Michael I. Friswell

Finite Element Model Updating in Structural Dynamics

Preface. 1. Introduction. 2. Finite Element Modelling. 3. Vibration Testing. 4. Comparing Numerical Data with Test Results. 5. Estimation Techniques. 6. Parameters for Model Updating. 7. Direct Methods Using Modal Data. 8. Iterative Methods Using Modal Data. 9. Methods Using Frequency Domain Data. 10. Case Study: an Automobile Body M. Brughmans, J. Leuridan, K. Blauwkamp. 11. Discussion and Recommendations. Index.

A Review of Morphing Aircraft

Aircraft wings are a compromise that allows the aircraft to fly at a range of flight conditions, but the performance at each condition is sub-optimal. The ability of a wing surface to change its geometry during flight has interested researchers and designers over the years as this reduces the design compromises required. Morphing is the short form for metamorphose; however, there is neither an exact definition nor an agreement between the researchers about the type or the extent of the geometrical changes necessary to qualify an aircraft for the title ‘shape morphing.’ Geometrical parameters that can be affected by morphing solutions can be categorized into: planform alteration (span, sweep, and chord), out-of-plane transformation (twist, dihedral/gull, and span-wise bending), and airfoil adjustment (camber and thickness). Changing the wing shape or geometry is not new. Historically, morphing solutions always led to penalties in terms of cost, complexity, or weight, although in certain circumstances, these were overcome by system-level benefits. The current trend for highly efficient and ‘green’ aircraft makes such compromises less acceptable, calling for innovative morphing designs able to provide more benefits and fewer drawbacks. Recent developments in ‘smart’ materials may overcome the limitations and enhance the benefits from existing design solutions. The challenge is to design a structure that is capable of withstanding the prescribed loads, but is also able to change its shape: ideally, there should be no distinction between the structure and the actuation system. The blending of morphing and smart structures in an integrated approach requires multi-disciplinary thinking from the early development, which significantly increases the overall complexity, even at the preliminary design stage. Morphing is a promising enabling technology for the future, next-generation aircraft. However, manufacturers and end users are still too skeptical of the benefits to adopt morphing in the near future. Many developed concepts have a technology readiness level that is still very low. The recent explosive growth of satellite services means that UAVs are the technology of choice for many investigations on wing morphing. This article presents a review of the state-of-the-art on morphing aircraft and focuses on structural, shape-changing morphing concepts for both fixed and rotary wings, with particular reference to active systems. Inflatable solutions have been not considered, and skin issues and challenges are not discussed in detail. Although many interesting concepts have been synthesized, few have progressed to wing tunnel testing, and even fewer have flown. Furthermore, any successful wing morphing system must overcome the weight penalty due to the additional actuation systems.

Damage identification using inverse methods

This paper gives an overview of the use of inverse methods in damage detection and location, using measured vibration data. Inverse problems require the use of a model and the identification of uncertain parameters of this model. Damage is often local in nature and although the effect of the loss of stiffness may require only a small number of parameters, the lack of knowledge of the location means that a large number of candidate parameters must be included. This paper discusses a number of problems that exist with this approach to health monitoring, including modelling error, environmental effects, damage localization and regularization.

A combined genetic and eigensensitivity algorithm for the location of damage in structures

Abstract Genetic algorithms have been the subject of considerable interest in recent years, since they appear to provide a robust search procedure for solving difficult problems. Due to the way the genetic algorithm explores the region of interest it avoids getting stuck at a particular local minimum and locates the global optimum. The genetic algorithm is slow in execution and is best applied to difficult problems. This paper applies a genetic algorithm to the problem of damage detection using vibration data. The objective is to identify the position of one or more damage sites in a structure, and to estimate the extent of the damage at these sites. The genetic algorithm is used to optimize the discrete damage location variables. For a given damage location site or sites, a standard eigensensitivity method is used to optimize the damage extent. This two-level approach incorporates the advantages of both the genetic algorithm and the eigensensitivity methods. The method is demonstrated on a simulated beam example and an experimental plate example.

Piezoelectric energy harvesting from broadband random vibrations

Energy harvesting for the purpose of powering low power electronic sensor systems has received explosive attention in the last few years. Most works using deterministic approaches focusing on using the piezoelectric effect to harvest ambient vibration energy have concentrated on cantilever beams at resonance using harmonic excitation. Here, using a stochastic approach, we focus on using a stack configuration and harvesting broadband vibration energy, a more practically available ambient source. It is assumed that the ambient base excitation is stationary Gaussian white noise, which has a constant power-spectral density across the frequency range considered. The mean power acquired from a piezoelectric vibration-based energy harvester subjected to random base excitation is derived using the theory of random vibrations. Two cases, namely the harvesting circuit with and without an inductor, have been considered. Exact closed-form expressions involving non-dimensional parameters of the electromechanical system have been given and illustrated using numerical examples.

Magnetopiezoelastic energy harvesting driven by random excitations

This letter considers a nonlinear piezomagnetoelastic energy harvester driven by stationary Gaussian white noise. The increase in the energy generated by this device has been demonstrated for harmonic excitation with slowly varying frequency in simulation and validated by experiment. This paper considers the simulated response of this validated model to random base excitation and shows that the system exhibits a stochastic resonance. If the variance of the excitation were known then the device may be optimized to maximize the power harvested, even under random excitation.

Crack Modeling for Structural Health Monitoring

There are a number of approaches to the modeling of cracks in beam structures reported in the literature, that fall into three main categories; local stiffness reduction, discrete spring models, and complex models in two or three dimensions. This paper compares the different approaches to crack modeling, and demonstrates that for structural health monitoring using low frequency vibration, simple models of crack flexibility based on beam elements are adequate. This paper also addresses the effect of the excitation for breathing cracks, where the beam stiffness is bilinear, depending on whether the crack is open or closed. Most structural health monitoring methods assume that the structure is behaving linearly, whereas in practice the response will be nonlinear to an extent that varies with the form of the excitation. This paper will demonstrate these effects for a simple beam structure.

Automatic choice of measurement locations for dynamic testing

This paper examines the problem of choosing an optimum set of measurement locations for experimental modal testing and suggests criteria whereby the suitability of the chosen locations can be assessed. Two methods of coordinate selection are used: one based on Guyan reduction and the other on the Fisher information matrix. Each begins with a detailed finite element model of the structure being tested. Both procedures reduce this model by one degree of freedom at a time until the number of degrees of freedom in the reduced model equals the number of measurement locations required. The choice of the eliminated coordinates is generally automatic, and the coordinates of the reduced model are those used for modal testing

Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass

A common energy harvesting device uses a piezoelectric patch on a cantilever beam with a tip mass. The usual configuration exploits the linear resonance of the system; this works well for harmonic excitation and when the natural frequency is accurately tuned to the excitation frequency. A new configuration is proposed, consisting of a cantilever beam with a tip mass that is mounted vertically and excited in the transverse direction at its base. This device is highly non-linear with two potential wells for large tip masses, when the beam is buckled. The system dynamics may include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. The electromechanical equations of motion for this system are developed, and its response for a range of parameters is investigated using phase portraits and bifurcation diagrams. The model is validated using an experimental device with three different tip masses, representing three interesting cases: a linear system; a low natural frequency, non-buckled beam; and a buckled beam. The most practical configuration seems to be the pre-buckled case, where the proposed system has a low natural frequency, a high level of harvested power and an increased bandwidth over a linear harvester.

The relationship between positive position feedback and output feedback controllers

The vibration control of structures may be approached in many ways. Often a robust controller is difficult to design as spillover from modes not considered in the controller design can cause the closed loop system to be unstable. One great advantage of positive position feedback (PPF) control is that the frequency response of the controller rolls off quickly, making the closed loop system robust to spillover. Unfortunately methods to design a PPF controller are not as advanced as other approaches in the control literature. This paper shows that a PPF controller may be formulated as an output feedback controller, and both centralized and decentralized controllers are considered. Optimal control methods are used to demonstrate how control design algorithms for output feedback systems may be used to design PPF controllers. The method is demonstrated using a single-degree-of-freedom system.