Auxiliary Functions for Different Types of Boundary Conditions

2009 ◽  
pp. 747-750
Keyword(s):  
Boundary Conditions ◽  
Auxiliary Functions ◽  
Different Types

scholarly journals A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-30 ◽  
Author(s):  
Dongyan Shi ◽  
Yunke Zhao ◽  
Qingshan Wang ◽  
Xiaoyan Teng ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Analysis Model ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Auxiliary Functions ◽  
Arbitrary Boundary Conditions ◽  
Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

scholarly journals An Advanced Galerkin Approach to Solve the Nonlinear \\[6pt]Reaction-Diffusion Equations With Different Boundary Conditions

2022 ◽  
Vol 14 (1) ◽  
pp. 30
Author(s):  
Hazrat Ali ◽  
Md. Kamrujjaman ◽  
Md. Shafiqul Islam
Keyword(s):  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Parabolic Partial Differential Equations ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Nonlinear Parabolic ◽  
Comparison Results ◽  
Different Types ◽  
Convergence And Stability Analysis

This study proposed a scheme originated from the Galerkin finite element method (GFEM) for solving nonlinear parabolic partial differential equations (PDEs) numerically with initial and different types of boundary conditions. The scheme is applied generally handling the nonlinear terms in a simple way and throwing over restrictive assumptions. The convergence and stability analysis of the method are derived. The error of the method is estimated. In the series, eminent problems are solved, such as  Fisher's equation, Newell-Whitehead-Segel equation, Burger's equation, and  Burgers-Huxley equation to demonstrate the validity, efficiency, accuracy, simplicity and applicability of this scheme. In each example, the comparison results are presented both numerically and graphically

scholarly journals ANALYSIS OF STUDENT FORMULA CAR FOR OPTIMUM SAFETY AND PERFORMANCE

2020 ◽  
pp. 137-142
Author(s):  
Rabi Pathak
Keyword(s):  
Boundary Conditions ◽  
Weight Reduction ◽  
Structural Performance ◽  
Complete Analysis ◽  
Loading Conditions ◽  
Different Types ◽  
And Performance ◽  
Reliability Performance ◽  
Ansys Workbench

The Formula Student competitions are held everyyear. This paper is the result of the analysis done on the sample car design that can be presented in the Formula Student competition. The purpose of the paper is to provide a final summary on chassis analysis and structural performance. It also talks about all the important analysis that is to be done on a Formula Student car to make it safe and perform well on the track. The design has been made such that it focusses on maximum adjustability, reliability, performance, safety, weight reduction and ease of manufacturing. The analysis was done to make sure the objectives of design are fulfilled. After going through many papers, documents, blogs and videos we found that many people get confused about the loading conditions and boundary conditions for different types of tests so this paper prioritizes to make people understand about those conditions as well as about the major tests required to perform complete analysis of Formula Student cars. The weight of the chassis was calculated as 36 kg approximately according to the data obtained from design modeler of Ansys workbench as well as Solidworks. The design sustained all the loading conditions and passed all the tests. Thus, one of the objective of this paper is to help other universities and passionate students to successfully design and analyze their cars that can pass all necessary tests included in the paper. KEYWORDS—Formula Student; FEA; Boundary Conditions; Loading Conditions; Ansys; Solidworks

scholarly journals Lamb waves in multilayered media: 3D and 6D formalisms

2019 ◽  
Vol 97 ◽  
pp. 03003
Author(s):  
Anna Avershyeva ◽  
Sergey Kuznetsov
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Fundamental Matrix ◽  
Elastic Anisotropy ◽  
Lamb Waves ◽  
Stratified Media ◽  
Multilayered Media ◽  
Different Types ◽  
Secular Equations ◽  
Fundamental Matrices

A mathematical model for analyzing Lamb waves propagating in stratified media with arbitrary elastic anisotropy is worked out. The model incorporates a combined Fundamental Matrix (FM) and Modified Transfer Matrix (MTM) methods. Multilayered unbounded plates with different types of boundary conditions imposed on the outer surfaces are considered. Closed form fundamental matrices and secular equations for dispersion relations are derived.

Investigation of Damping Potential of Strip Damper on a Real Turbine Blade

2016 ◽  
Author(s):  
M. Afzal ◽  
I. Lopez Arteaga ◽  
L. Kari ◽  
V. Kharyton
Keyword(s):  
Boundary Conditions ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Element Model ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Bladed Disk ◽  
Different Types

This paper investigates the damping potential of strip dampers on a real turbine bladed disk. A 3D numerical friction contact model is used to compute the contact forces by means of the Alternate Frequency Time domain method. The Jacobian matrix required during the iterative solution is computed in parallel with the contact forces, by a quasi-analytical method. A finite element model of the strip dampers, that allows for an accurate description of their dynamic properties, is included in the steady-state forced response analysis of the bladed disk. Cyclic symmetry boundary conditions and the multiharmonic balance method are applied in the formulation of the equations of motion in the frequency domain. The nonlinear forced response analysis is performed with two different types of boundary conditions on the strip: (a) free-free and (b) elastic, and their influence is analyzed. The effect of the strip mass, thickness and the excitation levels on the forced response curve is investigated in detail.

Theory of Viscoplastic Lubrication: Part 2—Applications

1992 ◽  
Vol 114 (3) ◽  
pp. 477-484 ◽  
Author(s):  
W. R. D. Wilson ◽  
X. B. Huang
Keyword(s):  
Boundary Conditions ◽  
Companion Paper ◽  
Slider Bearing ◽  
Reynolds Equations ◽  
Different Types ◽  
Branching Problem ◽  
Inlet Zone ◽  
Development Methods ◽  
Newtonian Behavior

The Reynolds equations for viscoplastic lubricants can be quite complex, involving multiple branches which depend on the form of the boundary conditions invoked in their development. Methods of visualizing and understanding the branching problem are explored. This information is used, together with the Reynolds equations developed in the companion paper, in analyses of the lubrication of a wide slider bearing and a metalforming inlet zone. The results of these analyses are used to draw general conclusions regarding the influence of different types of non-Newtonian behavior.

Research on the Water Absorbent Laws of Injection Wells Formation

2014 ◽  
Vol 1006-1007 ◽  
pp. 83-87
Author(s):  
Zhong Guo Wang ◽  
Guang Yu Zhang ◽  
Yi Qing Li ◽  
De Kai Zhou ◽  
Wen Ping Song
Keyword(s):  
Boundary Conditions ◽  
Coupling Effect ◽  
Oil Production ◽  
Reservoir Model ◽  
Injection Wells ◽  
Different Boundary Conditions ◽  
Different Types ◽  
Key Factor ◽  
Bottomhole Pressure

Layered injection commissioning technology has become a key factor to the oil production. For different types of formations, the paper analyzes the absorbent law in different homogeneous formations with different boundary conditions. The paper also creates a composite reservoir model, and then describes changes of absorbent law under coupling effect. The method to do all of the above work is to solve the equation of dimensionless bottomhole pressure in different formation and boundary conditions.

On Boundary Damping for Semi-Infinite Strings and Beams

2015 ◽  
Author(s):  
Tugce Akkaya ◽  
Wim T. van Horssen
Keyword(s):  
Boundary Conditions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Beam Equation ◽  
Infinite Domain ◽  
Different Types ◽  
Linear String ◽  
The One ◽  
Initial Boundary Value ◽  
Infinite Strings

In this paper, initial boundary value problems for a linear string and beam equation are considered. The main aim is to study the reflection of an incident wave at the boundary and the damping properties for different types of boundary conditions such as a mass-spring-dashpot for semi-infinite strings, and pinned, sliding, clamped and damping boundary conditions for semi-infinite beams. The system of transverse vibrations are divided into model 1 and model 2 which are described as a string problem and beam problem, respectively. In order to construct explicit solutions of the boundary value problem for the first model the D’Alembert method will be used to the one dimensional wave equation on the semi-infinite domain, and for the second model the method of Laplace transforms will be applied to a beam equation on a semi-infinite domain. It will be shown how waves are damped and reflected for different types of boundaries and how much energy is dissipated at the boundary.

scholarly journals Absorbing boundary conditions for wave‐equation migration

Geophysics ◽  
1980 ◽  
Vol 45 (5) ◽  
pp. 895-904 ◽  
Author(s):  
Robert W. Clayton ◽  
Björn Engquist
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Final Section ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Seismic Section ◽  
Difference Wave ◽  
Different Types ◽  
Almost All ◽  
The Cost

The standard boundary conditions used at the sides of a seismic section in wave‐equation migration generate artificial reflections. These reflections from the edges of the computational grid appear as artifacts in the final section. Padding the section with zero traces on either side adds to the cost of migration and simply delays the inevitable reflections. We develop stable absorbing boundary conditions that annihilate almost all of the artificial reflections. This is demonstrated analytically and with synthetic examples. The absorbing boundary conditions presented can be used with any of the different types of finite‐difference wave‐equation migration, at essentially no extra cost.

scholarly journals Predicted Infection Risk for Aerosol Transmission of SARS-CoV-2

2020 ◽  
Author(s):  
Martin Kriegel ◽  
Udo Buchholz ◽  
Petra Gastmeier ◽  
Peter Bischoff ◽  
Inas Abdelgawad ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Respiratory Rate ◽  
Attack Rate ◽  
Preventive Measures ◽  
Emission Rate ◽  
Credible Interval ◽  
Infection Risk ◽  
Second Step ◽  
Air Volume ◽  
Different Types

AbstractCurrently, the respiratory route is seen as the most important transmission path for SARS-CoV-2. In this investigation, models of other researchers which had the aim of predicting an infection risk for exposed persons in a room through aerosols emitted by an infectious case-patient were extended. As a novelty – usually neglected – parameters or boundary conditions, namely the non-stationarity of aerosols and the half-life of the aerosolized virus, were included and a new method for determining the quanta emission rate based on measurements of the particle emission rate and respiratory rate at different types of activities was implemented.As a second step, the model was applied to twelve outbreaks to compare the predicted infection risk with the observed attack rate. To estimate a “credible interval” of the predicted infection risk, the quanta emission rate, the respiratory rate as well as the air volume flow were varied.In nine out of twelve outbreaks, the calculated predicted infection risk via aerosols was found to be in the range of the attack rate (with the variation of the boundary conditions) and reasons for the observed larger divergence were discussed.The validation was considered successful and therefore the use of the model could be recommended to predict the risk of an infection via aerosols in given situations. Furthermore, appropriate preventive measures can be designed.

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