Influence of fluid viscosity on the response of buried structures in earthquakes

The use of high viscous pore fluid has been widely established to match the rate of excess pore pressure generation and subsequent dissipation in dynamic centrifuge tests. The appropriate viscosity is linked to the geometric and gravity scaling factors which corresponds to the use of pore fluid of 'N' cSt in a 'N'g centrifuge test. The use of either water (1 cSt) or pore fluid lower than 'N' cSt can influence the behaviour of soil liquefaction in a centrifuge test. In this paper, the floatation of a tunnel following soil liquefaction is investigated using pore fluids with two different viscosities. The results show that the uplift displacement of the tunnel is significantly affected by the pore fluid viscosity. © 2010 Taylor & Francis Group, London.

Dynamic buckling of an inclined strut

The dynamic compressive response of a sandwich plate with a metallic corrugated core is predicted. The back face of the sandwich plate is held fixed whereas the front face is subjected to a uniform velocity, thereby compressing the core. Finite element analysis is performed to investigate the role of material inertia, strain hardening and strain rate hardening upon the dynamic collapse of the corrugated core. Three classes of collapse mode are identified as a function of impact velocity: (i) a three-hinge plastic buckling mode of wavelength equal to the strut length, similar to the quasi-static mode, (ii) a 'buckle-wave' regime involving inertia-mediated plastic buckling of wavelength less than that of the strut length, and (iii) a 'stubbing' regime, with shortening of the struts by local fattening at the front face. The presence of strain hardening reduces the regime of dominance of the stubbing mode. The influence of material strain rate sensitivity is evaluated by introducing strain rate dependent material properties representative of type 304 stainless steel. For this choice of material, strain rate sensitivity has a more minor influence than strain hardening, and consequently the dynamic collapse strength of a corrugated core is almost independent of structural dimension. © 2012 Elsevier Ltd. All rights reserved.

The interaction of elasticity and rocking in flexible structures allowed to uplift

Numerous structures uplift under the influence of strong ground motion. Although many researchers have investigated the effects of base uplift on very stiff (ideally rigid) structures, the rocking response of flexible structures has received less attention. Related practical analysis methods treat these structures with simplified 'equivalent' oscillators without directly addressing the interaction between elasticity and rocking. This paper addresses the fundamental dynamics of flexible rocking structures. The nonlinear equations of motion, derived using a Lagrangian formulation for large rotations, are presented for an idealized structural model. Particular attention is devoted to the transition between successive phases; a physically consistent classical impact framework is utilized alongside an energy approach. The fundamental dynamic properties of the flexible rocking system are compared with those of similar linear elastic oscillators and rigid rocking structures, revealing the distinct characteristics of flexible rocking structures. In particular, parametric analysis is performed to quantify the effect of elasticity on uplift, overturning instability, and harmonic response, from which an uplifted resonance emerges. The contribution of stability and strength to the collapse of flexible rocking structures is discussed. © 2012 John Wiley & Sons, Ltd.

An efficient model for the dynamic behaviour of a single pile in viscoelastic soil

This paper presents a novel, three-dimensional, single-pile model, formulated in the wavenumber domain and adapted to account for boundary conditions using the superposition of loading cases. The pile is modelled as a column in axial vibration, and a Euler-Bernoulli beam in lateral vibration. The surrounding soil is treated as a viscoelastic continuum. The response of the pile is presented in terms of the stiffness and damping coefficients, and also the magnitude and phase of the pile-head frequency-response function. Comparison with existing models shows that excellent agreement is observed between this model, a boundary-element formulation, and an elastic-continuum-type formulation. This three-dimensional model has an accuracy equivalent to a 3D boundary-element model, and a runtime similar to a 2D plane-strain analytical model. Analysis of the response of the single pile illustrates a difference in axial and lateral vibration behaviour; the displacement along the pile is relatively invariant under axial loads, but in lateral vibration the pile exhibits localised deformations. This implies that a plane-strain assumption is valid for axial loadings and only at higher frequencies for lateral loadings. © 2013 Elsevier Ltd.

Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

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.

Wave propagation due to sinusoidal excitation in nonlinear one-dimensional soil column

The objective of the author's on-going research is to explore the feasibility of determining reliable in situ curves of shear modulus as a function of strain using the dynamic test. The purpose of this paper is limited to investigating what material stiffness is measured from a dynamic test, focusing on the harmonic excitation test. A one-dimensional discrete model with nonlinear material properties is used for this purpose. When a sinusoidal load is applied, the cross-correlation of signals from different depths estimates a wave velocity close to the one calculated from the secant modulus in the stress-strain loops under steady-state conditions. The variables that contributed to changing the average slope of the stress-strain loop also influence the estimate of the wave velocity from cross-correlation. Copyright ASCE 2007.

Factors affecting seismic response of submarine slopes

The response of submerged slopes on the continental shelf to seismic or storm loading has become an important element in the risk assessment for offshore structures and "local" tsunami hazards worldwide. The geological profile of these slopes typically includes normally consolidated to lightly overconsolidated soft cohesive soils with layer thickness ranging from a few meters to hundreds of meters. The factor of safety obtained from pseudo-static analyses is not always a useful measure for evaluating the slope response, since values less than one do not necessarily imply slope failure with large movements of the soil mass. This paper addresses the relative importance of different factors affecting the response of submerged slopes during seismic loading. The analyses use a dynamic finite element code which includes a constitutive law describing the anisotropic stress-strain-strength behavior of normally consolidated to lightly overconsolidated clays. The model also incorporates anisotropic hardening to describe the effect of different shear strain and stress histories as well as bounding surface principles to provide realistic descriptions of the accumulation of the plastic strains and excess pore pressure during successive loading cycles. The paper presents results from parametric site response analyses on slope geometry and layering, soil material parameters, and input ground motion characteristics. The predicted maximum shear strains, permanent deformations, displacement time histories and maximum excess pore pressure development provide insight of slope performance during a seismic event. © 2006 Author(s). This work is licensed under a Creative Commons License.

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.

CLF based designs with robustness to dynamic input uncertainties

The problem of robust stabilization of nonlinear systems in the presence of input uncertainties is of great importance in practical implementation. Stabilizing control laws may not be robust to this type of uncertainty, especially if cancellation of nonlinearities is used in the design. By exploiting a connection between robustness and optimality, "domination redesign" of the control Lyapunov function (CLF) based Sontag's formula has been shown to possess robustness to static and dynamic input uncertainties. In this paper we provide a sufficient condition for the domination redesign to apply. This condition relies on properties of local homogeneous approximations of the system and of the CLF. We show that an inverse optimal control law may not exist when these conditions are violated and illustrate how these conditions may guide the choice of a CLF which is suitable for domination redesign. © 1999 Elsevier Science B.V. All rights reserved.

Efficient numerical models for investigating the statistics of random dynamic systems

The study of random dynamic systems usually requires the definition of an ensemble of structures and the solution of the eigenproblem for each member of the ensemble. If the process is carried out using a conventional numerical approach, the computational cost becomes prohibitive for complex systems. In this work, an alternative numerical method is proposed. The results for the response statistics are compared with values obtained from a detailed stochastic FE analysis of plates. The proposed method seems to capture the statistical behaviour of the response with a reduced computational cost.

Dynamic compression of foam supported plates impacted by high velocity soil

The response of back-supported buffer plates comprising a solid face sheet and foam core backing impacted by a column of high velocity particles (sand slug) is investigated via a lumped parameter model and coupled discrete/continuum simulations. The buffer plate is either resting on (unattached) or attached to a rigid stationary foundation. The lumped parameter model is used to construct maps of the regimes of behaviour with axes of the ratio of the height of the sand slug to core thickness and the normalised core strength. Four regimes of behaviour are identified based on whether the core compression ends prior to the densification of the sand slug or vice versa. Coupled discrete/continuum simulations are also reported and compared with the lumped parameter model. While the model predicted regimes of behaviour are in excellent agreement with numerical simulations, the lumped parameter model is unable to predict the momentum transmitted to the supports as it neglects the role of elasticity in both the buffer plate and the sand slug. The numerical calculations show that the momentum transfer is minimised for intermediate values of the core strength when the so-called "soft-catch" mechanism is in play. In this regime the bounce-back of the sand slug is minimised which reduces the momentum transfer. However, in this regime, the impulse reduction is small (less than 10% of that transferred to a rigid structure). For high values of the core strength, the response of the buffer plate resembles a rigid plate with nearly no impulse mitigation while at low values of core strength, a slap event occurs when the face sheet impinges against the foundation due to full densification of the foam core. This slap event results in a significant enhancement of the momentum transfer to the foundation. The results demonstrate that appropriately designed buffer plates have potential as impulse mitigators in landmine loading situations. © 2013 Elsevier Ltd. All rights reserved.

The low velocity impact response of sandwich beams with a corrugated core or a Y-frame core

The low speed impact responses of simply-supported and clamped sandwich beams with corrugated and Y-frame cores have been measured in a drop-weight apparatus at 5 m s-1. The AISI 304 stainless steel sandwich beams comprised two identical face sheets and represented 1:20 scale versions of ship hull designs. No significant rate effects were observed at impact speeds representative of ship collisions: the drop-weight responses were comparable to the ones measured quasi-statically. Moreover, the corrugated and Y-frame core beams had similar performances. Three-dimensional finite element (FE) models simulated the experiments and were in good agreement with the measurements. The simulations demonstrated correctly that the sandwich beams collapsed by core indentation under both quasi-static loading and in the drop-weight experiments. These FE models were then used to investigate the sensitivity of impact response to (i) velocity, over a wider range of velocities than achievable with the drop-weight apparatus, and (ii) the presence of the back face sheet. The dynamic responses of sandwich beams with both front and back face sheets were found to be within 20% of the quasi-static responses for speeds less than approximately 5 m s-1. This suggests that quasi-static considerations are adequate to model the collision of a sandwich ship hull. By contrast, beams without a back face collapsed by Brazier buckling under quasi-static loading conditions, and by core indentation at a loading velocity of 5 m s-1. Thus, dynamic considerations are needed in ship hull designs that do not employ a back face. © 2014 Elsevier Ltd. All rights reserved.

Characterization and deformation response of orthotropic fibre networks with auxetic out-of-plane behaviour

In the present paper, highly porous fibre networks made of 316L fibres, with different fibre volume fractions, are characterized in terms of network architecture, elastic constants and fracture energies. Elastic constants are measured using quasi-static mechanical and modal vibration testing, yielding local and globally averaged properties, respectively. Differences between quasi-static and dynamic elastic constants are attributed to through-thickness shear effects. Regardless of the method employed, networks show signs of material inhomogeneity at high fibre densities, in agreement with X-ray nanotomography results. Strong auxetic (or negative Poisson's ratio) behaviour is observed in the through-thickness direction, which is attributed to fibre kinking induced during processing. Measured fracture energies are compared with model predictions incorporating information about in-plane fibre orientation distribution, fibre volume fraction and single fibre work of fracture. Experimental values are broadly consistent with model predictions, based on the assumption that this energy is primarily associated with plastic deformation of individual fibres within a process zone of the same order as the inter-joint spacing. © 2013 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved.

Stable dynamic walking over uneven terrain

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated "dynamic walking" biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents "transversal" dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems. © The Author(s) 2011.