Influence of Deformations Prior to Instability on the Dynamic Instability of Conical Shells Under Periodic Axial Load

1976 ◽  
Vol 43 (1) ◽  
pp. 87-91 ◽  
Author(s):  
J. Tani
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Axial Load ◽  
Basic Equation ◽  
Natural Frequencies ◽  
Dynamic Instability ◽  
Forced Vibrations ◽  
The Other ◽  
Conical Shells ◽  
Instability Regions

The dynamic instability of clamped, truncated conical shells under periodic axial load is studied using the Donnell-type basic equation and considering the effect of bending deformations before instability. Two principal instability regions are determined by combining Bolotin’s method and a finite-difference method. One of these belongs to double the natural frequencies of asymmetrical vibration; the other corresponds to the resonance of symmetrically forced vibrations. The effects of static axial load and end-plate mass on the principal instability regions are also investigated.

Boundary-layer flow between nodal and saddle points of attachment

1970 ◽  
Vol 41 (4) ◽  
pp. 823-835 ◽  
Author(s):  
J. C. Cooke ◽  
A. J. Robins
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Saddle Point ◽  
Difference Method ◽  
Series Solution ◽  
Nodal Point ◽  
Saddle Points ◽  
The Other ◽  
The Finite Difference Method ◽  
Layer Flow

A simplified example of this type of flow was examined in detail by developing two series, eventually matched, one about the nodal point and the other about the saddle point, and also by finite differences, marching from the nodal point to the saddle point. It was found that the results of marching the two series were in agreement with the finite difference method. The series solution near the saddle point is not unique, but numerical evidence indicates that the correct solution is that which has ‘exponential decay’ at infinity, and that this type of solution, if such exists, automatically emerges when the finite difference method is used.

Influence of Rotational Speed on Thermal Performance of Tri-Sector Rotary Regenerative Air Preheater

2016 ◽  
Author(s):  
Xun Chen ◽  
Xue-nong Duan ◽  
Li-min Wang ◽  
Yi Yang ◽  
Dun-dun Wang ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Rotational Speed ◽  
The Other ◽  
Heating Period ◽  
Height Range ◽  
Rotational Angle ◽  
Air Preheater ◽  
Deposition Area

This paper provides a detailed analysis of how a rotary regenerative air preheater’s performance parameters such as effectiveness, fluid and metal temperature fields, and ammonium bisulfate (ABS) deposition area vary with rotor rotational speed. A tri-sector rotary regenerative air preheater for a 600MW unit was studied as an example by use of effectiveness–modified number of transfer units (ε-NTU0) method and a finite difference method. The findings of the research are as follows: (1) There is a nonlinear relationship between matrix temperature distribution and rotational angle, and the degree of nonlinearity, represented by unsteady heat transfer correction factor Π, increases with decreasing rotational speed and varies between sectors; (2) There exist two equilibrium positions around the intersection points of matrix temperature curves for different rotational speeds, one occurring in the heating period and the other in the cooling period; (3) The act of reducing the rotor speed has two effects on ABS deposition. On the one hand, the height range of possible ABS deposition area will expand as the matrix temperature within the first third of gas sector’s angle range further decreases with decreasing rotational speed. On the other hand, after the rotational speed falls below a certain level, the hot-end matrix temperature climbs above the ABS formation temperature during part of the heating period, resulting in gasification and decomposition of the condensed product. The combined effect is yet to be examined through further theoretical and empirical analyses. (4) The trends of average outlet temperatures of primary and secondary air depend on rotor rotation direction and angles of sectors. (5) The effectiveness values calculated by ε-NTU0 method are greater than those acquired by the finite difference method, especially at low rotor rotational speeds.

scholarly journals Numerical analyses of embankment dams containing plastic concrete cut-off walls using finite difference method (A case study: The Karkheh Embankment Dam)

2021 ◽  
Vol 9 (3) ◽  
pp. 143-153
Author(s):  
Yadolah Pashang Pisheh ◽  
Seyd Majdeddin Mir Mohammad Hosseini
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
The Other ◽  
Numerical Analyses ◽  
Maximum Magnitude ◽  
Embankment Dam ◽  
Plastic Concrete ◽  
Clay Core

In this paper, numerical analyses have been performed on the Karkheh embankment dam with a clayey core and plastic concrete cut-off wall during construction, impounding, and permanent seepage stages. The dam has 127 meters height and is located in a high seismic hazard zone in Iran. Different stages of construction, water impounding, and steady state seepage were modelled and analyzed using the hyperbolic and Mohr-Coulomb models with the two dimensional finite difference method (FDM). So, nonlinear analyses were performed using FLAC 2D to investigate the settlements and the pore water pressure changes in different zones of the dam during above-mentioned stages and the results were compared to those of the other studies. The results show that at the end of the construction stage, the maximum settlement equal to 1.45m occurs inside the clay core at the height of 65m. Then, after impounding of the reservoir and steady state stage, the maximum magnitude of the horizontal deformations occurs in the downstream of the dam equal to 0.55m; however, these magnitudes reach to 0.17m at the crest of the dam. Moreover, it was shown that the maximum horizontal displacement of the plastic concrete cut-off wall has happened at the top of the wall in the clay core which is in a good agreement with the other studies’ result.

scholarly journals Nonparametric Malliavin–Monte Carlo Computation of Hedging Greeks

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 120
Author(s):  
Maria Elvira Mancino ◽  
Simona Sanfelici
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Finite Difference ◽  
Finite Difference Method ◽  
The Other ◽  
Monte Carlo Computation ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Discontinuous Payoffs ◽  
Weight Method

We propose a way to compute the hedging Delta using the Malliavin weight method. Our approach, which we name the λ-method, generally outperforms the standard Monte Carlo finite difference method, especially for discontinuous payoffs. Furthermore, our approach is nonparametric, as we only assume a general local volatility model and we substitute the volatility and the other processes involved in the Greek formula with quantities that can be nonparametrically estimated from a given time series of observed prices.

scholarly journals Application of the finite difference method for modeling cantilever bar vibrations

2020 ◽  
Vol 224 ◽  
pp. 02002
Author(s):  
M I Volnikov
Keyword(s):  
Mathematical Modeling ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Structural Mechanics ◽  
Forced Vibrations ◽  
Cantilever Beams ◽  
System Parameters ◽  
Free And Forced Vibrations ◽  
The Finite Difference Method

The paper is devoted to mathematical modeling of cantilever bars using the finite difference method. This method is widely used in structural mechanics for solving static problems. The novelty lies in the application of the finite difference method to simulate the dynamics of free and forced vibrations of the cantilever. Models have been developed that allow calculating the static and dynamic deflections of the cantilevers during free and forced vibrations, as well as simulating the vibrations of cantilever beams with attached vibration dampers. The resulting models of cantilever structures make it easy to modify system parameters, external influences and damping elements. All calculations were performed using the finite difference approach when moving along geometric and temporal coordinates.

Parametric Instability in a Taut String With a Periodically Moving Boundary

2014 ◽  
Vol 81 (6) ◽  
Author(s):  
K. Wu ◽  
W. D. Zhu
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Linear Model ◽  
Difference Method ◽  
Periodic Boundary ◽  
Moving Boundary ◽  
Nonlinear Models ◽  
Parametric Instability ◽  
Taut String ◽  
Instability Regions

Parametric instability in a taut string with a periodically moving boundary, which is governed by a one-dimensional wave equation with a periodically varying domain, is investigated. Parametric instability usually occurs when coefficients in governing differential equations of a system periodically vary, and the system is said to be parametrically excited. Since the governing partial differential equation of the string with a periodically moving boundary can be transformed to one with a fixed domain and periodically varying coefficients, the string is parametrically excited and instability caused by the periodically moving boundary is classified as parametric instability. The free linear vibration of a taut string with a constant tension, a fixed boundary, and a periodically moving boundary is studied first. The exact response of the linear model is obtained using the wave or d'Alembert solution. The parametric instability in the string features a bounded displacement and an unbounded vibratory energy, and parametric instability regions in the parameter plane are classified as period-i (i≥1) parametric instability regions, where period-1 parametric instability regions are analytically obtained using the wave solution and the fixed point theory, and period-i (i>1) parametric instability regions are numerically calculated using bifurcation diagrams. If the periodic boundary movement profile of the string satisfies certain condition, only period-1 parametric instability regions exist. However, parametric instability regions with higher period numbers can exist for a general periodic boundary movement profile. Three corresponding nonlinear models that consider coupled transverse and longitudinal vibrations of the string, only the transverse vibration, and coupled transverse and axial vibrations are introduced next. Responses and vibratory energies of the linear and nonlinear models are calculated for both stable and unstable cases using three numerical methods: Galerkin's method, the explicit finite difference method, and the implicit finite difference method; advantages and disadvantages of each method are discussed. Numerical results for the linear model can be verified using the exact wave solution, and those for the nonlinear models are compared with each other since there are no exact solutions for them. It is shown that for parameters in the parametric instability regions of the linear model, the responses and vibratory energies of the nonlinear models are close to those of the linear model, which indicates that the parametric instability in the linear model can also exist in the nonlinear models. The mechanism of the parametric instability is explained in the linear model and through axial strains in the third nonlinear model.

Study on Performance Evaluation of Automotive Radiator

2015 ◽  
Vol 2 (2) ◽  
Author(s):  
J P Yadav ◽  
Bharat Raj Singh
Keyword(s):  
Performance Evaluation ◽  
Comparative Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
The Other ◽  
Coolant Temperature ◽  
Flow Passage ◽  
Test Setup ◽  
Parametric Studies ◽  
Complete Set

A complete set of numerical parametric studies on automotive radiator has been presented in detail in this study. The modeling of radiator has been described by two methods, one is finite difference method and the other is thermal resistance concept. In the performance evaluation, a radiator is installed into a test-setup and the various parameters including mass flow rate of coolant, inlet coolant temperature; etc. are varied. A comparative analysis between different coolants is also shown. One coolant as water and other as mixture of water in propylene glycol in a ratio of 40:60 is used. It is observed that that the water is still the best coolant but its limitation is that it is corrosive and contains dissolved salts that degrade the coolant flow passage.

scholarly journals Solusi numerik model matematika SHEIR pada penyebaran penyakit campak dengan vaksinasi Dan kekebalan kelompok

SAINTIFIK ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 15-20
Author(s):  
Darmawati Darmawati
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Herd Immunity ◽  
The Other ◽  
Transmission Dynamics ◽  
Other Hand ◽  
Nonstandard Finite Difference

In this paper, mathematical model of measles transmission dynamics considering vaccination and herd immunity is discussed. The solution of the model is investigated using euler, atangana, dan nonstandard finite difference method. After comparing the solutions of the model, we observe that the solutions obtained by using euler and atangana method diverge for certain step. On the other hand, the solutions obtained by using nonstandard finite difference always converge.

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