Forcing Function Research Articles

Flexural Characteristics of Tapered Bar in Relation to Taper Angle Measurements

Flexural motion of a cantilever bar can be used to monitor the taper angle measurements of the bar without incorporating any geometric measurement. This provides non-destructive taper measurement with fast processing in manufacturing line. The laser ablation of a free end of the cantilever bar enables to generate a recoil pressure at the irradiated surface while resulting in external forcing function for the initiation of the flexural motion. Consequently, in the present study, laser induced ablation of free end tapered cantilever bar and resulting displacement and frequency of the flexural motion is examined. The study is extended to include influence of positive and negative bar taper angles on the flexural characteristics. In addition, deviation of displacement and frequency of the flexural motion due to tapered bar from the parallel bar is examined. It is found that the flexural characteristics of the tapered bar enable to determine taper angle of the bar with high accuracy.

The Checklist Manifesto

The Checklist Manifesto

Optical-RF frequency stability transformer

An optical technique based on stability transfer among modes of a monolithic optical microresonator is proposed for long term frequency stabilization of a radio frequency (RF) oscillator. We show that locking the frequency difference of two microresonator modes with dissimilar sensitivity to an applied forcing function to a master RF oscillator improves the long term stability of a slave RF oscillator locked to the frequency difference of another pair of modes with nearly identical sensitivity to the same forcing function. For instance, the stability of a 10 MHz master oscillator with Allan deviation of 10(-7) at 10(3) s can be improved and transferred to a slave oscillator with identical free running stability performance, so that the resultant Allan deviation of the slave oscillator becomes equal to 10(-13) at 10(3) s. The suggested method does not require absolute frequency references.

Impact-induced vibration in complex flexible multi-body systems: numerical and experimental investigation of press machines

This article is concerned with the numerical and experimental investigations of impact-induced vibrations in highly non-linear complex multibody system applications. In order to accurately model the impact response of such complex systems, a computational procedure based on the integration of finite element and multibody system algorithms is used. This procedure, which employs the finite element floating frame of reference formulation, allows for defining arbitrary joint constraint and forcing functions, for accurately capturing the coupling between the rigid body motion and the elastic deformation, and for modeling the impact forces between rigid and flexible bodies in the multibody system model. The system equations of motion are developed using the augmented Lagrangian formulation that allows for the use of sparse matrix techniques. The algorithm used in this study ensures that the kinematic constraint equations are satisfied at the position, velocity, and acceleration levels. The impact-induced vibration of a highly non-linear press machine is numerically and experimentally examined in this study. In order to accurately model the dynamic behavior of such a press machine, it is necessary to model the transfer feeder elastic deformations resulting from the impulsive impact forces. The deformations of the transfer press system as well as those of its frame are modeled in this investigation using the floating frame of reference formulation that allows for effectively reducing the number of degrees of freedom by filtering out very high-frequency modes of vibration using component mode synthesis techniques. The formulations of several relative angle and angular velocity kinematic constraints that are required to model this multibody system are developed in order to model transfer feeder complex rotational components. The numerical results obtained using the three-dimensional multibody system transfer press model developed in this study are validated using experimental results.

Stability of Homogeneous Smart Beams based on the First Order Shear Deformation Theory Located on a Continuous Elastic Foundation

1 Abstract—This paper studies stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter and foundation coefficient on the stability of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data. Keywords—Stability, Homogeneous beam- Piezoelectric layer. I. INTRODUCTION HE applications of the smart materials have drawn attention in aerospace engineering, civil engineering, mechanical and even bio-engineering. The analysis of a coupled piezoelectric structure has recently been keenly researched because piezoelectric materials are more extensively used either as actuators or sensors. Examples include the analytical modelling and behaviour of a beam with surface-bonded or embedded piezoelectric sensors and actuators (1-3), and the use of piezoelectric materials in composite laminates and for vibration control (4). The use of finite element method in the analysis of piezoelectric coupled structures has been studied (5-8). Crawley and de Luis (9) developed the analytical model for the static and dynamic response of a beam structure with segmented piezoelectric actuators either bonded or embedded in a laminated composite. LaPeter and Cudney (10) proposed an analytic model for the segmented piezoelectric actuators bonded on a beam or a plate, and found the equivalent forcing functions of the actuators. The piezoelectric bimorph column structures were used as sensing elements. Dobrucki and Pruchnicki (11) presented an analysis theory of an axisymmetric piezoelectric bimorph. They also described a sensing theory for using the axisymmetric piezoelectric bimorph. Chandrashekhara and Bhatia (12) developed a finite element model for the active buckling control of laminated composite plates with surface bonded or embedded piezoelectric sensors that are either continuous or segmented. The dynamic buckling behavior of the laminated plate subjected to a linearly increasing compression load is investigated in their work. Chase and Bhashyam (13) derived optimal design equations to actively stabilize laminated plates loaded in excess of the critical buckling load using a large number of sensors and actuators. To the author's knowledge, there is no analytical solution available in the open literatures for stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation. In the present work, stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation studied. Appling the Hamilton's principle, the equilibrium equations of beam are derived and solved. The effects of applied voltage, dimensionless geometrical parameter and foundation coefficient on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

The effect of ribbing and pressurization on the vibro-acoustic response of a turbulent boundary layer excited panel

One of the largest contributors to interior aircraft noise is the direct radiation from the wall panels excited by turbulent boundary layer (TBL) flows. The wall panels are designed with ribbing to increase their stiffness and strength while maintaining a relatively low weight. The effect of the ribbing on the vibro-acoustic response is examined for TBL flow excitation. Normal modes of a typical aluminum aircraft panel are computed and compared with and without the ribs. Wavenumber transforms of the mode shapes reveal increased sensitivity of the ribbed panel to high wavenumber excitation. TBL forcing functions are then converted into modal space and used to compute the radiated sound power of each panel. The increase in radiated sound power will be discussed in terms of wavenumber sensitivity. A preload due to pressurization is then applied to the ribbed panel and the modes, wavenumber spectrum and radiated sound power are recomputed. The pressurization causes a significant change in the modal content and subsequently the wavenumber spectrum and radiated power. The general effect of preload will be discussed in the context of interior aircraft noise predictions.

Development of the CAP Water Quality Model and Its Application to the Geum River, Korea

The completely mixed flow and plug flow (CAP) water quality model was developed for streams with discontinuous flows, a condition that often occurs in low base flow streams with in-stream hydraulic structures, especially during dry seasons. To consider the distinct physical properties of each reach effectively, the CAP model stream network can include both plug flow (PF) segments and completely mixed flow (CMF) segments. Many existing water quality models are capable of simulating various constituents and their interactions in surface water bodies. More complicated models do not necessarily produce more accurate results because of problems in data availability and uncertainties. Due to the complicated and even random nature of environmental forcing functions, it is not possible to construct an ideal model for every situation. Therefore, at present, many governmental level water quality standards and decisions are still based on lumped constituents, such as the carbonaceous biochemical oxygen demand (CBOD), the total nitrogen (TN) or the total phosphorus (TP). In these cases, a model dedicated to predicting the target concentration based on available data may provide as equally accurate results as a general purpose model. The CAP model assumes that its water quality constituents are independent of each other and thus can be applied for any constituent in waters that follow first order reaction kinetics. The CAP model was applied to the Geum River in Korea and tested for CBOD, TN, and TP concentrations. A trial and error method was used for parameter calibration using the field data. The results agreed well with QUAL2EU model predictions.

Dynamo-driven plasmoid ejections above a spherical surface

Magnetic buoyancy is believed to drive the transport of magnetic flux tubes from the convection zone to the surface of the Sun. The magnetic fields form twisted loop-like structures in the solar atmosphere. In this paper we use helical forcing to produce a large-scale dynamo-generated magnetic field, which rises even without magnetic buoyancy. A two layer system is used as computational domain where the upper part represents the solar atmosphere. Here, the evolution of the magnetic field is solved with the stress--and--relax method. Below this region a magnetic field is produced by a helical forcing function in the momentum equation, which leads to dynamo action. We find twisted magnetic fields emerging frequently to the outer layer, forming arch-like structures. In addition, recurrent plasmoid ejections can be found by looking at space--time diagrams of the magnetic field. Recent simulations in spherical coordinates show similar results.

Warm Season Subseasonal Variability and Climate Extremes in the Northern Hemisphere: The Role of Stationary Rossby Waves

Abstract This study examines the nature of boreal summer subseasonal atmospheric variability based on the new NASA Modern-Era Retrospective Analysis for Research and Applications (MERRA) for the period 1979–2010. An analysis of the June, July, and August subseasonal 250-hPa meridional υ-wind anomalies shows distinct Rossby wave–like structures that appear to be guided by the mean jets. On monthly subseasonal time scales, the leading waves [the first 10 rotated empirical orthogonal functions (REOFs) of the 250-hPa υ wind] explain about 50% of the Northern Hemisphere υ-wind variability and account for more than 30% (60%) of the precipitation (surface temperature) variability over a number of regions of the northern middle and high latitudes, including the U.S. northern Great Plains, parts of Canada, Europe, and Russia. The first REOF in particular consists of a Rossby wave that extends across northern Eurasia where it is a dominant contributor to monthly surface temperature and precipitation variability and played an important role in the 2003 European and 2010 Russian heat waves. While primarily subseasonal in nature, the Rossby waves can at times have a substantial seasonal mean component. This is exemplified by REOF 4, which played a major role in the development of the most intense anomalies of the U.S. 1988 drought (during June) and the 1993 flooding (during July), though differed in the latter event by also making an important contribution to the seasonal mean anomalies. A stationary wave model (SWM) is used to reproduce some of the basic features of the observed waves and provide insight into the nature of the forcing. In particular, the responses to a set of idealized forcing functions are used to map the optimal forcing patterns of the leading waves. Also, experiments to reproduce the observed waves with the SWM using MERRA-based estimates of the forcing indicate that the wave forcing is dominated by submonthly vorticity transients.

Analytical solutions for the resonance response of Goupillaud-type elastic media using [formula omitted]-transform methods

The resonance frequency spectrum is first derived for an m-layered Goupillaud-type elastic medium that is subjected to a discrete sinusoidal forcing function that varies harmonically with time at one end and held fixed at the other end. Analytical stress solutions are obtained from a coupled first-order system of difference equations using z-transform methods, where the determinant of the resulting global system matrix in the z-space |Am| is a palindromic polynomial with real coefficients. The zeros of the palindromic polynomial are distinct and are proven to lie on the unit circle for 1≤m≤5 and for certain classes of multilayered designs identified by tridiagonal Toeplitz matrices. An important result is the physical interpretation that all the positive angles, coterminal with the angles corresponding to the zeros of |Am| on the unit circle, represent the resonance frequency spectrum for the discrete model. A sequence of resonance frequencies for the discrete model appears to be universal for all multilayered designs with an odd number of layers, as it is independent of any design parameters.The resonance frequency results for the discrete model are then extended to describe the resonance frequency spectrum for the continuous model, where the forcing function applied at one end of the strip is continuous and varies harmonically with time while the other end is held fixed. The proposed natural frequency spectrum for a free-fixed m-layered Goupillaud-type strip is confirmed by independently solving a simplified form of the frequency equation, obtained after applying a transformation of the spatial variable. Our results suggest that the natural frequency spectrum depends on the layer impedance ratios and it is inversely proportional to the equal wave travel time for each layer.The results are used to identify layered designs with a common frequency spectrum and modify an existing design to obtain a desired frequency spectrum. Other connections are made with previous stress optimization results, the Chebyshev polynomials of the first and second kind, as well as the natural frequencies of a free-fixed non-Goupillaud-type layered strip.

SIMULATIONS OF TURBULENT DYNAMOS DRIVEN BY THE MAGNETIC HELICITY FLUX

We present results of numerical simulations of driven magnetohydrodynamic turbulence in a periodic box with an imposed large-scale sinusoidal shear. We produce strong large-scale magnetic fields through dynamo action. This dynamo action is highly dependent on the spectral properties of the forcing function. In particular, we can produce either dynamo or antidynamo action by choosing particular forcing functions for the small-scale turbulence. Our results show that the large-scale electromotive force is well correlated with the local accumulation of eddy-scale magnetic helicity. Conversely, the electromotive force is very weakly correlated with the large-scale magnetic field strength or its product with kinetic helicity. We argue that in these simulations large-scale dynamo action is driven by an inverse cascade of magnetic helicity, ultimately caused by the tendency of anisotropic turbulence to create a magnetic helicity flux.

Natural convection in a sidewall heated cube using an immersed boundary method

Numerical simulation of a square cavity was conducted to validate an implementation of an Immersed Boundary Method (IBM). The cavity consists of two differentially heated side walls and adiabatic top and bottom walls. A Cartesian grid is used with a finite volume, fractional step pressure correction method. Simulations use Dirichlet boundaries for vertical walls and Neumann boundaries for horizontal walls. The Immersed Boundary Method involves modifying the Navier--Stokes equations to include a forcing function in the momentum and energy equations that creates a virtual boundary. This method is useful because the boundary does not necessarily have to coincide with grid points; however, it is much less computationally expensive than other similar methods such as the cut cell method. The IBM is commonly used in simulations involving complex objects and can also accommodate moving boundaries. A standard numerical simulation with grid aligned with the boundary is first compared with previous results. The same geometry is then simulated by tilting the grid at various angles and using the IBM for each of the walls, and comparing these results with those initially obtained. We detail the implementation method and common problems associated with this. Velocity and temperature profiles are presented and the IBM is shown to maintain second order spatial accuracy. References E. A. Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 161(1):35--60, 2000. doi:10.1006/jcph.2000.6484 T. Gao, Y. H. Tseng, and X. Y. Lu. An improved hybrid cartesian/immersed boundary method for fluid-solid flows. International Journal for Numerical Methods in Fluids, 55(12):1189--1211, 2007. doi:10.1002/fld.1522 M. P. Kirkpatrick and S. W. Armfield. Experimental and large eddy simulation results for the purging of salt water from a cavity by an overflow of fresh water. International Journal of Heat and Mass Transfer, 48(2):341--359, 2005. doi:10.1016/j.ijheatmasstransfer.2004.08.016 M. P. Kirkpatrick, S. W. Armfield, and J. H. Kent. A representation of curved boundaries for the solution of the navier-stokes equations on a staggered three-dimensional cartesian grid. Journal of Computational Physics, 184(1):1--36, 2003. doi:10.1016/S0021-9991(02)00013-X B. P. Leonard and Simin Mokhtari. Beyond first-order upwinding: The ultra-sharp alternative for non-oscillatory steady-state simulation of convection. International Journal for Numerical Methods in Engineering, 30(4):729--766, 1990. doi:10.1002/nme.1620300412 S. H. Peng and L. Davidson. Large eddy simulation for turbulent buoyant flow in a confined cavity. volume 22, pages 323--331, 2001. doi:10.1016/S0142-727X(01)00095-9 C. S. Peskin. Numerical-analysis of blood-flow in heart. Journal of Computational Physics, 25(3):220--252, 1977. doi:10.1016/0021-9991(77)90100-0 J. Salat, S. Xin, P. Joubert, A. Sergent, F. Penot, and P. Le Quere. Experimental and numerical investigation of turbulent natural convection in a large air-filled cavity. International Journal of Heat and Fluid Flow, 25:824--832, 2004. doi:10.1016/j.ijheatfluidflow.2004.04.003 Y. H. Tseng and J. H. Ferziger. A ghost-cell immersed boundary method for flow in complex geometry. Journal of Computational Physics, 192(2):593--623, 2003. doi:10.1016/j/jcp.2003.07.024 N. Zhang and Z. C. Zheng. An improved direct-forcing immersed-boundary method for finite difference applications. Journal of Computational Physics, 221(1):250--268, 2007. doi:10.1016/j.jcp.2006.06.012 N. Zhang, Z. C. Zheng, and S. Eckels. Study of heat-transfer on the surface of a circular cylinder in flow using an immersed-boundary method. International Journal of Heat and Fluid Flow, 29(6):1558--1566, 2008. doi:10.1016/j.ijheatfluidflow.2008.08.009

Transient motions of an oscillating system caused by forcing terms proportional to the velocity of the structural motion

Damping limits the motions of an oscillator, which is a dynamic system. The selection of formulations for damping is discussed. If the forcing of the dynamic system contains terms that are proportional to the velocity of motion of the oscillator (drag-type forcing functions), these effects will additionally contribute to dampening the oscillations. Should the total damping under certain conditions become apparently negative, the oscillations will grow until the damping has again become positive. Investigations into damping effects that apparently are negative, and discussions where apparent negative damping might appear in practical applications are of great interest.

Chandrasekhar–Kendall functions in astrophysical dynamos

Some of the contributions of Chandrasekhar to the field of magnetohydrodynamics are highlighted. Particular emphasis is placed on the Chandrasekhar–Kendall functions that allow a decomposition of a vector field into right- and left-handed contributions. Magnetic energy spectra of both contributions are shown for a new set of helically forced simulations at resolutions higher than what has been available so far. For a forcing function with positive helicity, these simulations show a forward cascade of the right-handed contributions to the magnetic field and nonlocal inverse transfer for the left-handed contributions. The speed of inverse transfer is shown to decrease with increasing value of the magnetic Reynolds number.

Process Study of Dry-Season Circulation in the Pearl River Estuary and Adjacent Coastal Waters using a Triple-Nested Coastal Circulation Model

The Pearl River Estuary (PRE) on the east coast of Guangdong Province in South China is a complicated hydrodynamic system affected by various forcing functions including tides, wind forcing, and sea surface heat and freshwater fluxes. The PRE also receives a large amount of freshwater runoff from the Pearl River through eight major river inlets. In this study, the three-dimensional circulation, hydrography, and associated temporal variability in the PRE and adjacent coastal waters during the dry season from December to March are examined using a triple-nested coastal ocean circulation modelling system based on the Princeton Ocean Model. Four numerical experiments are conducted by driving the triple-nested modelling system with different combinations of external forcing functions. Analysis of multi-year model results from the four experiments demonstrates that the estuarine plume in the dry season is close to the western shore of the PRE, mainly due to the combination of the low Pearl River discharge and the influence of the southwestward coastal current over the inner shelf of the northern South China Sea. Temperature and salinity inside the estuarine plume in the dry season are weakly stratified in the vertical, with large horizontal salinity gradients near the frontal zone of the plume. Baroclinic dynamics play a very important role in the plume, with the frontal circulation forced by the combination of wind, tides and the Pearl River discharge. In the offshore deep waters of the PRE during the dry season, vertical stratification in the top 15 m is weak and circulation can be approximated by barotropic dynamics forced by wind and tides.

THE INFLUENCE OF DRIVING FUNCTION ON FLOW DRIVEN BY PUMPING WITHOUT VALVES

Auid dynamics driven by pumping without valves (valveless pumping) shows interesting physics. Especially, the driving function to generate valveless pump mechanism is one of important factors. We consider a closed system of valveless pump which consists of flexible tube part and stiffer part. Fluid and structure (elastic tube) interaction motions are generated by the periodic compress-and-release actions on an asymmetric location of the elastic loop of tubing. In this work, we demonstrate how important the driving forcing function affects a net flow in the valveless circulatory system and investigate which parameter set of the system gives a more efficient net flow around the loop.

Self-Ordered Front under Temporally Irregular Forcing: Ratchet-Like Transport of the Quasi-Periodically Forced Front

Ratchet-like transport of the quasi-periodically forced “bistable” front joining two states of the different stability in the reaction-diffusion system is considered by use of the piecewise linear rate (reaction) function of the reaction kinetics. We approximate the oscillatory force acting on the front in the system by the bi-harmonic forcing functions being a superposition of the single-harmonic components (the Fourier modes) of the different frequencies, either commensurate or incommensurable ones. By considering the response of the self-ordered front to the oscillatory forces used we analyze the effect of the temporally irregular oscillations of the ac forcing on the ratchet-like shuttling of the ac driven front. By comparing the average characteristics of the spurious drift derivable in both cases of the periodically and quasi-periodically forced fronts we show that the temporally irregular fluctuations of the oscillatory force shrink the spurious drift of the front. More specifically, we find the performance of the ratchet-like shuttling of the self-ordered fronts is much lesser pronounced with the quasi-periodic, temporally irregular ac forcing if compared to that derivable by the rigorously periodic forcing, in both cases of the symmetrical and asymmetrical rate functions satisfying the different symmetry. The average characteristics of the spurious drift, that describe the dependence of the mean drift velocity of the ac driven front versus both the amplitude (strength) and the frequency of the oscillatory forces used are presented.

Pre-Observational Evolution of Surface Temperature in Romania as Inferred from Borehole Temperature Measurements

Temperature data from nine boreholes in the Carpathian orogen in Romania were used to obtain information on the ground surface temperature history (GSTH) in the last 250 years. The temperature measurements were taken with a thermistor probe (sensitivity in the 10 mK range) using the stop-and-go technique, at 10 m intervals, in the depth range of 20–580 m. The least squares inverse modelling approach of Tarantola and Valette (J Geophys 50:159–170, 1982) was used to infer the GSTH. Long-term air temperature records available from the Romanian weather station network were used as a comparison term for the first 100–150 years of the GSTH, and as a forcing function in a POM-SAT model that combines borehole temperature profiles (BTPs) and meteorological time series (surface air temperature, SAT) to produce information on the so-called pre-observational mean (POM). Results from a global circulation model for the Romanian area are incorporated in the discussion as well.

Fitting dynamic models with forcing functions: application to continuous glucose monitoring in insulin therapy.

The artificial pancreas is an emerging technology to treat type 1 diabetes (T1D). It has the potential to revolutionize diabetes care and improve quality of life. The system requires extensive testing, however, to ensure that it is both effective and safe. Clinical studies are resource demanding and so a principle aim is to develop an in silico population of subjects with T1D on which to conduct pre-clinical testing. This paper aims to reliably characterize the relationship between blood glucose and glucose measured by subcutaneous sensor as a major step towards this goal. Blood-and sensor-glucose are related through a dynamic model, specified in terms of differential equations. Such models can present special challenges for statistical inference, however. In this paper we make use of the BUGS software, which can accommodate a limited class of dynamic models, and it is in this context that we discuss such challenges. For example, we show how dynamic models involving forcing functions can be accommodated. To account for fluctuations away from the dynamic model that are apparent in the observed data, we assume an autoregressive structure for the residual error model. This leads to some identifiability issues but gives very good predictions of virtual data. Our approach is pragmatic and we propose a method to mitigate the consequences of such identifiability issues. Copyright © 2011 John Wiley & Sons, Ltd.

Comparing three basic models for seasonal influenza

In this paper we report the use of the open source Spatiotemporal Epidemiological Modeler (STEM, www.eclipse.org/stem) to compare three basic models for seasonal influenza transmission. The models are designed to test for possible differences between the seasonal transmission of influenza A and B. Model 1 assumes that the seasonality and magnitude of transmission do not vary between influenza A and B. Model 2 assumes that the magnitude of seasonal forcing (i.e., the maximum transmissibility), but not the background transmission or flu season length, differs between influenza A and B. Model 3 assumes that the magnitude of seasonal forcing, the background transmission, and flu season length all differ between strains. The models are all optimized using 10 years of surveillance data from 49 of 50 administrative divisions in Israel. Using a cross-validation technique, we compare the relative accuracy of the models and discuss the potential for prediction. We find that accounting for variation in transmission amplitude increases the predictive ability compared to the base. However, little improvement is obtained by allowing for further variation in the shape of the seasonal forcing function.