Structural-Acoustic Optimization of Sandwich Panels

Sandwich panels, comprising face sheets enclosing a core, are increasingly common structural elements in a variety of applications, including aircraft fuselages and flight surfaces, vehicle panels, lightweight enclosures, and bulkheads. The design flexibility associated with such composite structures provides significant opportunities for tailoring the structure to the load and dynamic response requirements for the particular application. Design flexibility encompasses the details of the face sheets and the core. This paper deals with the numerical optimization of different sandwich configurations for the purposes of achieving reduced structural acoustic response. Laminated face sheets and core geometries, comprising honeycomb and truss-like structures, are considered. The relative importance of the mass and stiffening properties of the core and face sheets are discussed. The optimization work is carried out using commercial codes. Benefits and limits of using an optimization algorithm based on gradient methods are highlighted.

A Probabilistic Analysis for Static and Dynamic Frequency of Blade With Uncertain Boundary Conditions

A probabilistic analysis method is developed for frequencies analysis of turbine blade with uncertain boundary condition at the root of blade. The Ritz method is used to derive the eigenvalues equation of the rotating blade with uncertain root boundary condition. The matrix perturbation technique is employed for the probabilistic analysis to obtain the deterministic part of natural frequencies and vibration modes, the sensitivity matrix, the covariance matrix and the coefficient of variance (COV) for the natural frequencies. The effects of variations in the expectation and the variance of joint stiffness on the expectation and the variance of the natural frequencies are investigated.

Order-Tuned Vibration Absorbers for Cyclic Rotating Flexible Structures

This paper investigates the use of order-tuned absorbers to attenuate vibrations of flexible blades in a bladed disk assembly subjected to engine order excitation. The blades are modeled by a cyclic chain of N oscillators, and a single vibration absorber is fitted to each blade. These absorbers exploit the centrifugal field arising from rotation so that they are tuned to a given order of rotation, rather than to a fixed frequency. A standard change of coordinates based on the cyclic symmetry of the system essentially decouples the governing equations of motion, yielding a closed form solution for the steady-state response of the overall system. These results show that optimal reduction of blade vibrations is achieved by tuning the absorbers to the excitation order n, but that the resulting system is highly sensitive to small perturbations. Intentional detuning (meaning that the absorbers are slightly over- or under-tuned relative to n) can be implemented to improve the robustness of the design. It is shown that by slightly undertuning the absorbers there are no system resonances near the excitation order of interest and that the resulting system is robust to mistuning (i.e., small random uncertainties in the system parameters) of the absorbers and/or blades. These results offer a basic understanding of the dynamics of a bladed disk assembly fitted with order-tuned vibration absorbers, and serve as a first step to the investigation of more realistic models, where, for example, imperfections and nonlinear effects are considered, and multi-DOF and general-path absorbers are employed.

Multi Mode Vibration Control and Broder Band Motion Control of Three Dimensional Shaking Table

This paper deals with a new system design method for motion and vibration control of a three-dimensional flexible shaking table. An integrated modeling and controller design procedure for flexible shaking table system is presented. An experimental three-dimensional shaking table is built. “Reduced-Order Physical Model” procedure is adopted. A state equation system model is composed and a feedback controller is designed by applying LQI control law to achieve simultaneous motion and vibration control. Adding a feedforward, two-degree-of-freedom control system is designed. Computer simulations and control experiments are carried out and the effectiveness of the presented procedure is investigated. The robustness of the system is also investigated.

Optimizing Distributed-Contact Friction in Ring Dampers

This paper describes the vibration analysis and optimization of a base structure and a beam-like attached damper sub-system that couple in vibration through distributed-contact friction damping. The objective is to tune the characteristics of the damper sub-system to maximize energy dissipation, and therefore to control vibration of the base structure. Applications of the concept to noise and vibration phenomena associated with automotive disk brake rotors are discussed. Per-cycle energy dissipation is examined as a function of damper preload for two classes of sub-systems: dampers that are split rings, and dampers that are continuous rings. End-effects and the manner in which energy dissipation is distributed spatially along the damper are also discussed. Of potential technological application, for a given excitation frequency, the damper sub-system’s design can be optimized to reduce vibration of the base structure.

Railway Bridges Identification Techniques

Output-only methodologies are nowadays well established to extract modal parameters in many areas of engineering, such as civil, mechanical and aeronautical. In the past, civil engineering tests have been mainly developed for road bridges, with the vehicle passage over the bridge deck representing the main source of excitation with some contribution given by the ambient noise. In the road bridge cases, the excitation is considered to be a function of the road surface roughness, the vehicles speed, the weight and suspension vehicles characteristics, and also the random access of the vehicles over the bridge, whilst for the railway case, not all these issues are correctly addressed, and other characteristics rise-up, possibly advantageous for a correct identification process; to demonstrate this statement, we can bear in mind how the random access of the vehicles becomes meaningless for railway bridges, the single train being a quasi deterministic source; furthermore, the influence of the train weight should be considered if compared to usual road vehicles. Since output-only techniques are conceived for random excitation noise, their use in these conditions is considerably stressed and special care, or alternative techniques, has to be considered to avoid errors. In this sense, the bridge reference model becomes more important and some special techniques have to be developed.

Model Updating Using a Quadratic Form

The paper presents a method for model updating, called Quadratic Compression Method (QCM). The updated model has a fixed structure with some free parameters. Algebraic manipulations of the eigenvalue equation lead to a simplified equation with a lower dimension. This equation is then solved in a Least Squares sense. The method is shown to belong to the class of Minimization of the Error in the Characteristic Equation (MECE), with a particular choice of the weighting matrix. The paper presents also a weighted version of the method, called WQCM, which is motivated by reducing the effect of measuring noise. In addition to the theoretic analysis, the superior robustness to noise properties of QCM and WQCM are demonstrated by simulations and experimentally.

Random Loads Fatigue: The Use of Spectral Methods Within Multibody Simulation

The evaluation of the fatigue damage performed by using the Power Spectral Density function (PSD) of stress and strain state is proving to be extremely accurate for a family of random processes characterized by the property of being stationary. The present work’s original contribution is the definition of a methodology which extracts stress and strain PSD matrices from components modelled using a modal approach (starting from a finite element modelling and analysis) within mechanical systems modelled using multibody dynamic simulation and subject to a generic random load (i.e. multiple-input, with partially correlated inputs). This capability extends the actual stress evaluation scenario (principally characterised by the use of finite element analysis approach) to the multibody dynamic simulation environment, more powerful and useful to simulate complex mechanical systems (i.e. railway, automotive, aircraft and aerospace systems). As regards the fatigue damage evaluation, a synthesis approach to evaluate an equivalent stress state expressed in terms of the PSD function of Preumont’s “equivalent von Mises stress (EVMS)”, starting from the complete stress state representation expressed in terms of PSD stress matrix and easily usable in the consolidated spectral methods, is proposed. This approach allows and has allowed the use of the above methods such as the Dirlik formula as a damage evaluation method. An additional result is the conception and implementation of a frequency domain method for the component’s most probable state of stress, allowing quickly identification of the most stressed and damageble locations. The described methodologies were developed and embedded into commercial simulation codes and verified by using as a test case a simple reference multibody model with a simple flexible component.

Machine Fault Detection Using Genetic Programming

Applications of genetic programming (GP) include many areas. However applications of GP in the area of machine condition monitoring and diagnostics is very recent and yet to be fully exploited. In this paper, a study is presented to show the performance of machine fault detection using GP. The time domain vibration signals of a rotating machine with normal and defective gears are processed for feature extraction. The extracted features from original and preprocessed signals are used as inputs to GP for two class (normal or fault) recognition. The number of features and the features are automatically selected in GP maximizing the classification success. The results of fault detection are compared with genetic algorithm (GA) based artificial neural network (ANN)- termed here as GA-ANN. The number of hidden nodes in the ANN and the selection of input features are optimized using GAs. Two different normalization schemes for the features have been used. For each trial, the GP and GA-ANN are trained with a subset of the experimental data for known machine conditions. The trained GP and GA-ANN are tested using the remaining set of data. The procedure is illustrated using the experimental vibration data of a gearbox. The results compare the effectiveness of both types of classifiers with GP and GA based selection of features.

Non-Linear Dynamic Analysis of a Cable-Stayed Beam

The dynamic behaviour of a simple clamped beam suspended at the other end by an inclined cable stay is surveyed in this paper. The sag due to the cable weight, as well as the non-linear coupling between the cable and the beam motions are taken into account. The formulation for in-plane vibration follows closely that of Gattulli et al. [1] and confirms their findings for the overall features of the equations of motion and the system modal properties. A reduced non-linear mathematical model, with two degrees of freedom, is also developed, following again the steps of Gattulli and co-authors [2,3]. Hamilton’s Principle is evoked to allow for the projection of the displacement field of both the beam and the cable onto the space defined by the first two modes, namely a “global” mode (beam and cable) and a “local” mode (cable). The method of multiple scales is then applied to the analysis of the reduced equations of motion, when the system is subjected to the action of a harmonic loading. The steady-state solutions are characterised in the case of internal resonance between the local and the global modes, plus external resonance with respect to either one of the modes considered. A numerical application is presented, for which multiple-scale results are compared with those of numerical integration. A reasonable qualitative and quantitative agreement is seen to happen particularly in the case of external resonance with the higher mode. Discrepancies should obviously be expected due to strong non-linearities present in the reduced equations of motion. That is specially the case for external resonance with the lower mode.