometry parameters and boundary conditions are studied.     

Vibration analysis and design optimization of viscoelastic sandwich cylindrical shell

Damping properties of viscoelastic sandwich structure can be improved by changing some parameters such as thickness of the layers, distribution of partial treatments, slippage between layers at the interfaces, cutting and its distribution at the top and core layers. Since the optimization problem may result in a thick core layer, for achieving more accuracy a new higher-order Taylor's expansion of transverse and in-plane displacement fields is developed for the core layer of sandwich cylindrical shell in which the displacement fields at the core layer are compatibly described in terms of the displacement fields at the elastic faces. The presented model includes fewer parameters than the previously developed models and therefore decreases the number of degree of freedom in the finite element modeling. The transverse normal stress in the core layer is also considered. The formulations are developed to consider the slippage between layers at the interfaces. Finally, by combining the finite element method and the optimization algorithms based on the genetic algorithm and sequential quadratic programming technique, a design optimization methodology has been formulated to maximize the damping characteristics using the optimal number and location of cuts and partial treatments with optimal thicknesses of top and core layers.     

A finite element model for sandwich viscoelastic beams: Experimental and numerical assessment

Among the passive control systems for attenuation of vibrations in structures, those that use viscoelastic materials as a damping core in laminated-plate-like components are focused herein. In the present work an assessment of a time-domain formulation for numerical modelling of viscoelastic materials is made. This formulation, which is called Golla–Hughes method (GHM), is based on a second-order time-domain realization of Laplace-domain motion equations. The GHM parameters used in the characterization of a viscoelastic material are experimentally determined and a sandwich GHM-based finite element model is presented and validated through numerical comparisons with classic formulation results. Finally, a time-domain simulation of an experimentally tested sandwich beam is carried out.     

PREDICTION AND MEASUREMENT OF SOME DYNAMIC PROPERTIES OF SANDWICH STRUCTURES WITH HONEYCOMB AND FOAM CORES

Some dynamical properties of sandwich beams and plates are discussed. The types of elements investigated are three-layered structures with lightweight honeycomb or foam cores with thin laminates bonded to each side of the core. A six order differential equation governing the apparent bending of sandwich beams is derived using Hamilton's principle. Bending, shear and rotation are considered. Boundary conditions for free, clamped and simply supported beams are formulated. The apparent bending stiffness of sandwich beams is found to depend on the frequency and the boundary conditions for the structure. Simple measurements on sandwich beams are used to determine the bending stiffness of the entire structure and at the same time the bending stiffness of the laminates as well as the shear stiffness of the core. A method for the prediction of eigenfrequencies and modes of vibration are presented. Eigenfrequencies for rectangular and orthotropic sandwich plates are calculated using the Rayleigh-Ritz technique assuming frequency dependent material parameters. Predicted and measured results are compared.