The use of spatial impulse responses to characterise flexible forming processes with mobile tools

A novel test method for the characterisation of flexible forming processes is proposed and applied to four flexible forming processes: Incremental Sheet Forming (ISF), conventional spinning, the English wheel and power hammer. The proposed method is developed in analogy with time-domain control engineering, where a system is characterised by its impulse response. The spatial impulse response is used to characterise the change in workpiece deformation created by a process, but has also been applied with a strain spectrogram, as a novel way to characterise a process and the physical effect it has on the workpiece. Physical and numerical trials to study the effects of process and material parameters on spatial impulse response lead to three main conclusions. Incremental sheet forming is particularly sensitive to process parameters. The English wheel and power hammer are strongly similar and largely insensitive to both process and material parameters. Spinning develops in two stages and is sensitive to most process parameters, but insensitive to prior deformation. Finally, the proposed method could be applied to modelling, classification of existing and novel processes, product-process matching and closed-loop control of flexible forming processes. © 2012 Elsevier B.V.

Transient response of structures with uncertain properties to nonlinear shock loading

A method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading. The displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself, expressed in terms of a nonlinear Hertzian contact stiffness. Application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only. The theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam, a plate, a thin and a thick cylinder and for the impact between two cylinders. The modal density of the flexural modes for a thick slender cylinder is derived analytically. Good agreement is found between experimental, simulated and published results, showing the reliability of the method for a wide range of situations including impacts and pyroshock applications. © 2013 Elsevier Ltd. All rights reserved.

Predicting the response of structures to transient shock loading.

This work concerns the prediction of the response of an uncertain structure to a load of short duration. Assuming an ensemble of structures with small random variations about a nominal form, a mean impulse response can be found using only the modal density of the structure. The mean impulse response turns out to be the same as the response of an infinite structure: the response is calculated by taking into account the direct field only, without reflections. Considering the short duration of an impulsive loading, the approach is reasonable before the effect of the reverberant field becomes important. The convolution between the mean impulse response and the shock loading is solved in discrete time to calculate the response at the driving point and at remote points. Experimental and numerical examples are presented to validate the theory presented for simple structures such as beams, plates, and cylinders.

Fixed-lag blind equalization and sequence estimation in digital communications systems using sequential importance sampling

We present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo (MCMC) techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We will demonstrate this method by simulation and compare its performance to existing techniques.

Shock dynamics of random structures.

Predicting the response of a structure following an impact is of interest in situations where parts of a complex assembly may come into contact. Standard approaches are based on the knowledge of the impulse response function, requiring the knowledge of the modes and the natural frequencies of the structure. In real engineering structures the statistics of higher natural frequencies follows those of the Gaussian Orthogonal Ensemble, this allows the application of random point process theory to get a mean impulse response function by the knowledge of the modal density of the structure. An ensemble averaged time history for both the response and the impact force can be predicted. Once the impact characteristics are known in the time domain, a simple Fourier Transform allows the frequency range of the impact excitation to be calculated. Experimental and numerical results for beams, plates, and cylinders are presented to confirm the validity of the method.

Seismic response of stone masonry spires: Analytical modeling

Stone masonry spires are vulnerable to seismic loading. Computational methods are often used to predict the dynamic linear elastic response of masonry towers and spires, but this approach is only applicable until the first masonry joint begins to open, limiting the ability to predict collapse. In this paper, analytical modeling is used to investigate the uplift, rocking and collapse of stone spires. General equations for static equilibrium of the spire under lateral acceleration are first presented, and provide a reasonable lower bound for predicting collapse. The dynamic response is then considered through elastic modal analysis and rigid body rocking. Together, these methods are used to provide uplift curves and single impulse overturning collapse curves for a complete range of possible spire geometries. Results are used to evaluate the historic collapse of two specific stone spires. © 2012 Elsevier Ltd.

Seismic response of stone masonry spires: Computational and experimental modeling

Analytical methods provide a global context from which to understand the dynamics of stone spires, but computational and experimental methods are useful to predict more specific behavior of multiple block structures. In this paper, the spire of St. Mary Magdalene church in Waltham-on-the-Wolds, UK, which was damaged in the 2008 Lincolnshire Earthquake, is used as a case study. Both a physical model and a discrete element computational model of the spire were created and used to investigate collapse under constant horizontal acceleration, impulse base motion, and earthquake ground motion. Results indicate that the global behavior compares well with analytical modeling, but local block displacements evident in DEM and experimental results also reduce the stability of the structure. In this context, the observed damage to St. Mary Magdalene church is evaluated and discussed. © 2012 Elsevier Ltd.

The soft impact response of composite laminate beams

The quasi-static and dynamic responses of laminated beams of equal areal mass, made from monolithic CFRP and Ultra high molecular weight Polyethylene (UHMWPE), have been measured. The end-clamped beams were impacted at mid-span by metal foam projectiles to simulate localised blast loading. The effect of clamping geometry on the response was investigated by comparing the response of beams bolted into the supports with the response of beams whose ends were wrapped around the supports. The effect of laminate shear strength upon the static and dynamic responses was investigated by testing two grades of each of the CFRP and UHMWPE beams: (i) CFRP beams with a cured matrix and uncured matrix, and (ii) UHMWPE laminates with matrices of two different shear strengths. Quasi-static stretch-bend tests indicated that the load carrying capacity of the UHWMPE beams exceeds that of the CFRP beams, increases with diminishing shear strength of matrix, and increases when the ends are wrapped rather than through-bolted. The dynamic deformation mode of the beams is qualitatively different from that observed in the quasi-static stretch-bend tests. In the dynamic case, travelling hinges emanate from the impact location and propagate towards the supports; the beams finally fail by tensile fibre fracture at the supports. The UHMWPE beams outperform the CFRP beams in terms of a lower mid-span deflection for a given impulse, and a higher failure impulse. Also, the maximum attainable impulse increases with decreasing shear strength for both the UHMWPE and CFRP beams. The ranking of the beams for load carrying capacity in the quasi-static stretch-bend tests is identical to that for failure impulse in the impact tests. Thus, the static tests can be used to gauge the relative dynamic performances of the beams. © 2013 Elsevier Ltd. All rights reserved.