The paper explains the advantages of using Lanczos/Schur vectors when performing dynamic analyses of very large models: faster computation of low spectrum eigenproperties, reduced computer storage requirements, increased robustness of test-analysis models, and sensor location by the effective independence method without solving large size eigenproblems.

M. Rade&#x15f;

Application of Lanczos and Schur Vectors in Structural Dynamics

Complex vibrations of cylindrical shells embedded in a temperature field are studied, and the Bubnov-Galerkin method in higher approximations and in the Fourier representation is applied. Both lack and influence of temperature field on the shell dynamics are analyzed.

A.V. Krysko

J. Awrejcewicz

E.S. Kuznetsova

V.A. Krysko

Chaotic Vibrations of Closed Cylindrical Shells in a Temperature Field

This work deals with the application of a nature-inspired optimization technique to solve an inverse problem represented by the identification of an aircraft landing gear model. The model is described in terms of the landing gear geometry, internal volumes and areas, shock absorber travel, tire type, and gas and oil characteristics of the shock absorber. The solution to this inverse problem can be obtained by using classical gradient-based optimization methods. However, this is a difficult task due to the existence of local minima in the design space and the requirement of an initial guess. These aspects have motivated the authors to explore a nature-inspired approach using a method known as LifeCycle Model. In the present formulation two nature-based methods, namely the Genetic Algorithms and the Particle Swarm Optimization were used. An optimization problem is formulated in which the objective function represents the difference between the measured characteristics of the system and its model counterpart. The polytropic coefficient of the gas and the damping parameter of the shock absorber are assumed as being unknown: they are considered as design variables. As an illustration, experimental drop test data, obtained under zero horizontal speed, were used in the non-linear landing gear model updating of a small aircraft.

Felipe A.C. Viana

Valder Steffen Jr.

Marcelo A.X. Zanini

Sandro A. Magalh&#xe3;es

Luiz C.S. G&#xf3;es

Identification of a Non-Linear Landing Gear Model Using Nature-Inspired Optimization

A composite high-aspect-ratio wing of a high-altitude long-endurance (HALE) aircraft was modeled with FEM by MSC/NASTRAN, and the nonlinear static equilibrium state is calculated under design load with follower force effect, but without load redistribution. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the deformed structure are obtained. Planar doublet lattice method is used to calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear results, the nonlinear displacement of the wing tip is higher. The results indicate that the critical nonlinear flutter is of the flap/chordwise bending type because of the chordwise bending having quite a large torsion component, with low critical speed and slowly growing damping, which dose not appear in the linear analysis. Furthermore, it is shown that the variation of the nonlinear flutter speed depends on the scale of the load and on the chordwise bending frequency. The research work indicates that, for the very flexible HALE aircraft, the nonlinear aeroelastic stability is very important, and should be considered in the design progress. Using present FEM software as the structure solver (e.g. MSC/NASTRAN), and the unsteady aerodynamic code, the nonlinear aeroelastic stability margin of a complex system other than a simple beam model can be determined.

Chang Chuan Xie

Jia Zhen Leng

Chao Yang

Geometrical Nonlinear Aeroelastic Stability Analysis of a Composite High-Aspect-Ratio Wing

In the last several years, there has been increasing interest in the use of friction joints for enhancing damping in structures. The joints themselves are responsible for the major part of the energy dissipation in assembled structures. The dissipated work in a joint depends on both the applied normal force and the excitation force. For the case of a constant amplitude excitation force, there is an optimal normal force which maximizes the damping. A &#x2018;passive&#x2019; approach would be employed in this instance. In most cases however, the excitation force, as well as the interface parameters such as the friction coefficient, normal pressure distribution, etc., are not constant. In these cases, a &#x2018;semi-active&#x2019; approach, which implements an active varying normal force, is necessary. For the &#x2018;passive&#x2019; and &#x2018;semi-active&#x2019; approaches, the normal force has to be measured. Interestingly, since the normal force in a friction joint influences the local stiffness, the natural frequencies of the assembled structure can be tuned by adjusting the normal force. Experiments and simulations are performed for a simple laboratory structure consisting of two superposed beams with friction in the interface. Numerical simulation of the friction interface requires non-linear models. The response of the double beam system is simulated using a numerical algorithm programmed in MATLAB which models point-to-point friction with the Masing friction model. Numerical predictions and measurements of the double beam free vibration response are compared. A practical application is then described, in which a friction beam is used to damp the vibrations of the work piece table on a milling machine. The increased damping of the table reduces vibration amplitudes, which in turn results in enhanced surface quality of the machined parts, reduction in machine tool wear, and potentially higher feed rates. Optimal positioning of the friction beams is based on knowledge of the mode shapes, which are obtained from experimental modal analysis. The modal damping and the natural frequencies for the two dominant modes are measured for several combinations of excitation force and normal force.

L. Gaul

J. Roseira

J. Becker

Structural Damping with Friction Beams

The objective of this article is to propose decision indicators to guide the analyst in the optimal definition of an ensemble of superelements in a complex structural assembly. These indicators are constructed based on comparisons between the unreduced physical model and the approximate solution provided by a nominally reduced superelement model. First, the low contribution substructure slave modes are filtered. Then, the minimum dynamical residual expansion is used to localize the superelements which are the most responsible for the response prediction errors. Moreover, it is shown that static residual vectors, which are a natural result of these calculations, can be included to represent the contribution of important truncated slave modes and consequently correct the deficient superelements. The proposed methodology is illustrated on a subassembly of an aeroengine model.

B. Dupont

E. Pillet

S. Cogan

Superelement Verification in Complex Structural Models

The presence of a crack in a structure modifies the energy dissipation pattern. As a consequence, damaged structures can present high localized damping. Experimental tests have revealed that crack nucleation and growth increase structural damping which makes this phenomenon useful as a damage locator. This paper examines the energy flow patterns caused by localized damping in rods, beams and plates using the Energy Finite Element Method (EFEM), the Spectral Element Method (SEM) and the Energy Spectral Element Method (ESEM) in order to detect and locate damage. The analyses are performed at high frequencies, where any localized structural change has a strong influence in the structural response. Simulated results for damage detection in rods, beams, and their couplings calculated by each method and using the element loss factor variation to model the damage, are presented and compared. Results for a simple thin plate calculated with EFEM are also discussed.

E.R.O. Santos

V.S. Pereira

J.R.F. Arruda

J.M.C. Dos Santos

Structural Damage Detection Using Energy Flow Models

The identification of the rigid body properties of a structure is an important matter in various structural dynamic applications, namely in structural modification (coupling/uncoupling), optimization and vibration control. In most situations, the experimental route is the only via to obtain the desired dynamic properties. This goal is achieved by an inverse process which starts from the measurement of Frequency Response Functions (FRFs) and ends on matrices describing the mass distribution of a rigid body.The objective of the present article is the evaluation and comparison of the performance of three different kinds of identification methods that share a common characteristic &#x2013; they all use FRFs as inputs to the inverse process. One of them, the Inertia Restraint Method (IRM) makes use of the accelerance FRF (information condensed at zero frequency), while the other two methods make use of receptance FRFs as inputs, although in different manners; in one of them the properties are evaluated directly from the measurement data &#x2013; Direct Physical Parameter Identification Method (DPPIM) &#x2013; whereas the other type requires a modal identification procedure as an intermediate step &#x2013; Modal Method (MM). An actual experimental structure forms the case study to illustrate the performance of the three different techniques.

R.A.B. Almeida

A.P.V. Urgueira

N.M.M. Maia

Evaluation of the Performance of Three Different Methods Used in the Identification of Rigid Body Properties

With dynamic testing, engineers describe activities focused on the identification of some properties of vibrating structures. This step requires for the measurements of excitations and responses signals, applying appropriate sensors directly on the test article. These instruments modify the system's mass and stiffness distributions and eventually the eigen-properties of the structure. These errors become unacceptable especially when testing lightweight structures. This paper shows the results of some tests performed on a small compressor with the purpose of identifying the blades&#x2019; natural frequencies and modes. It compares the acquisitions performed with standard accelerometers and two different contact-less systems using as exciters either a micro-hammer or a micro inertial shaker. The paper shows how the contact-less sensors provide good quality data and consistent results in the mode identification phase.

L. Bregant

M. Bressanutti

Optical Fibres Contactless Sensor for Dynamic Testing of Lightweight Structures

Modeling beam reinforced thin plates at mid and high frequencies through the most commonly used methods such as finite and boundary element methods frequently leads to unsatisfactory results, since the accuracy of these methods depends on the relation between the dimensions of the elements in which the structure was discretized and the wavelength. Due to this characteristic, the modeling using these techniques will require that the size of the elements becomes smaller as the frequency increases, while its number needs to be increased. For structures that are usual in some areas, like the aerospace industry, this will be possible only with an unreasonable computational effort, which is responsible for restricting the use of these methods practically to low-frequency applications. Semi-analytical methods such as the spectral element method do not need mesh refinement at higher frequencies, but they were very limited in the geometries and boundary conditions that can be treated. This paper presents a spectral element for rectangular thin plates reinforced symmetrically along the sides with Euler beams, which can be used to model plates with arbitrary boundary conditions. The method was verified by comparing its results with those obtained from a Finite Element model.

N.B.F. Campos

On the Modeling of Beam Reinforced Thin Plates Using the Spectral Element Method

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;

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Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.

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