The vibro-acoustic analysis of built-up systems using a hybrid method with parametric and non-parametric uncertainties

An existing hybrid finite element (FE)/statistical energy analysis (SEA) approach to the analysis of the mid- and high frequency vibrations of a complex built-up system is extended here to a wider class of uncertainty modeling. In the original approach, the constituent parts of the system are considered to be either deterministic, and modeled using FE, or highly random, and modeled using SEA. A non-parametric model of randomness is employed in the SEA components, based on diffuse wave theory and the Gaussian Orthogonal Ensemble (GOE), and this enables the mean and variance of second order quantities such as vibrational energy and response cross-spectra to be predicted. In the present work the assumption that the FE components are deterministic is relaxed by the introduction of a parametric model of uncertainty in these components. The parametric uncertainty may be modeled either probabilistically, or by using a non-probabilistic approach such as interval analysis, and it is shown how these descriptions can be combined with the non-parametric uncertainty in the SEA subsystems to yield an overall assessment of the performance of the system. The method is illustrated by application to an example built-up plate system which has random properties, and benchmark comparisons are made with full Monte Carlo simulations. © 2012 Elsevier Ltd. All rights reserved.

Vibration of a high-altitude tethered balloon with application to climate engineering

A balloon tethered at an altitude of 20 km could deliver a particulate cloud leading to global cooling. Tethering a balloon at this altitude poses significant problems with respect to vibration and stability, especially in regions of high wind. No-one has ever proposed, yet alone launched, a balloon at an altitude of 20 km tethered to the ground. Owing to wind, the tether needs to be 23 km in length and is to be fixed to a ship at sea or on land in equatorial regions. Whilst the balloon at 20 km is subject to relatively modest wind conditions, at jet stream altitudes (10km) the tether will experience much higher wind loadings, not only because of the high wind speeds of up to 300 km / hr but also because of the high air density. A tether of circular cross section in these high winds will be subject to horizontal and downward drag forces that would bring the aerostat down. For this reason it is advantageous to consider a self-aligning tether of an aerodynamic cross section whereby it is possible to reduce the drag substantially. One disadvantage of a non-circular tether is the possibility of flutter and galloping instabilities. It is reasonably straightforward to model these phenomena for short lengths of aerofoil, but the situation becomes more complex for a 20 km tensioned tether with large deflection and curvature, variable wind speed, variable air density and variable tension. Analysis using models of infinite length are used to establish the stability at a local scale where the tension, aerodynamic and geometric properties are considered constant. Dispersion curve analysis is useful here. But for dynamics on a long-wavelength scale (several km) then a full non-linear analysis is required. This non-linear model can be used to establish the local values of tension appropriate for the dispersion analysis. This keynote presentation will give some insight into these issues.

Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. © 2009 Society for Industrial and Applied Mathematics.

Friction-induced vibration: Model development and comparison with large-scale experimental tests

This paper presents a comparison between theoretical predictions and experimental results from a pin-on-disc test rig exploring friction-induced vibration. The model is based on a linear stability analysis of two systems coupled by sliding contact at a single point. Predictions are compared with a large volume of measured squeal initiations that have been post-processed to extract growth rates and frequencies at the onset of squeal. Initial tests reveal the importance of including both finite contact stiffness and a velocity-dependent dynamic model for friction, giving predictions that accounted for nearly all major clusters of squeal initiations from 0 to 5 kHz. However, a large number of initiations occurred at disc mode frequencies that were not predicted with the same parameters. These frequencies proved remarkably difficult to destabilise, requiring an implausibly high coefficient of friction. An attempt has been made to estimate the dynamic friction behaviour directly from the squeal initiation data, revealing complex-valued frequency-dependent parameters for a new model of linearised dynamic friction. These new parameters readily destabilised the disc modes and provided a consistent model that could account for virtually all initiations from 0 to 15 kHz. The results suggest that instability thresholds for a wide range of squeal-type behaviour can be predicted, but they highlight the central importance of a correct understanding and accurate description of dynamic friction at the sliding interface. © 2013 Elsevier Ltd. All rights reserved.

Vibration decay along deepwater moorings with complex geometry and configuration, as a tool for truncation

This paper is concerned with the difficulties in model testing deepwater structures at reasonable scales. An overview of recent research efforts to tackle this challenge is given first, introducing the concept of line truncation. Passive truncation has traditionally been the preferred method by industry; however, these techniques tend to suffer in capturing accurately line dynamic response and so reproducing peak tensions. In an attempt to improve credibility of model test data the proposed truncation procedure sets up the truncated model, based on line dynamic response rather than quasi-static system stiffness. Vibration decay of transverse elastic waves due to fluid drag forces is assessed and it is found that below a certain length criterion, the transverse vibrational characteristics for each line are inertia driven, hence with respect to these motions the truncated model can assume a linear damper whose coefficient depends on the local line properties and vibration frequency. Initially a simplified taut string model is assumed for which the line is submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a general guideline for the truncation length criterion, which is suitable for any kind of line with any top motion. The focus of this paper is to extend this work to a more complex line configuration of a conventional deepwater mooring line and so enhance the generality of the truncation guideline. The paper will close with an example case study of a spread mooring system, applying this method to create an equivalent numerical model at a reduced depth that replicates exactly the static and dynamic characteristics of the full depth system. Copyright © 2012 by ASME.

Directly and parametrically excited bi-stable vibration energy harvester for broadband operation

Despite many recent advances, the wide-spread adoption of vibrational energy harvesting has been limited by the low levels of generated output power and confined operational frequency band. Recent work by the authors on parametrically excited harvesters has demonstrated over an order of magnitude power improvement. This paper presents an investigation into the simultaneous employment of both direct and parametric resonance, as well as the incorporation of bi-stability, in an attempt to further improve the mechanical-to-electrical energy conversion efficiency by broadening the output power spectrum. Multiple direct and parametric resonant peaks from a multi-degree-of-freedom system were observed and an accumulative ∼10 Hz half-power bandwidth was recorded for the first 40 Hz. Real vibration data was also employed to analysis the rms power response effectiveness of the proposed system. © 2013 IEEE.

Efficient parametric uncertainty analysis within the hybrid Finite Element/Statistical Energy Analysis method

This paper is concerned with the development of efficient algorithms for propagating parametric uncertainty within the context of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) approach to the analysis of complex vibro-acoustic systems. This approach models the system as a combination of SEA subsystems and FE components; it is assumed that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. The method has been recently generalised by allowing the FE components to possess parametric uncertainty, leading to two ensembles of uncertainty: a non-parametric one (SEA subsystems) and a parametric one (FE components). The SEA subsystems ensemble is dealt with analytically, while the effect of the additional FE components ensemble can be dealt with by Monte Carlo Simulations. However, this approach can be computationally intensive when applied to complex engineering systems having many uncertain parameters. Two different strategies are proposed: (i) the combination of the hybrid FE/SEA method with the First Order Reliability Method which allows the probability of the non-parametric ensemble average of a response variable exceeding a barrier to be calculated and (ii) the combination of the hybrid FE/SEA method with Laplace's method which allows the evaluation of the probability of a response variable exceeding a limit value. The proposed approaches are illustrated using two built-up plate systems with uncertain properties and the results are validated against direct integration, Monte Carlo simulations of the FE and of the hybrid FE/SEA models. © 2013 Elsevier Ltd.

Wave dispersion and power flow analysis of an infinite aerofoil-shaped beam

Classic flutter analysis models an aerofoil as a two degree-of-freedom rigid body supported by linear and torsional springs, which represent the bending and torsional stiffness of the aerofoil section. In this classic flutter model, no energy transfer or dissipation can occur in the span-wise direction of the aerofoil section. However, as the aspect ratio of an aerofoil section increases, this span-wise energy transfer - in the form of travelling waves - becomes important to the overall system dynamics. This paper extends the classic flutter model to include travelling waves in the span-wise direction. Namely, wave dispersion and power flow analysis of an infinite, aerofoil-shaped beam, subject to bending, torsion, tension and a constant wind excitation, is used to investigate the overall system stability. Examples of potential applications for these high aspect ratio aerofoil sections include high-altitude balloon tethers, towed cables, offshore risers and mooring lines.

Hopping robot based on free vibration of an elastic curved beam

This study presents a novel approach to the design of low-cost and energy-efficient hopping robots, which makes use of free vibration of an elastic curved beam. We found that a hopping robot could benefit from an elastic curved beam in many ways such as low manufacturing cost, light body weight and small energy dissipation in mechanical interactions. A challenging problem of this design strategy, however, lies in harnessing the mechanical dynamics of free vibration in the elastic curved beam: because the free vibration is the outcome of coupled mechanical dynamics between actuation and mechanical structures, it is not trivial to systematically design mechanical structures and control architectures for stable locomotion. From this perspective, this paper investigates a case study of simple hopping robot to identify the design principles of mechanics and control. We developed a hopping robot consisting of an elastic curved beam and a small rotating mass, which was then modeled and analyzed in simulation. The experimental results show that the robot is capable of exhibiting stable hopping gait patterns by using a small actuation with no sensory feedback owing to the intrinsic stability of coupled mechanical dynamics. Furthermore, an additional analysis shows that, by exploiting free vibration of the elastic curved beam, cost of transport of the proposed hopping locomotion can be in the same rage of animals' locomotion including human running. © 2011 IEEE.