Forcing Function Research Articles

Pull-in instability and nonlinear vibration of microbeam with piezoelectric patch driven by electrostatic force using modified couple stress theory

The static and dynamic pull-in characteristics of electrostatically and piezo-electrically actuated microbeam are investigated. The static pull-in voltage is evaluated using analytical methods based on MCST, CCMT and validated through the use of FE based COMSOL multiphysics tools. The dynamic pull-in voltage obtained from numerical technique and verified with existing literature, lower than the static pull-in voltage. The piezoelectric patch has a significant influence on the pull-in voltage and an effect on the aspect ratio. Moreover, the pull-in band and instability zone of the microbeam with weak and hard forcing function have been investigated using multiple scale method.

A vibration-based method to estimate the low-wavenumber wall pressure field in a turbulent boundary layer

When an elastic structure is excited by a low-speed turbulent flow, it generates flow-induced vibration which is primarily due to the low-wavenumber components of the wall pressure field (WPF) beneath the turbulent boundary layer (TBL). Therefore, to accurately predict the vibration response of the structure, an accurate estimation of the low-wavenumber WPF is needed. While existing TBL models for WPF well predict the convective region, they exhibit significant discrepancies in predicting the low-wavenumber levels. This numerical study aims to explore the feasibility of estimation of the low-wavenumber WPF by analysing vibration data obtained from a structure excited by a TBL. An inverse method is proposed based on the relationship between the TBL forcing function and structural vibrations in the wavenumber domain. The random TBL force is simulated with deterministic loading using the uncorrelated wall plane wave technique. A model of a simply supported plate under a TBL excitation is developed to demonstrate the proposed method. The plate's acceleration data is then used to estimate the WPF in the low-wavenumber range. It is shown how using multiple discrete frequencies in the analysis can reduce the required snapshots for accurate estimation of the WPF.

Artemis I Versus Wind-Tunnel Buffet-Induced Forces and Structural Responses

This paper presents comparisons of buffet forcing functions (BFFs) and associated structural responses for the Space Launch System from two data sources: 1) Artemis I (AR01) Developmental Flight Instrumentation (DFI) and 2) transonic wind-tunnel (WT) tests. Failures of DFI sensors prevented the development of a complete set of flight-based BFFs, where each BFF is based on azimuthal integration over 360 deg of unsteady pressures acquired by sensor rings placed at many longitudinal stations along the vehicle. Instead, a set of equivalent flight- and WT-based BFFs was developed based on functional DFI and WT sensors that share the same locations. Root-mean-square (rms) levels of equivalent BFFs from flight and WT data are in-family for most of the cardinal Mach numbers. However, at stations downstream of the solid rocket booster (SRB) forward attachment (FA) protuberance, the rms of flight-based BFFs exceeds their WT counterparts. Strikingly, vortex shedding off the FA protuberance occurs at lower frequencies during flight than in WT experiments. This frequency shift propagates onto the spectrum of flight-measured versus WT-based structural responses. As a result of this frequency mismatch, at certain AR01 vortex shedding frequencies, the flight responses are an order of magnitude higher than their WT-based counterparts. Thus, at AR01 vortex shedding frequencies, the WT-based BFFs do not provide an accurate estimation of the flight environments. Away from AR01 vortex shedding frequencies, the AR01-based responses are within or sometimes exceed a range of WT-based responses. This observation indicates that, outside of frequencies that are impacted by vortex shedding, the WT-based BFFs are fairly well representative of the flight environments.

Verification and Validation of CFD analysis for 1/7th scale model of APR1400 for CVAP

This paper presents a methodology for analyzing the internal flow of the APR1400 Reactor Vessel Internals (RVI) using Computational Fluid Dynamics (CFD). The Comprehensive Vibration Assessment Program (CVAP) is performed to verify the structural integrity of reactor internals for flow-induced vibrations prior to the commercial operation of nuclear power plants. To classify the APR1400 as a valid prototype, it is necessary to demonstrate through successful CVAP that there are no adverse effects. In this study, CFD is used to calculate the local velocity and flow distribution to generate the forcing functions caused by turbulent flow for analysis programs in the CVAP. The Verification &Validation (V&V) procedure recommended by the American Society of Mechanical Engineers (ASME) is performed to verify the accuracy of CFD based on reliability, and it is compared with tests on a scale model. This paper provides valuable insights into the analysis and V&V process for CVAP using CFD, which can help ensure the safe and reliable operation of nuclear power plants.

Vorticity and magnetic dynamo from subsonic expansion waves. II. Dependence on the magnetic Prandtl number, forcing scale, and cooling time

The amplification of astrophysical magnetic fields takes place via dynamo instability in turbulent environments. Vorticity is usually present in any dynamo, but its role is not yet fully understood. This work is an extension of previous research on the effect of an irrotational subsonic forcing on a magnetized medium in the presence of rotation or a differential velocity profile. We aim to explore a wider parameter space in terms of Reynolds numbers, the magnetic Prandtl number, the forcing scale, and the cooling timescale in a Newtonian cooling. We studied the effect of imposing that either the acceleration or the velocity forcing function be curl-free and evaluated the terms responsible for the evolution vorticity. We used direct numerical simulations to solve the fully compressible, resistive magnetohydrodynamic equations with the Pencil Code. We studied both isothermal and non-isothermal regimes and addressed the relative importance of different vorticity source terms. We report no small-scale dynamo for the models that do not include shear. We find a hydro instability, followed by a magnetic one, when a shearing velocity profile is applied. The vorticity production is found to be numerical in the purely irrotational acceleration case. Non-isothermality, rotation, shear, and density-dependent forcing, when included, contribute to increasing the vorticity. As in our previous study, we find that turbulence driven by subsonic expansion waves can amplify the vorticity and magnetic field only in the presence of a background shearing profile. The presence of a cooling function makes the instability occur on a shorter timescale. We estimate critical Reynolds and magnetic Reynolds numbers of 40 and 20, respectively.

Non-uniformly sampled simulated price impact of an order-book

We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic forcing function with non-uniformly sampled times between order book events in the setting of fractional diffusion. This models the fluid limit of an order book by modelling the continuous arrival, cancellation and diffusion of orders in the presence of information shocks. We study the impulse response and stylised facts of orders undergoing anomalous diffusion for different forcing functions and model parameters. Concretely, we demonstrate the price impact for flash limit-orders and market orders and show how the numerical method generates kinks in the price impact. We use cubic spline interpolation to generate smoothed price impact curves. The work promotes the use of non-uniform sampling in the presence of diffusive dynamics as the preferred simulation method.

Identification of excitation frequencies of a vibrating beam using Dynamic Mode Decomposition

Identifying modal parameters for the different vibrational conditions for any structure or machine is very important for its structural health monitoring. Researchers have proposed different methodologies to determine that structure’s excitation or natural frequency. In the initial design phase, researchers have to rely on building the FE model and then analyze its natural and excitation frequencies. However, for the complex structure, it is difficult to handle a huge dataset of the vibrational information of the mesh for multi-frequency excitations and it becomes computationally expensive to analyze the system’s performance. This work presents the data-driven technique called Dynamic Mode Decomposition (DMD) which addresses this problem by discovering the system’s dynamics using system’s high-dimensional spatiotemporal data. The present work studies the FE vibration of fixed-fixed beams with single and multi-frequency harmonic forcing functions with and without noise for real-time scenarios. Here, DMD is applied to the sequential spatiotemporal data of displacement of the vibrating beams, and dominant frequencies and corresponding mode shapes are identified to predict the actual time dynamics of the system under different conditions in simulation and experimental conditions. This study also involves the failure of the DMD to capture the periodic oscillation (standing wave) in the beam and proposes the application of the Hankel matrix (time-delay coordinate) to capture the actual dynamical parameters of the system. The resulting predicted frequencies match the actual excitation frequencies, and the accuracy is improved with a number of stackings of the given time series data through the Hankel matrix at different rank truncations.

Dynamic impact of transiting weather systems on coastal currents in the northern Gulf of Mexico

Moving weather systems determine the history of wind variations with patterns as the systems transit through the ocean. These weather systems are integrated entities that can provide a system level perspective. A vessel-based survey repeatedly occupying a 30-km transect 12 times in 36 h provided non-aliased measurements of velocity field that showed how the along-shelf transport varied by more than three-fold in response to a transiting high-pressure weather system following an atmospheric cold front. To further illustrate the impact of different weather systems, we analyzed time series data from moored ADCPs, which showed influence on the velocity field from infrequent summertime cold fronts and remote hurricanes moving through the region, one on the west and the other on the east of the study site. Rotary spectrum analysis showed that the flow field rotated mostly clockwise with a smaller but non-negligible counterclockwise component, consistent with near inertial oscillations mixed with weak tidal currents. A theoretical model is presented by a Laplace transform and a general relationship between the velocity field and forcing functions is obtained, which shows that the contributions to the rotary velocity field from various forcing functions are through mathematical convolutions between the forcing functions and the complex frictional-rotary inertial function (CFRIF). These convolutions include an integrated effect of history of the forcing. CFRIF is effectively a frictional rotary filter that favors inertial oscillations. The wind-stress induced velocity field over a few days is computed and it shows significant variations after the passage of a cold front, with a magnitude consistent with observations. The wind-stress induced velocity is a few times greater than the density driven flow during the ship-based observations. The weather systems passing through the region can impact coastal currents causing a great variability over short time scales.

Parameterized Internal Wave Mixing in Three Ocean General Circulation Models

AbstractThe non‐local model of mixing based on internal wave breaking, IDEMIX, is implemented as an enhancement of a turbulent kinetic energy closure model in three non‐eddy resolving general circulation ocean models that differ in the discretization and choice of computational grids. In IDEMIX internal wave energy is generated by an energy flux resulting from near‐inertial waves induced by wind forcing at the surface, and at the bottom, by an energy flux that parameterizes the transfer of energy between baroclinic and barotropic tides. In all model simulations with IDEMIX, the mixing work is increased compared to the reference solutions without IDEMIX, reaching values in better agreement with finestructure observations. Furthermore, the horizontal structure of the mixing work is more realistic as a consequence of the heterogeneous forcing functions. All models with IDEMIX simulate deeper thermocline depths related to stronger shallow overturning cells in the Indo‐Pacific. In the North Atlantic, deeper mixed layers in simulations with IDEMIX are associated with an increased Atlantic overturning circulation and an increase of northward heat transports toward more realistic values. The response of the deep Indo‐Pacific overturning circulation and the weak bottom cell of the Atlantic to the inclusion of IDEMIX is incoherent between the models, suggesting that additional unidentified processes and numerical mixing may confound the analysis. Applying different tidal forcing functions leads to simulation differences that are small compared to differences between the different models or between simulations with IDEMIX and without IDEMIX.

Assessment of reliable wave climate at jetty on open coasts: role of 2D spatio-temporal spectrum

ABSTRACT The development of coastal roads and bridges is important to overcome traffic congestion in densely populated coastal cities like Mumbai. In the present study, the importance of assessment of wave conditions required for the extension of jetties to facilitate the transportation of bridge components to build the sea link bridge during non-monsoon season is envisaged so that zero downtime for operability at jetties is ascertained. Coupled hydrodynamic spectral wave model (Telemac-2D and TOMAWAC) used to hindcast waves reveals that the application of spatio-temporal varying 2D directional spectrum (from ERA-5) over the offshore boundary as a forcing function helps in propagation of realistic wave climate of Mahim Bay, Mumbai. Coupling of the TOMAWAC-ARTEMIS model is essential to obtain reliable wave conditions near the jetties (nearshore) for predominant directions. The study reveals that under existing conditions, downtime at proposed jetties will be for 30 days wherein Hs ≥ 0.3 m. As such to achieve zero downtime, the existing bund on the seaward side of jetties was extended optimally (70 m) so that smooth operability for the entire non-monsoon is achieved. Thus, application of spatio-temporal varying 2D spectrum in optimising the length of the guide bund has been found promising for speedy transportation of proposed bridge components. The study also reveals that there is an insignificant climatological impact on wave conditions.

Numerical investigation of smart material-based structures for vibration energy-harvesting applications

Abstract The present work deals with energy-harvesting devices, which are useful in scavenging power using piezoelectric materials. Utilizing classical beam theory and classical plate theory, finite element modelling has been carried out to optimize the performance of output power of a cantilever beam and a flexible rectangular plate. Harmonic oscillations and base excitation will be the two different forcing functions used to drive the system. Based on this, numerical investigations of the performance of output power for the piezoelectric cantilever beam and flexible rectangular plate with different cases are considered. The present work is also useful for designing the piezoelectric cantilever beams and plates to extract maximum output power within the frequency ranges from 0 to 200 Hz. Numerical investigations on the piezoelectric cantilever beam and flexible rectangular plate with different cases reveal that the performance of output power is influenced by factors like load resistance, applications of with and without host structures, and different design parameters like unimorph, bimorph, embedded, line- and cross-type piezoelectric patch arrangements.

Unsteady cylinder wakes from arbitrary bodies with differentiable physics-assisted neural network.

This work describes a hybrid predictive framework configured as a coarse-grained surrogate for reconstructing unsteady fluid flows around multiple cylinders of diverse configurations. The presence of cylinders of arbitrary nature causes abrupt changes in the local flow profile while globally exhibiting a wide spectrum of dynamical wakes fluctuating in either a periodic or chaotic manner. Consequently, the focal point of the present study is to establish predictive frameworks that accurately reconstruct the overall fluid velocity flowfield such that the local boundary layer profile, as well as the wake dynamics, are both preserved for long time horizons. The hybrid framework is realized using a base differentiable flow solver combined with a neural network, yielding a differentiable physics-assisted neural network (DPNN). The framework is trained using bodies with arbitrary shapes, and then it is tested and further assessed on out-of-distribution samples. Our results indicate that the neural network acts as a forcing function to correct the local boundary layer profile while also remarkably improving the dissipative nature of the flowfields. It is found that the DPNN framework clearly outperforms the supervised learning approach while respecting the reduced feature space dynamics. The model predictions for arbitrary bodies indicate that the Strouhal number distribution with respect to spacing ratio exhibits similar patterns with existing literature. In addition, our model predictions also enable us to discover similar wake categories for flow past arbitrary bodies. For the chaotic wakes, the present approach predicts the chaotic switch in gap flows up to the mid-time range.

Milanković Forcing in Deep Time

AbstractAstronomical (or Milanković) forcing of the Earth system is key to understanding rhythmic climate change on time scales ≳104 y. Paleoceanographic and paleoclimatological applications concerned with past astronomical forcing rely on astronomical calculations (solutions), which represent the backbone of cyclostratigraphy and astrochronology. Here we present state‐of‐the‐art astronomical solutions over the past 3.5 Gyr. Our goal is to provide tuning targets and templates for interpreting deep‐time cyclostratigraphic records and designing external forcing functions in climate models. Our approach yields internally consistent orbital and precession‐tilt solutions, including fundamental solar system frequencies, orbital eccentricity and inclination, lunar distance, luni‐solar precession rate, Earth's obliquity, and climatic precession. Contrary to expectations, we find that the long eccentricity cycle (LEC) (previously assumed stable and labeled “metronome,” recent period ∼405 kyr), can become unstable on long time scales. Our results reveal episodes during which the LEC is very weak or absent and Earth's orbital eccentricity and climate‐forcing spectrum are unrecognizable compared to the recent past. For the ratio of eccentricity‐to‐inclination amplitude modulation (recent individual periods of ~2.4 and ~1.2 Myr, frequently observable in paleorecords) we find a wide distribution around the recent 2:1 ratio, that is, the system is not restricted to a 2:1 or 1:1 resonance state. Our computations show that Earth's obliquity was lower and its amplitude (variation around the mean) significantly reduced in the past. We therefore predict weaker climate forcing at obliquity frequencies in deep time and a trend toward reduced obliquity power with age in stratigraphic records. For deep‐time stratigraphic and modeling applications, the orbital parameters of our 3.5‐Gyr integrations are made available at 400‐year resolution.

Identification of the Aeromechanical Parameters of a Compressor Rotor from Blade Tip Timing Data

Abstract This article presents a maximum likelihood approach to identifying the mistuning, aerodynamic forcing functions, and aerodynamic influence coefficients of compressor rotor blades from noisy experimental measurements of blade deflection. The maximum likelihood estimation approach leads naturally to a nonlinear least squares optimization problem that can be solved using numerical optimization techniques such as quasi-Newton methods. An eigenmode decomposition approach is presented that permits the optimization objective function and gradient to be efficiently calculated so that the optimization is computationally feasible, even for experiments involving very large data sets. Simulation results show that the method has the potential to accurately identify the mistuning and aerodynamic nodal diameter forcing functions, but obtaining accurate results for influence coefficients may not be possible if there is significant disk flexibility. We demonstrate the method using both simulated and experimental blade vibration data from rotor 2 of the Purdue University three-stage axial compressor research facility collected using a light probe tip timing system as the rotor is slowly accelerated or decelerated through a Campbell diagram crossing.

Density of mode-locking property for quasi-periodically forced Arnold circle maps

Abstract We show that the mode-locking region of the family of quasi-periodically forced Arnold circle maps with a topologically generic forcing function is dense. This gives a rigorous verification of certain numerical observations in [M. Ding, C. Grebogi and E. Ott. Evolution of attractors in quasiperiodically forced systems: from quasiperiodic to strange nonchaotic to chaotic. Phys. Rev. A 39(5) (1989), 2593–2598] for such forcing functions. More generally, under some general conditions on the base map, we show the density of the mode-locking property among dynamically forced maps (defined in [Z. Zhang. On topological genericity of the mode-locking phenomenon. Math. Ann. 376 (2020), 707–72]) equipped with a topology that is much stronger than the $C^0$ topology, compatible with smooth fiber maps. For quasi-periodic base maps, our result generalizes the main results in [A. Avila, J. Bochi and D. Damanik. Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Duke Math. J.146 (2009), 253–280], [J. Wang, Q. Zhou and T. Jäger. Genericity of mode-locking for quasiperiodically forced circle maps. Adv. Math.348 (2019), 353–377] and Zhang (2020).

Asymptotic expansions about infinity for solutions of nonlinear differential equations with coherently decaying forcing functions

This paper studies, in fine details, the long-time asymptotic behavior of decaying solutions of a general class of dissipative systems of nonlinear differential equations in complex Euclidean spaces. The forcing functions decay, as time tends to infinity, in a coherent way expressed by combinations of the exponential, power, logarithmic and iterated logarithmic functions. The decay may contain sinusoidal oscillations not only in time but also in the logarithm and iterated logarithm of time. It is proved that the decaying solutions admit corresponding asymptotic expansions, which can be constructed concretely. In the case of the real Euclidean spaces, the real-valued decaying solutions are proved to admit real-valued asymptotic expansions. Our results unite and extend the theory investigated in many previous works.

Influences of Software Changes on Oxycodone Prescribing at an Australian Tertiary Emergency Department: A Retrospective Review.

Opioid prescribing and dispensing from emergency departments is a noteworthy issue given widespread opioid misuse and diversion in many countries, contributing both physical and economic harm to the population. High patient numbers and the stochastic nature of acute emergency presentations to emergency departments (EDs) introduce challenges for prescribers who are considering opioid stewardship principles. This study investigated the effect of changes to electronic prescribing software on prescriptions with an auto-populated quantity of oxycodone immediate release (IR) from an Australian tertiary emergency department following the implementation of national recommendations for reduced pack sizes. A retrospective review of oxycodone IR prescriptions over two six-month periods between 2019 and 2021 was undertaken, either side of a software adjustment to reduce the default quantities of tablets prescribed from 20 to 10. Patient demographic details were collected, and prescriber years of practice calculated for inclusion in linear mixed effects regression modelling. A reduction in the median number of tablets prescribed per prescription following the software changes (13.5 to 10.0, p < 0.001) with little change in the underlying characteristics of the patient or prescriber populations was observed, as well as an 11.65% reduction in the total number of tablets prescribed. The prescriber's years of practice, patient age and patient sex were found to influence increased prescription sizes. Reduced quantity of oxycodone tablets prescribed was achieved by alteration of prescribing software prefill parameters, providing further evidence to support systems-based policy interventions to influence health care providers behaviour and to act as a forcing function for prescribers to consider opioid stewardship principles.

On a Particular Particular Solution

Summary The usual process for solving a nonhomogeneous system of linear differential equations is to find the general complementary homogeneous solution first and then construct a particular solution from it. When can we flip the script on this process and compute a particular solution first? This paper argues this is possible when the nonhomogeneous forcing function is analytic. It presents two different series expansions for this particular particular solution using power series methods, and reveals a surprising connection to the more familiar variation of parameters formula.

Bernoulli factories and duality in Wright–Fisher and Allen–Cahn models of population genetics

Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright–Fisher diffusion and the Kingman coalescent, where the former describes the stochastic evolution of neutral allele frequencies in a large population forwards in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backwards in time. As well as providing a richer description than either model in isolation, duality often yields equations satisfied by quantities of interest. We employ the so-called Bernoulli factory – a celebrated tool in simulation-based computing – to derive duality relations for broad classes of genetics models. As concrete examples, we present Wright–Fisher diffusions with general drift functions, and Allen–Cahn equations with general, nonlinear forcing terms. The drift and forcing functions can be interpreted as the action of frequency-dependent selection. To our knowledge, this work is the first time a connection has been drawn between Bernoulli factories and duality in models of population genetics.

Mathematical analysis of a time-delayed model for cocoa yield

Abstract Cocoa is an important crop that is predominantly grown in the western part of Africa. However, there have been fluctuations and declining trends in production and several factors have been identified to be responsible for this. A significant factor is the effect of climate variation, which could result in a low farm-level yield. Therefore, to understand the contribution of climate variability on the farm-level yield, we construct and analyse a time-delayed model to capture the effect of rainfall on cocoa production. This work uses a system of differential equations to model the crop transition from the flowering stage to pod formation, pod ripening and then to harvesting. We introduce a periodic forcing function into the model of flowering to account for the impact of seasonal rainfall variations. This leads to a novel nonlinear parametrically forced ODE for the flowering with periodically varying coefficients, which is coupled to a time-delayed model for the ripened pod formation and then harvesting. We perform an analysis of all parts of the system proving that it has a periodic solution when (parametrically) forced periodically, and we then conduct an asymptotic analysis on this periodic solution to show how its rich behaviour depends on the parameters of the climatic forcing in the model.