Boundary Conditions and Sensitivities of Mass-Elastic Systems

1988 ◽  
Vol 110 (4) ◽  
pp. 464-467
Author(s):  
D. Morrison
Keyword(s):  
Boundary Conditions ◽  
External Disturbance ◽  
Practical Interest ◽  
Short Paper ◽  
Practical Applications ◽  
General Terms ◽  
Elastic Systems ◽  
Seismic Applications

It has been noted in numerous practical applications that the sensitivities of mass elastic systems to external disturbance are closely bound up with the nonzero values of the normalized boundary and field actions, both forces and displacements. This leads in many cases to rapid analyses without, for example, the need for a separate calculation of “participation factors” in seismic applications. This short paper sets down some relationships in general terms and indicates examples of practical interest.

scholarly journals A neutral core of degressively proportional allocations under lexicographic preferences of agents

2021 ◽  
Author(s):  
Katarzyna Cegiełka ◽  
Piotr Dniestrzański ◽  
Janusz Łyko ◽  
Arkadiusz Maciuk ◽  
Maciej Szczeciński
Keyword(s):  
European Union ◽  
Numerical Analysis ◽  
Theoretical Analysis ◽  
Boundary Conditions ◽  
Case Studies ◽  
The European Union ◽  
Practical Applications ◽  
Lexicographic Preferences ◽  
Degree Of Acceptance ◽  
Feasible Solutions

AbstractOne of the main problems of practical applications of degressively proportional allocations of goods and burdens is lack of uniqueness of this principle. Even under given boundary conditions of allocation, i.e. determined minimal and maximal amounts of a good that can be assigned in a given allocation, there are usually many feasible solutions. The lack of formal rules of allocation is the reason why the allocation is typically a result of negotiations among its agents. A number of allocations favor some of agents or their groups, therefore other agents cannot accept them. The aim of this paper is to indicate a way of reducing the set of all feasible solutions exclusively to those that are neutral to all agents. As a result of the term of lexicographic preference of allocation agents defined on the basis of the relation theory followed by a numerical analysis of sets of all feasible solutions, it is possible to determine a core of this set in the form of a subset of all feasible solutions that are acceptable by all agents. In addition, this subset can be further divided into smaller subsets with regard to the degree of acceptance of their elements. Theoretical analysis is complemented by case studies, one of which is application of this idea to the allocation of seats in the European Parliament among the member states of the European Union.

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

scholarly journals Detecting Semantic Anomalies

2020 ◽  
Vol 34 (04) ◽  
pp. 3154-3162
Author(s):  
Faruk Ahmed ◽  
Aaron Courville
Keyword(s):  
Object Recognition ◽  
Anomaly Detection ◽  
Practical Interest ◽  
Practical Relevance ◽  
Practical Applications ◽  
Task Learning ◽  
Recent Interest ◽  
Semantic Awareness

We critically appraise the recent interest in out-of-distribution (OOD) detection and question the practical relevance of existing benchmarks. While the currently prevalent trend is to consider different datasets as OOD, we argue that out-distributions of practical interest are ones where the distinction is semantic in nature for a specified context, and that evaluative tasks should reflect this more closely. Assuming a context of object recognition, we recommend a set of benchmarks, motivated by practical applications. We make progress on these benchmarks by exploring a multi-task learning based approach, showing that auxiliary objectives for improved semantic awareness result in improved semantic anomaly detection, with accompanying generalization benefits.

Vibrations and Power Flows in a Coupled Beam System

2007 ◽  
Vol 129 (5) ◽  
pp. 616-622 ◽  
Author(s):  
Wen L. Li ◽  
Murilo W. Bonilha ◽  
Jie Xiao
Keyword(s):  
Boundary Conditions ◽  
Analytical Method ◽  
Power Flow ◽  
Practical Interest ◽  
Current Method ◽  
Beam System ◽  
The Subject ◽  
Coupled Beams ◽  
Elastically Restrained ◽  
Excellent Accuracy

Vibrations of and power flow between coupled beams have been the subject of many investigations, and various techniques have been developed over the years. However, most of the existing methods will require a certain level of modifications or adaptations to account for the variations in the coupling and∕or boundary conditions. In this study, a general analytical method is developed for predicting the vibrations of and power flow between two-coupled beams. The coupling between the beams is generically represented by two (translational and rotational) springs of arbitrary stiffnesses. Thus, many rigid and nonrigid connectors of practical interest can be directly taken into account. In addition, because the beams are elastically restrained at each end, the current method can be universally applied to different boundary conditions by simply varying the stiffnesses of the boundary springs. Numerical results are presented to show the excellent accuracy of the proposed approach.

Evaluation of the influence of boundary confinement on the behaviour of unsaturated swelling clay soils

2009 ◽  
Vol 46 (3) ◽  
pp. 339-356 ◽  
Author(s):  
Greg Siemens ◽  
James A. Blatz
Keyword(s):  
Boundary Conditions ◽  
Volume Expansion ◽  
Experimental Testing ◽  
Mean Stress ◽  
Equilibrium Limit ◽  
Practical Applications ◽  
Swelling Soils ◽  
Liquid Infiltration ◽  
Volume State ◽  
The Impact

Swelling soils are found in many regions throughout the world. Damage caused to infrastructure by these types of soils is measured annually in billions of dollars. These excessive damages are, in part, due to the lack of proper design, resulting from a need for better tools for practitioners to assess the impact of swelling soils in typical design applications. This paper presents an experimental testing program with interpretations to provide a framework for predicting the behaviour of swelling soils under general stress and volume state conditions for practical applications. The experimental testing adopted a new automated triaxial apparatus that controls boundary stress and strain while applying liquid infiltration conditions at the perimeter or center of triaxial specimens. Results demonstrate the influence of a range of boundary conditions on the behaviour of swelling soil during liquid infiltration. The range of boundary conditions examined in the experimental testing include constant mean stress (CMS), where the mean stress applied during the swelling stage is constant; constant volume (CV), where the volume is held constant during the liquid infiltration; as well as a flexible spring-type boundary condition (CS) that applies increases in stress as a specified function of the volume increase. These boundary conditions represent the broad spectrum of experiences in the field. The experimental results show the dominance of boundary conditions on the development of swell pressure and volume expansion to give evidence for a new swell equilibrium limit (SEL) relationship. The SEL shows promise in providing a framework for swelling soils to predict the final soil state under wetting conditions for the range of boundary conditions examined. Application of the SEL relationship in practice is presented as a concept for examining swelling induced pressures and volume expansion in applications of liquid infiltration of swelling soils.

A Variational Approach to the Dynamics of Structures Having Mixed or Discontinuous Boundary Conditions

1984 ◽  
Vol 51 (4) ◽  
pp. 831-836 ◽  
Author(s):  
P. J. Torvik
Keyword(s):  
Boundary Conditions ◽  
Variational Approach ◽  
Natural Frequencies ◽  
Elastic Solid ◽  
Approximate Solutions ◽  
Forced Response ◽  
Field Equations ◽  
Elastic Circular Plate ◽  
Discontinuous Boundary ◽  
Elastic Systems

A procedure is developed whereby the steady-state forced response and the modes of free vibration for elastic systems having mixed or discontinuous boundary conditions can be determined. Approximate solutions are obtained as a superposition of a set of functions, each of which satisfies the field equations but not the boundary conditions. The coefficients of this expansion are obtained through applying a variational principle developed from Hamilton’s principle which for simple harmonic motion, is equivalent to Reissner’s principle. The reduction from the general elastic solid to the elastic plate is given, as are some results obtained for the first several natural frequencies of an elastic circular plate, free on a portion of the boundary and clamped on the remainder.

scholarly journals Free Vibration Analysis of Moderately Thick Rectangular Plates with Variable Thickness and Arbitrary Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-25 ◽  
Author(s):  
Dongyan Shi ◽  
Qingshan Wang ◽  
Xianjie Shi ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Practical Interest ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Solution Algorithms ◽  
Wide Range

A generalized Fourier series solution based on the first-order shear deformation theory is presented for the free vibrations of moderately thick rectangular plates with variable thickness and arbitrary boundary conditions, a class of problem which is of practical interest and fundamental importance but rarely attempted in the literatures. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions, the current method can be generally applied to a wide range of boundary conditions with no need of modifying solution algorithms and procedures. Under the current framework, the one displacement and two rotation functions are generally sought, regardless of boundary conditions, as an improved trigonometric series in which several supplementary functions are introduced to remove the potential discontinuities with the displacement components and its derivatives at the edges and to accelerate the convergence of series representations. All the series expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. The effectiveness and reliability of the presented solution are demonstrated by comparing the present results with those results published in the literatures and finite element method (FEM) data, and numerous new results for moderately thick rectangular plates with nonuniform thickness and elastic restraints are presented, which may serve as benchmark solution for future researches.

Analysis of Flexibility and Stability of Crane Telescopic Boom with Elastic Restraint and Second-Order Effect

2013 ◽  
Vol 774-776 ◽  
pp. 109-113
Author(s):  
Liang Du ◽  
Nian Li Lu ◽  
Peng Lan
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Effect ◽  
Second Order ◽  
Analysis Model ◽  
Characteristic Equations ◽  
Lateral Deflection ◽  
Practical Applications ◽  
Vertical Stability

The cylinder support crane telescopic booms deformation and stability analysis model in the lifting plane is equivalent with the multistep column with elastic restraint. To analyze the lateral flexibility and vertical stability of the telescopic booms with elastic restraint accurately, this paper established the deflection differential equations of multi-sectioned telescopic booms with second-order effect, introduced proper boundary conditions, obtained the precise recurrence lateral deflection differential equations and the buckling characteristic equations of arbitrary sectioned telescopic booms, and some practical applications of the buckling characteristic equations were presented. Took certain five-sectioned telescopic booms as example, by comparing the results with ANSYS method, the accuracy of the equations deduced in this paper was verified.

scholarly journals Buckling and Vibration Performance of a Composite Laminated Plate with Elastic Boundaries Subjected to Local Thermal Loading

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yonggan Sun
Keyword(s):  
Boundary Conditions ◽  
Thermal Loading ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Practical Applications ◽  
Composite Laminated Plate ◽  
Heated Area ◽  
Two Stages ◽  
Fixed Boundaries

In this paper, a model is established for the calculation of the vibrations of a composite laminated plate with elastic boundary conditions subjected to local thermal loading. The model is based on first-order shear deformation theory using the finite element method. The influence of boundary conditions, heating area, and heating location on buckling and vibrations of a composite laminated plate was investigated, and there were two stages in which the critical temperature increased sharply during the transition from free boundary to simply supported and rigid fixed boundaries. The thermal buckling of locally heated laminated plates is generally not checked in practical applications unless the heated area exceeds approximately 10% of the total area of the plates. The stronger the boundary constraint is, the greater the influence of the heated area is on the vibrational frequencies of the composite laminated plate.

Experimental and Numerical Analysis of the Transient Behavior of the Oil De-Congealing Process in an Aero Fuel-Cooled Oil Cooler Under Low-Temperature Conditions

2021 ◽  
Author(s):  
Foster Kwame Kholi ◽  
Jaehyun Park ◽  
Kyeongho Lee ◽  
Man Yeong Ha ◽  
Michael Klingsporn ◽  
...  
Keyword(s):  
Low Temperature ◽  
Boundary Conditions ◽  
Critical Role ◽  
Transient Behavior ◽  
Analysis Model ◽  
Practical Applications ◽  
Fuel Flow ◽  
Commercial Code ◽  
Study Results ◽  
Oil Cooler

Abstract The fuel-cooled oil cooler (FCOC) in the lubrication circuit plays a critical role in the aero gas-turbine engine's aerothermal management. However, the low temperature of the operating environment can congeal the oil and reduce the FCOC efficiency. The oil bypass valve (OBV) installed on the FCOC prevents pressure loss. Its failure may cause overheating, requiring preemptive performance prediction. Experimental and numerical analyses were used to evaluate the cooler's de-congealing performance under typical boundary conditions of pressure and temperature, OBV configurations, and re-routing of feed oil and fuel flow paths. The temporal variation of oil and fuel mass flow rates, temperature, and pressure of the feed oil and fuel provided an insight into the de-congealing process and duration. The experimental data were used to develop a one-dimensional (1D) flow and thermal network analysis model based on the effectiveness (e)-NTU method to predict the transient oil de-congealing performance of the FCOC. The customized commercial code predicted the de-congealing phenomena using empirical correlations with property correction schemes, showing good agreement with the experiment. The findings revealed various ways to enhance the de-congealing performance of the FCOC. The study results showed that the operating boundary conditions, OBV location and status, and flow arrangements affect de-congealing behavior and time. The present numerical model provides results quickly and can effectively predict experimentally costly and complicated cases. The attempted estimates of steady heat rejection and detailed methodology could guide future studies and practical applications.

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