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Wave Propagation in Two-Dimensional Structures Using a Wave/Finite Element Technique
No full textISVR Technical Memorandum No. 96
VIBROACOUSTIC CHARACTERISTICS OF DAMPED LAMINATED SHELLS AND PANELS
No full textLaminated panels are being used increasingly widely in automotive applications because of their high strength-to-weight ratio compared to metallic materials. Their use in lightweight vehicles is thus beneficial in terms of emissions, but raises issues for noise and
vibration performance. Modelling and design of laminated panels with complex layups is much more demanding than for more conventional structures, and damping effects are often neglected. In this paper the vibroacoustic characteristics of damped laminated panels
are investigated in terms of wave propagation, energy flow and loss factor showing some significant effects of damping. In particular a formulation of the complex Poynting’s vector and an expression to evaluate the energy velocity for the general case of a viscoelastic anisotropic panel is obtained using a finite element model of just a small segment of the laminated panel. A numerical example concerning a curved viscoelastic laminated panel is shown in order to illustrate some results
Mode veering in weakly coupled systems
No full textThe phenomenon of mode veering occurs in systems with a varying parameter. As the parameter varies, so do the natural frequencies. When two natural frequencies approach each other they often veer apart, instead of crossing. The veering is accompanied by rapid variations in the eigenvectors. This phenomenon is analysed in this paper with the focus being on weakly coupled systems of modes or oscillators. The system has any number of degrees of freedom or modes. The system is defined to be uncoupled when the motion in all but one of the modes is blocked. A small stiffness, mass or gyroscopic parameter is assumed to couple the uncoupled-blocked modes. The natural frequencies of the uncoupled system depend on the variable parameter and can cross at certain critical frequencies. The natural frequencies of the coupled system are seen to veer at these critical frequencies in the presence of arbitrarily small coupling, with the eigenvectors rotating and swapping from one branch to another. The separation of the branches around the critical frequencies is seen to depend on the coupling parameter. Examples including a 2 degree of freedom system, a multi-degree of freedom system and a plate with an attached variable oscillator are presented to illustrate the results
Dispersion phenomena in coupled waveguides: veering, locking and strong coupling effects
No full textThe dispersion curves describe wave propagation in a structure. There might be a number of branches at a given frequency, each representing a wave mode. In complicated structures it is often tempting to interpret the dispersion curves in terms of waves in simpler structures. For example, waves in a fluid-filled cylinder might be interpreted as axial, bending or torsion waves in the in vacuo cylinder, or fluid waves in a rigid walled cylinder. The simpler wave modes are coupled in the real structure leading to complicated dispersion phenomena. This paper characterises these phenomena in general terms and discusses the circumstances under which they occur. Some are well known: propagating, evanescent and oscillatory attenuating waves, for which the wavenumber is real, imaginary or complex respectively, and cut-off of waves at some frequency. In more complicated structures weak coupling phenomena arise when branches of the dispersion curves interact. These occur in the vicinity of the frequency at which the dispersion curves in the uncoupled waveguides would cross: if two dispersion curves (representing either propagating or evanescent waves) come close together as frequency increases then the curves either veer apart or lock together, forming a pair of attenuating oscillatory waves, which may later unlock into a pair of either propagating or evanescent waves. Which phenomenon occurs depends on the product of the gradients of the dispersion curves. The wave mode shapes which describe the deformation of the structure under the passage of a wave change rapidly around this critical frequency. Other phenomena can be attributed to strong coupling effects, where arbitrarily light coupling changes the qualitative nature of the dispersion curves, and in particular the change from a pair of propagating or evanescent waves to evanescent or oscillatory attenuating waves. These effects are analysed, quantified, discussed and illustrated with examples. Copyright © (2011) by the International Institute of Acoustics & Vibration
Dynamic and acoustic properties of visco-elastic laminated structures using a Wave Finite Element method.
No full textNumerical computation of wave characteristics in composite laminated structures is obtained using a Wave Finite Element (WFE) method. The technique involves developing a valid FE model of a small segment of the structure, typically using a commercial FE package, and post-processing the system matrices numerically using the theory of wave propagation in periodic structures. The method is briefly described. Viscoelasticity and pre-stress are taken into account, and some of their effects on complex dispersion curves, group velocity, energy velocity, and global loss factor are shown and briefly discussed. An energy balance formulation, obtained from the complex Poynting’s theorem, and an expression to evaluate the energy velocity for the general case of viscoelastic anisotropic panels are also provided and discussed. Numerical examples concerning a curved sandwich panel are presented
Estimation of the loss factor of viscoelastic laminated panels from finite element analysis
No full textA wave finite element (WFE) method is applied for predicting wave dispersion, wave attenuation and dissipation in viscoelastic laminated panels. The method involves postprocessing (using periodic structure theory) of element matrices of a small segment of the structure, which is modelled using a stack of three dimensional finite elements meshed through the cross-section. Each layer can be discretised using either one solid element or more solid elements in order to more accurately represent interlaminar stress and strain. The finite element model of the segment of the structure is typically very small, resulting in very small computation cost. Formulations for the evaluation of the global loss factor using the WFE approach are given. In particular a formulation to calculate the average loss factor in the general case of an anisotropic component is proposed. Numerical examples are then shown. These concern the evaluation of the dispersion curves and of the global loss factor for damped laminated panels of different constructions
Modelling the Dynamics of Laminated Panels Using a Wave and Finite Element Method
No full textThe use of laminated panels is increasing because they are stiff, light and offer the engineer flexibility in design. Constructions include composite laminates with various stacking sequences, foam cores, viscoelastic layers etc. The generality and complexity of construction raises issues regarding modelling their dynamics and optimising their design. In this paper a wave and finite element (WFE) method for modelling the dynamic behaviour of plane and axisymmetric laminated structures is described. A small segment of the structure is modelled using conventional finite element (FE) methods, usually using a commercial package. This typically involves a stack of solid elements meshed through the thickness, allowing the shear distribution, in particular in soft layers, to be correctly represented. The mass and stiffness matrices are found, periodicity conditions applied, and an eigenvalue problem solved to find the dispersion relations and hence the characteristics of wave propagation, attenuation and damping. The frequency dependence of viscoelastic material properties and pre-stress can be taken into account straightforwardly. A hybrid FE/WFE approach to determining transmission characteristics of joints is described. Numerical examples are presented, including
anisotropic, plane and cylindrical foam-cored laminate sandwich constructions with pre-stress. The method is simple in application, provides accurate results at low computational cost and is a valuable tool for evaluating the vibroacoustic behaviour of multi-layer panels and optimising their design
The loss-factor of pre-stressed laminated curved panels and cylinders using a Wave and Finite Element method
No full textIn this paper a Wave and Finite Element (WFE) post-processing technique is applied to predict the effects of pre-stress on the damping of curved panels. It is seen that pre-stress substantially reduces the global loss factor, especially of those modes of vibration which involve considerable radial displacement. This is particularly significant for aerospace structures since ground-test results typically do not include pre-loads. The WFE approach and its extension to include pre-stress effects are briefly described. Numerical examples concerning a pressurised viscoelastic cylinder and a pre-loaded curved laminated panel are presented
Calculation of coupling loss factors using a hybrid finite element/wave and finite element approach
No full textThe vibration of built-up structures at higher frequencies can be analysed using energy based methods such as the Statistical Energy Analysis (SEA). Central to SEA is the calculation of the coupling loss factors (CLFs) between the subsystems. This can be difficult, for example when complex joints connect wave-bearing substructures of complicated constructions (laminates, truss cored or sandwiched panels, etc.). In this paper, we present a hybrid finite element/ wave and finite element approach for predicting these CLFs. Each substructure is modelled using the wave and finite element (WFE) method where a small segment of the structure is modelled using standard finite element (FE) techniques and then periodic structure theory is used to predict the wave characteristics of the substructure. The propagating waves in the substructure are treated as SEA subsystems. The joint is modelled using standard FEs, and the joint FE model is coupled with the WFE models of the substructures to yield the scattering properties of the joint. These can then be used to predict the diffuse field transmission efficiency and CLFs between the various subsystems. The strength of the approach is two-fold. First, the substructures and joints can be arbitrarily complicated. Second, the full power of existing FE libraries/packages can be used to obtain the WFE models of the substructures and the FE model of the joint. Numerical examples are presented to illustrate the approach
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