scholarly journals Nonlinear Dynamics of Swinging Clapper Bells under Arbitrary or Resonant Forcing Functions

2020 ◽  
Vol 10 (16) ◽  
pp. 5528
Author(s):  
Pietro Croce
Keyword(s):  
Case Studies ◽  
Numerical Solutions ◽  
Oscillation Amplitude ◽  
Rigid Body Dynamics ◽  
Fine Tuning ◽  
Time Interval ◽  
Time Step ◽  
Forcing Function ◽  
Resonant Forcing ◽  
Forcing Functions

Study of swinging clapper bells involves aspects encompassing sound and acoustic engineering, mechanical engineering, and structural engineering. From the musical point of view, clapper bells are directly played idiophone instruments, where the playing device, the clapper, although directly excited, is not explicitly controlled by the bell ringer. The achievement of a clear and optimal sound mainly depends on the acoustic characteristics of the bell and on the regularity of the clapper strokes, which is not only governed by the ringing style and the relevant parameters of clapper and bell but also by the real time corrections to the excitation introduced by trained bell ringers. In fact, despite centuries of experience allowed to optimize the bell performances, standardizing proportions and mounting arrangements, effective sound control requires some fine tuning of the forcing function. Another crucial topic, especially in view of assessing existing structures, regards the evaluation of time histories of the actions transmitted by the bell to the pivots and the study of the interactions between the bell and the supporting structures, belfries, and bell-towers. “Ringability” of swinging bells and bell-structure interactions are usually tackled in the framework of rigid body dynamics, so arriving at an initial value problem, governed by a system of two second order nonlinear ordinary differential equations (ODEs), whose solutions are piecewise-defined functions. In the relevant literature, numerical solutions of the system are commonly sought using built-in algorithms provided in advanced software packages; since the use of such general algorithms is subject to some restrictions, especially regarding the forcing functions, validity of the results is often limited. The present study focuses on an innovative procedure to solve the equations of motion. The method, extremely fast and effective, is based on original numerical explicit-implicit predictor-corrector integration algorithms with constant time step, duly validated reproducing the outcomes of relevant reference case studies. Each time the clapper strikes the bell a new “piece” of the solution is initialized, so avoiding user interventions in the elaboration phase. Independently on the oscillation amplitude and on the duration of the considered time interval, the algorithms can successfully manage undamped oscillations; friction and viscosity damped oscillations; free oscillations in transient and stationary phases; and can be applied also to solve stiff equations. Furthermore, the capability of the proposed methods to deal with arbitrary forcing functions is particularly innovative. The outcomes of relevant case studies, regarding the oscillations of the old tenor bell of the Great St. Mary church in Cambridge, confirm the potentialities of the method, also highlighting some topical issues, involving, for example, the assessment of damping equivalence. Finally, a pioneering feature of the algorithms is their ability to handle and to define “resonant” forcing functions, continuously tuning the frequency of the excitation to the natural frequency of the oscillation, according to the oscillation amplitude.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

scholarly journals Coupling Disease-Progress-Curve and Time-of-Infection Functions for Predicting Yield Loss of Crops

2000 ◽  
Vol 90 (8) ◽  
pp. 788-800 ◽  
Author(s):  
L. V. Madden ◽  
G. Hughes ◽  
M. E. Irwin
Keyword(s):  
Yield Loss ◽  
Numerical Solutions ◽  
Disease Incidence ◽  
Time Interval ◽  
Short Time Interval ◽  
Time Duration ◽  
Plant Yield ◽  
Disease Progress ◽  
Time Of Infection ◽  
Over Time

A general approach was developed to predict the yield loss of crops in relation to infection by systemic diseases. The approach was based on two premises: (i) disease incidence in a population of plants over time can be described by a nonlinear disease progress model, such as the logistic or monomolecular; and (ii) yield of a plant is a function of time of infection (t) that can be represented by the (negative) exponential or similar model (ζ(t)). Yield loss of a population of plants on a proportional scale (L) can be written as the product of the proportion of the plant population newly infected during a very short time interval (X′(t)dt) and ζ(t), integrated over the time duration of the epidemic. L in the model can be expressed in relation to directly interpretable parameters: maximum per-plant yield loss (α, typically occurring at t = 0); the decline in per-plant loss as time of infection is delayed (γ; units of time-1); and the parameters that characterize disease progress over time, namely, initial disease incidence (X0), rate of disease increase (r; units of time-1), and maximum (or asymptotic) value of disease incidence (K). Based on the model formulation, L ranges from αX0 to αK and increases with increasing X0, r, K, α, and γ-1. The exact effects of these parameters on L were determined with numerical solutions of the model. The model was expanded to predict L when there was spatial heterogeneity in disease incidence among sites within a field and when maximum per-plant yield loss occurred at a time other than the beginning of the epidemic (t > 0). However, the latter two situations had a major impact on L only at high values of r. The modeling approach was demonstrated by analyzing data on soybean yield loss in relation to infection by Soybean mosaic virus, a member of the genus Potyvirus. Based on model solutions, strategies to reduce or minimize yield losses from a given disease can be evaluated.

An Elongating String Under the Action of a Transverse Force

1957 ◽  
Vol 24 (4) ◽  
pp. 609-616
Author(s):  
Werner Goldsmith
Keyword(s):  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Transverse Force ◽  
Transverse Displacement ◽  
Fixed Frequency ◽  
Constant Acceleration ◽  
Forcing Function ◽  
Subsonic Regime ◽  
Arbitrary Amplitude ◽  
Analytical Expressions

Abstract The motion of a uniform undamped flexible string whose length increases with time has been investigated when an arbitrary time-dependent force acts transversely at the free end. The method of characteristics has been employed to derive analytical expressions for the transverse displacement in the subsonic regime. Cases are considered when the free end of the wire moves either at constant velocity or at constant acceleration. Numerical solutions are presented in dimensionless form for a sinusoidal forcing function of arbitrary amplitude and fixed frequency. The possibility of the existence of resonances in the string has been examined.

A Flexible Component-Based ePortfolio

2011 ◽  
pp. 292-304 ◽  
Author(s):  
S. J. Cotterill ◽  
J. F. Aiton ◽  
P. M. Bradley ◽  
G. R. Hammond ◽  
A. M. McDonald ◽  
...  
Keyword(s):  
Case Studies ◽  
Clinical Skills ◽  
Scientific Basis ◽  
Fine Tuning ◽  
Research Approach ◽  
Action Research Approach ◽  
Evaluation Phase ◽  
Technical Features ◽  
The Uk ◽  
Flexible Component

This chapter provides case studies of embedding the ePortfolio in the curricula of two medical schools in the UK, one of which is outcomes based, while the other uses a series of patient scenarios to inform the teaching of clinical skills within a curriculum that emphasises the scientific basis of medicine. These case studies describe the implementation, evaluation, and process of embedding the portfolio within the respective curricula. They also illustrate the flexibility of a component-based ePortfolio to serve different pedagogic requirements. Research and evaluation issues are discussed, including an action-research approach with “fine-tuning” of technical features and pedagogy during the evaluation phase.

scholarly journals An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination

2014 ◽  
Vol 24 (3) ◽  
pp. 635-646 ◽  
Author(s):  
Deqiong Ding ◽  
Qiang Ma ◽  
Xiaohua Ding
Keyword(s):  
Numerical Simulation ◽  
Global Stability ◽  
Difference Equations ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Numerical Solutions ◽  
Time Step ◽  
The Stability ◽  
Nsfd Scheme ◽  
Nonstandard Finite Difference

Abstract In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our proof of global stability utilizes the method of Lyapunov functions. Numerical simulation illustrates the effectiveness of our results

Forcing Function Effects on Unsteady Aerodynamic Gust Response: Part 1 — Forcing Functions

1992 ◽  
Author(s):  
Gregory H. Henderson ◽  
Sanford Fleeter
Keyword(s):  
Linear Theory ◽  
Static Pressure ◽  
Pressure Fluctuations ◽  
Perforated Plate ◽  
Flow Angle ◽  
Unsteady Aerodynamic ◽  
Forcing Function ◽  
Forcing Functions ◽  
Relative Flow ◽  
Gust Response

The fundamental gust modeling assumption is investigated by means of a series of experiments performed in the Purdue Annular Cascade Research Facility. The unsteady periodic flow field is generated by rotating rows of perforated plates and airfoil cascades. In this paper, the measured unsteady flow fields are compared to linear-theory gust requirements, with the resulting unsteady gust response of a downstream stator cascade correlated with linear theory predictions in an accompanying paper. The perforated-plate forcing functions closely resemble linear-theory forcing functions, with the static pressure fluctuations small and the periodic velocity vectors parallel to the downstream mean-relative flow angle over the entire periodic cycle. In contrast, the airfoil forcing functions exhibit characteristics far from linear-theory gusts, with the alignment of the velocity vectors and the static pressure fluctuation amplitudes dependent on the rotor-loading condition, rotor solidity and the inlet mean-relative flow angle. Thus, these unique data clearly show that airfoil wakes, both compressor and turbine, are not able to be modeled with the boundary conditions of current state-of-the-art linear unsteady aerodynamic theory.

scholarly journals An Attention-Based Spatiotemporal Gated Recurrent Unit Network for Point-of-Interest Recommendation

2019 ◽  
Vol 8 (8) ◽  
pp. 355 ◽  
Author(s):  
Chunyang Liu ◽  
Jiping Liu ◽  
Jian Wang ◽  
Shenghua Xu ◽  
Houzeng Han ◽  
...  
Keyword(s):  
Behavioral Intention ◽  
Early Stage ◽  
Time Interval ◽  
Time Step ◽  
Attention Model ◽  
Point Of Interest ◽  
Poi Recommendation ◽  
Real World Datasets ◽  
Current Sequence ◽  
Gated Recurrent Unit

Point-of-interest (POI) recommendation is one of the fundamental tasks for location-based social networks (LBSNs). Some existing methods are mostly based on collaborative filtering (CF), Markov chain (MC) and recurrent neural network (RNN). However, it is difficult to capture dynamic user’s preferences using CF based methods. MC based methods suffer from strong independence assumptions. RNN based methods are still in the early stage of incorporating spatiotemporal context information, and the user’s main behavioral intention in the current sequence is not emphasized. To solve these problems, we proposed an attention-based spatiotemporal gated recurrent unit (ATST-GRU) network model for POI recommendation in this paper. We first designed a novel variant of GRU, which acquired the user’s sequential preference and spatiotemporal preference by feeding the continuous geographical distance and time interval information into the GRU network in each time step. Then, we integrated an attention model into our network, which is a personalized process and can capture the user’s main behavioral intention in the user’s check-in history. Moreover, we conducted an extensive performance evaluation on two real-world datasets: Foursquare and Gowalla. The experimental results demonstrated that the proposed ATST-GRU network outperforms the existing state-of-the-art POI recommendation methods significantly regarding two commonly-used evaluation metrics.

scholarly journals Atmospheric Temperature and CO2: Hen-or-Egg Causality?

Sci ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 77
Author(s):  
Demetris Koutsoyiannis ◽  
Zbigniew Kundzewicz
Keyword(s):  
Atmospheric Carbon Dioxide ◽  
Common Knowledge ◽  
Carbon Dioxide Concentration ◽  
Co2 Concentration ◽  
Atmospheric Temperature ◽  
Time Interval ◽  
Reverse Causality ◽  
Time Step ◽  
Relationship Of ◽  
The Relationship

It is common knowledge that increasing CO2 concentration plays a major role in enhancement of the greenhouse effect and contributes to global warming. The purpose of this study is to complement the conventional and established theory that increased CO2 concentration due to human emissions causes an increase of temperature, by considering the reverse causality. Since increased temperature causes an increase in CO2 concentration, the relationship of atmospheric CO2 and temperature may qualify as belonging to the category of “hen-or-egg” problems, where it is not always clear which of two interrelated events is the cause and which the effect. We examine the relationship of global temperature and atmospheric carbon dioxide concentration at the monthly time step, covering the time interval 1980–2019, in which reliable instrumental measurements are available. While both causality directions exist, the results of our study support the hypothesis that the dominant direction is T → CO2. Changes in CO2 follow changes in T by about six months on a monthly scale, or about one year on an annual scale. We attempt to interpret this mechanism by involving biochemical reactions, as at higher temperatures soil respiration, and hence CO2 emission, are increasing.

a retrospective view of Richardson's book on weather prediction*

1967 ◽  
Vol 48 (8) ◽  
pp. 514-551 ◽  
Author(s):  
George W. Platzman
Keyword(s):  
Vertical Velocity ◽  
Stability Criterion ◽  
Weather Prediction ◽  
Pressure Change ◽  
Time Interval ◽  
Time Step ◽  
Initial Field ◽  
Static Approximation ◽  
Modern Development ◽  
The Stability

In 1922 Lewis F. Richardson published a comprehensive numerical method of weather prediction. He used height rather than pressure as vertical coordinate but recognized that a diagnostic equation for the vertical velocity is a necessary corollary to the quasi-static approximation. His vertical-velocity equation is the principal, substantive contribution of the book to dynamic meteorology. A comparison of Richardson's model with one now in operational use at the U. S. National Meteorological Center shows that, if only the essential attributes of these models are considered, there is virtually no fundamental difference between them. Even the vertical and horizontal resolutions of the models are similar. Richardson made a forecast at two grid points in central Europe and obtained catastrophic results, in particular a surface pressure change of 145 mb in 6 hours. This failure resulted partly, as Richardson believed, from inadequacies of upper wind data. Underlying this was a more fundamental difficulty which he did not seem to recognize clearly at the time he wrote his book: the impossibility of using observed winds to calculate pressure change from the pressure-tendency equation, a principle stated many years earlier by Margules. However, he did point in the direction in which a remedy was later found: suppression or smoothing of the initial field of horizontal velocity divergence. The 6-hr time interval used by Richardson violates the condition for computational stability, a constraint then unknown. It is sometimes said that this is one of the reasons his calculation failed, but that interpretation is misleading because the stability criterion becomes relevant only after several time steps have been made. Since Richardson did not go beyond a calculation of initial tendencies—in other words, he took only one time step—violation of the stability criterion had no effect on the result. Richardson's book surely must be recorded as a major scientific achievement. Nevertheless, it appears to have had little influence in the decades that followed, and indeed, the modern development of numerical weather prediction, which began about twenty-five years later, did not evolve primarily from Richardson's work. Shaw said it would be misleading to regard the book as “a soliloquy on the scientific stage,” but in fact that is what it proved to be. The intriguing problem of explaining this strange irony is one that leads beyond the obvious facts that when Richardson wrote, computers were nonexistent and upper-air data insufficient.

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