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IIT Hyderabad

Department of Mechanical and Aerospace Engineering

The present work reviews different approaches adopted for modeling the geometrical or centrifugal stiffening of a beam due to rotation about an axis perpendicular to its longitudinal axis. The longitudinal displacement of the beam consists of three components: the axial displacement of the neutral axis (elastic extension), displacement associated with rotation of the plane section and the displacement due to the foreshortening effect. A widely used approach for modeling the geometrical stiffening is based on the foreshortening effect, which essentially is the longitudinal shrinkage due to the transverse motion of the beam. This approach uses nonlinear strain–displacement relations. As a result, the equations of motion and associated boundary conditions are nonlinear. The geometric stiffening terms in the nonlinear models are fundamentally a linear/quadratic function of the high-frequency axial elastic deformation. Various nonlinear models are discussed and summarized based on the different approximations of the strain–displacement relation. The solution procedure of these nonlinear models is complicated and computationally expensive due to coupling between high-frequency axial and low-frequency bending modes. Simplifying the model by direct linearization of the equations of motion eliminates the geometrical stiffening term resulting in an incorrect model. Different approaches to include geometrical stiffening terms in the linear model are discussed. One of the approaches is linearizing the nonlinear terms arising from the coupled axial-transverse motion around the steady-state axial solutions. The steady-state axial equilibrium equation can be linear or nonlinear depending on the type of strain measure employed. A comparison of the solution of these different linear/nonlinear steady-state axial equilibrium equations is presented. The applicability of these models based on the steady-state axial equations is tested, and the rotation speed limit within which these models are valid is also discussed. In another approach, the equations of motion are derived using a time-independent centrifugal force. The resulting equations are equivalent to those governing the transverse vibrations of beams subject to an external axial force. Nevertheless, another approach proposed by Kane et al. (1987) uses stretch as a variable in the formulation instead of the axial displacement. The linear geometrical stiffening models are discussed in detail. Further, the effects of geometric properties of the blade, such as taper, twist angle, pre-setting angle and asymmetry in cross-section on the modal characteristics are brought out. A comparison of the different beam theories used in studying the dynamics of rotating blades is also presented. © 2022 Elsevier Ltd

World University root node

Journal of Sound and Vibration

Modeling of geometrical stiffening in a rotating blade—A review

Soft robotic grasping has rapidly spread through the academic robotics community in recent years and pushed into industrial applications. At the same time, multimaterial 3D printing has become widely available, enabling the monolithic manufacture of devices containing rigid and elastic sections. We propose a novel design technique that leverages both technologies and can automatically design bespoke soft robotic grippers for fruit-picking and similar applications. We demonstrate the novel topology optimisation formulation that generates multi-material soft grippers, can solve internal and external pressure boundaries, and investigate methods to produce air-tight designs. Compared to existing methods, it vastly expands the searchable design space while increasing simulation accuracy. © 2023 IEEE.

2023 IEEE International Conference on Soft Robotics, RoboSoft 2023

Automated design of pneumatic soft grippers through design-dependent multi-material topology optimization

The design of bistable arches is challenging due to their inherent nonlinear behaviour.It is known that the arch profiles of bistable arches in their two force-free equilibrium states are related to each other through a bilateral relationship.The closed-form analytical form of the bilateral relationship helps in designing the as-fabricated profile of the bistable arches when their toggled shape is completely specified.However, in certain cases, the arch profiles cannot be designed solely using the bilateral relationship.In this paper, we address such cases and present a design method to obtain arch-profiles using shape optimization in conjunction with the bilateral relationship.Such cases include: (1) arch-profiles that are partially specified in the first or/and second states; (2) arch-profiles that extremise the travel have a prescribed change in slope and have a specific ratio of travel between stable and unstable states.Towards this, the arch-profiles are represented using a set of finite variables corresponding to the mode weights of the basis set in which their shape is described.We formulate the optimization problem for each design case with the constraint to restrict the solutions in design space where the arches are bistable.After describing the procedure for numerically solving the optimization problem, design of arch-profiles using this method is illustrated through examples. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Lecture Notes in Mechanical Engineering

Design of Bistable Arch-Profiles by Using Bilateral Relationship and Shape Optimization

Direct numerical simulation (DNS) of a turbulent flow in an elevated jet in crossflow has been carried out at a Reynolds number (Re) of 3500 based on the outer width of the stack and crossflow velocity. The jet to crossflow velocity ratio is kept constant at V R = 2. Second order spatial and temporal discretization have been used to solve the Navier-Stokes equations employing a high-resolution grid to determine the essential characteristics of the coherent and the incoherent flow fields accurately. The large-scale coherent and small-scale incoherent flow fields are extracted using a reference signal-based phase-averaged method that uses a reference signal against which the phases are identified in each cycle to minimize the phase jitter. The rate of decay of circulation of the stack-wake vortices is observed to be more than that of the jet-wake which has a lower circulation value. The contribution of the incoherent fluctuations to the total turbulent kinetic energy is more compared to its coherent counterpart in the wake as well as jet region, except for the near-wake of the stack. The normal and shear stresses of both coherent and incoherent fields reveal a relatively higher contribution in the near-wake of both stack-wake and jet-wake, while the far-wake shows the opposite trend. The anisotropy factor of both the large-scale coherent and the small-scale fluctuating fields provides the evidence of total anisotropy of the stack-wake. The characterization of both types of fluctuating fields is also carried out using the anisotropy-invariant-map which displays the one-component limit for the coherent fluctuating field in most of the regions, but the anisotropy state of the incoherent fluctuating field is found to switch among various limits, namely, the axisymmetric contraction, the axisymmetric expansion, and isotropic limits. © 2023 Author(s).

Physics of Fluids

Characterization of the turbulent field behavior of an elevated jet-in crossflow investigated using direct numerical simulation

The clean-burning characteristics of hydrogen make it ideal alternative fuel for combustion applications. Pure hydrogen has many issues like storage, transportation, cost, and flashback while burning. Therefore, blending hydrogen with other hydrocarbon fuels could be the solution. The present study uses a chemiluminescence imaging technique to examine the effect of hydrogen blends with the premixed Liquefied Petroleum Gas (LPG)/air flames. A single swirl burner with a bluff body configuration is used for this study. The hydrogen is added by a mass fraction of 5% and 10% with LPG. Simultaneous OH* and CH* chemiluminescence measurements were carried out to identify the reaction zone in the premixed LPG/hydrogen/air flames. Also, natural luminescence and flame structrues are observed by direct imaging. It is observed that by adding hydrogen with LPG, the reaction zone moves downstream rather than attaching with burner exit. As hydrogen has a higher flame speed, it is expected that adding hydrogen would bring the flame front upstream, and further addition will lead to flashback. But in the present case, the addition of hydrogen with LPG leads to more distributed combustion than flamelet. This could help in delaying flashbacks comparing with other fuel blends like methane/hydrogen/air flames. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Chemiluminescence Study of Influence of Hydrogen Addition on the Turbulent Premixed LPG/air Flames

The study investigates the impact of the density ratio [Formula presente] on droplet breakup for non-Newtonian fluids using numerical simulations. An in-house solver based on OpenFOAM version 4.x libraries and coupled Level Set - Volume of Fluid method for interface capturing is employed. Non-Newtonian rheology was modelled as power-law fluid with power-law index varying from 0.2-1.8 to simulate both shear thinning and shear thickening fluid regimes. A parametric study consisting of 65 two-dimensional axisymmetric simulations were performed to analyse the secondary breakup after different ρr. Correction factors have been proposed to the estimation of critical Weber number (Wecr) for first and second critical droplet breakup for power law fluids. The resulting Wecr formulation was found be within +/- 2 of the present simulation dataset. The study further examines the near vicinity flow field and discusses the flow dynamics like Hill and Wake vortices, their growth and vortex strength due to the combined effect of density ratio and non-Newtonian rheology. The effect of density ratio on deformation ratio and deformation rate at flow balancing and initiation points were incorporated in the Internal Flow Theory (IFT) for power law fluids. Lastly, effect of the density ratio and power-law index on Werim has been analysed. © 2023 Elsevier Ltd

International Journal of Multiphase Flow

Effect of density ratios on droplet breakup for newtonian and power-law fluids

We investigate the dynamic characteristics corresponding to the structural fluctuations of a cantilever suspended in a turbulent flow. To investigate the intricate dynamics of the flow–structure interaction, first, we explore the ability of network analysis to identify the different dynamic states and probe the viability of using quantifiers of network topology as precursors for the onset of limit-cycle oscillations. By increasing the Reynolds number, we observe that the structural oscillations, measured using a strain gauge, transition from low-amplitude chaotic oscillations to large-amplitude periodic oscillations associated with limit-cycle oscillations. We characterize the dynamic states of the system by constructing the weighted correlation network from the time series of strain and identifying the network properties that have the potential to be used as precursors for the onset of limit-cycle oscillations. Furthermore, we use Pearson correlation to illustrate the evolution of mutual statistical influence between the structural oscillations and the flowfield. We use this information and the Granger causality to identify the causal dependence between the structural oscillations and velocity fluctuations. By identifying the causal variable during each regime, we illustrate the directional dependence through a cause–effect relationship in this flow–structure interaction as it transitions to limit-cycle oscillations. © 2023, AIAA International. All rights reserved.

AIAA Journal

Transition to Limit-Cycle Oscillation in Fluid-Structure Interactions: Mutual Correlations and Causal Dependencies

This article presents innovative approaches for managing residual stresses and distortion in additive manufacturing (AM) of metal components (baseplate material: EN8; filler wire material: ER70S-6). The experiments are conducted with two approaches for thermal management—passive and active. The passive approach of experiments is performed by varying the selected process parameters to study their effect on residual stresses and distortion. The chosen parameters are current, torch speed, geometry, continuous or a delay in the deposition, and cooling arrangement. Based on the understanding gained from the passive approach, the active approach of thermal management was implemented by insulating the substrate with and without adaptive current and heating the substrate. The experimental results were corroborated with the simulation to understand the process better. A comparative study for hardness was made based on the T8/5 extracted from the simulation. These experiments and simulations endorse passive and active thermal management as effective tools that can alter the distortion and residual stress pattern and the mechanical properties of an AM component. The investigation concludes that the process parameters that lead to higher heat input vis-à-vis an increase in current or a decrease in speed increase the distortion. On the other hand, the parameters that affect the rate of heat distribution vis-à-vis torch speed and geometry affect the residual stresses. When current, traverse speed and a/b ratio were kept the same, active thermal management with a heated base reduced distortion from 1.226 mm to 0.431 mm, a 65% reduction compared to passive thermal management. Additionally, the maximum residual stress was reduced from 492.31 MPa to 250.68 MPa, with residual stresses decreasing from 418.57 MPa to 372 MPa. Overall, active thermal management resulted in a 63% reduction in distortion, lowering it from 1.35 mm to 0.50 mm using external heating. The components that are difficult to complete because of the in-process distortion are expected to be manufactured with thermal management, e.g., heating the substrate is an effective measure to manage the in-process distortion. Thermal management techniques depend on geometry; for instance, a concave surface, because of self-heating, reduces the cooling rate and has relatively less variation in hardness. © 2023 by the authors.

Fulltext

Metals

Active and Passive Thermal Management in Wire Arc Additive Manufacturing

Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in an incompressible annular hyperelastic plate. The governing differential equations for a two-dimensional plate system are derived using a variational principle with no apriori kinematic assumptions in the thickness direction. A linear bifurcation analysis is performed to investigate the stability behaviour of the growing hyperelastic annular plate by considering both axisymmetric and asymmetric perturbations. The resulting differential equations are then solved numerically using the compound matrix method to evaluate the critical growth factor that leads to wrinkling. The effect of boundary constraints, thickness, and radius ratio of the annular plate on the critical growth factor is studied. For most of the considered cases, an asymmetric bifurcation is the preferred mode of instability for an annular plate. Our results are useful to model the physics of wrinkling phenomena in growing planar soft tissues, swelling hydrogels, and pattern transition in two-dimensional films growing on an elastic substrate. © 2022 The Author(s)

International Journal of Mechanical Sciences

Wrinkling as a mechanical instability in growing annular hyperelastic plates

Pressurised cylindrical channels made of soft materials are ubiquitous in biological systems, soft robotics and metamaterial designs. In this paper, we study large deformation and subsequent instability of a thick-walled and compressible hyperelastic cylinder under internal pressure and external constraints. The applied pressure can lead to elastic bifurcations along the axial or circumferential direction. Perturbation theory is used to derive the partial differential equations that govern the bifurcation behaviour of the cylindrical channel. Two cases of boundary conditions on the outer surface of the cylinder, namely, free and constrained are studied to understand their influence on the instability behaviour. The derived equations are solved numerically using the compound matrix method to evaluate the critical pressure for instability. The effects of the wall-thickness of the cylinder and the compressibility of the material on the critical pressure is investigated for both the boundary conditions. The results reveal that for an isotropic material, the bifurcation occurs along the axial direction of the cylinder at lower critical pressure compared to circumferential direction for all cases considered herein. Finally, the tuneability of the bifurcation behaviour of transversely isotropic cylinder is demonstrated by considering reinforcements along the cylinder's axis, triggering bifurcation in the circumferential direction in certain cases. The findings of the study indicate that the instability-induced pattern formation will be useful for designing shape changing material systems such as soft robotics and soft metamaterials. © 2022 The Author(s)