1,721,020 research outputs found
Effect of pre-stress on the global loss factor of viscoelastic laminated curved panels and cylinders.
No full textAxially Moving Beams with Varying Length: Wave Reflection and Propagation Approach
No full textThe present paper analyses the dynamic of a clamped-free beam with axially transport of mass and varying length. The transverse vibration of the beam is described in term of harmonic propagating and decaying waves in dispersive medium. Reflection and propagation matrices for non-homogeneous and time-varying boundary conditions are given and a simple model that capture the dynamic behaviour of the system is defined. The analysis has proved that this method could be a valuable choice to gain important and concise results such as continuous change in the frequencies with time, increase or decrease of the transverse deformed shapes, energy evaluation within the domain with respect to the time. Eventually, an approximate formula to compute the continuous change in the natural frequencies together with investigations about the nature of the time rate of change of the vibrational energy are provided
Modelling moving one-dimensional waveguides using waves and finite element analysis
No full textOne approach to the numerical analysis of complex waveguides is the Wave Finite Element (WFE) method. In this method conventional Finite Elements (FEs) are used to discretise a small segment of a waveguide. The FE model of just this small part of the structure is post-processed using periodicity conditions, and an eigenproblem is then solved to predict dispersion characteristics and wavemodes. Once the wave characteristics are predicted, free vibration and response of the structure as a whole can be modelled in terms of these waves. This paper presents an extension of the method to moving one-dimensional waveguides. In particular an axially moving beam is considered. The FE formulation of a moving beam element is
developed and the WFE method is applied to find the wave properties of such a beam. Natural frequencies are obtained using the Phase Closure Principle and the Dynamic Stiffness Matrix, both formulated in terms of wavemodes and dispersion relation obtained from the WFE eigenproblem. The analytical equation of transverse motion of the travelling beam is also solved in terms of propagating and decaying waves, and the frequency equation is obtained using the phase closure principle. Numerical results are shown
Further developments of the System Equivalent Reduction Expansion Process for Finite Element Models validation of spacecrafts
No full textReduction of large size Finite Element models is a common technique in dynamic analysis. In particular validation of Finite Element models requires comparison between the FE model and the experimental data usually carried out using the Modal Assurance Criteria or Cross Orthogonality Checks. This is particularly true in space industry, where the FE model of a satellite has several hundreds of thousand of Degrees of Freedoms (DOFs), while experimental data, which can be acquired at a limited number of locations, typically correspond to a few hundred of DOFs. The System Equivalent Reduction Process (SEREP) technique has been identified as a particularly suitable method for spacecraft FE models. However, the reduced system matrices obtained using SEREP can be rank deficient, which limits the use of the reduced model for further analysis (e.g. forced response modelling). The present paper shows an alternate form of the SEREP technique in order to overcome this issue. The method is described and a numerical example, using data from the FE model of the Aeolus satellite, is provided in order to show the robustness and suitability of the proposed methodology
Veering and Strong Coupling Effects in Structural Dynamics
No full textMode veering is the phenomenon associated with the eigenvalue loci for a system with a variable parameter: Two branches approach each other and then rapidly veer away and diverge instead of crossing. The veering is accompanied by rapid variations in the eigenvectors. In this paper, veering in structural dynamics is analyzed in general terms. First, a discrete conservative model with stiffness, mass, and/or gyroscopic coupling is considered. Rapid veering requires weak coupling: if there is instead strong coupling then there is a slow evolution of the eigenvalue loci rather than rapid veering. The uncoupled-blocked system is defined to be that where all degrees-of-freedom (DOFs) but one are blocked. The skeleton of the system is the loci of the eigenvalues of the uncoupled-blocked system as the variable parameter changes. These loci intersect at certain critical points in the parameter space. Following a perturbation analysis, veering is seen to comprise rapid changes of the eigenvalues in small regions of the parameter space around the critical points: for coupling terms of order u veering occurs in a region of order u around the critical points, with the rate of change of eigenvalues being of order iuâ '1. This is accompanied by rapid rotations in the eigenvectors. The choice of coordinates in the model and application to continuous systems is discussed. For nonconservative systems, it is seen that veering also occurs under certain circumstances. Examples of 2DOFs, multi-DOFs (MDOFs), and continuous systems 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
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
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