scholarly journals PGD for Solving the Biharmonic Equation

2012 ◽  
Author(s):  
GuangTao Xu ◽  
Francisco Chinesta ◽  
Adrien Leygue ◽  
Michel Visonneau
Keyword(s):  
Stream Function ◽  
Degrees Of Freedom ◽  
Linear Problem ◽  
Flow Problem ◽  
Order Partial Differential Equation ◽  
Single Degree Of Freedom ◽  
Research Fields ◽  
Separated Representation ◽  
C1 Continuity ◽  
Hermite Interpolations

Biharmonic problem has been raised in many research fields, such as elasticity problem in plate geometries or the Stokes flow problem formulated by using the stream function. The fourth order partial differential equation can be solved by applying many techniques. When using finite elements C1 continuity must be assured. For this purpose Hermite interpolations constitute an appealing choice, but it imply the consideration of many degrees of freedom at each node with the consequent impact on the resulting discrete linear problem. Spectral approaches allow exponential convergence whilst a single degree of freedom is needed. However, the enforcement of boundary conditions remains a tricky task. In this paper we propose a separated representation of the stream function which transform the 2D solution in a sequence of 1D problems, each one be solved by using a spectral approximation.

A Method for Type Synthesis of Mechanisms Using Phase Diagrams

1994 ◽  
Author(s):  
Sio-Hou Lei ◽  
Ying-Chien Tsai
Keyword(s):  
Phase Diagram ◽  
Degrees Of Freedom ◽  
Practical Application ◽  
Type Synthesis ◽  
Planar Mechanisms ◽  
Simple Loop ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Synthesis Of Mechanisms

Abstract A method for synthesizing the types of spatial as well as planar mechanisms is expressed in this paper by using the concept of phase diagram in metallurgy. The concept represented as a type synthesis technique is applied to (a) planar mechanisms with n degrees of freedom and simple loop, (b) spatial mechanisms with single degree of freedom and simple loop, to enumerate all the possible mechanisms with physically realizable kinematic pairs. Based on the technique described, a set of new reciprocating mechanisms is generated as a practical application.

scholarly journals THE DYNAMIC RESPONSE OF OFFSHORE STRUCTURES TO TIME-DEPENDENT FORCES

1964 ◽  
Vol 1 (9) ◽  
pp. 29
Author(s):  
William S. Gaither ◽  
David P. Billington
Keyword(s):  
Degrees Of Freedom ◽  
Wind Waves ◽  
Offshore Structures ◽  
Time Dependent ◽  
Wave Forces ◽  
Ocean Bottom ◽  
Single Wave ◽  
Single Degree Of Freedom ◽  
The Many ◽  
Floating Objects

This paper is addressed to the problem of structural behavior in an offshore environment, and the application of a more rigorous analysis for time-dependent forces than is currently used. Design of pile supported structures subjected to wave forces has, in the past, been treated in two parts; (1) a static analysis based on the loading of a single wave, and (2) a dynamic analysis which sought to determine the resonant frequency by assuming that the structure could be approximated as a single-degree-of-freedom system. (Ref. 4 and 6) The behavior of these structures would be better understood if the dynamic nature of the loading and the many degrees of freedom of the system were included. A structure which is built in the open ocean is subjected to periodic forces due to wind, waves, floating objects, and due occasionally to machinery mounted on the structure. To resist motion, the structure relies on the stiffness of the elements from which it is built and the restraints of the ocean bottom into which the supporting legs are driven.

A Study of the Effects of Negative Friction-Speed Slope on Brake Squeal

1995 ◽  
Author(s):  
Yongbin Yuan
Keyword(s):  
Degrees Of Freedom ◽  
Element Model ◽  
Compression Modulus ◽  
Brake Squeal ◽  
Single Degree Of Freedom ◽  
Beam Elements ◽  
Negative Friction ◽  
Unstable Vibration ◽  
Almost All ◽  
Friction Induced Vibration

Abstract Brake squeal is caused by friction-induced vibration of brake systems. It may take place due to several possible mechanisms. The inverse variation of friction coefficient with relative sliding speed, also called negative μ-v slope, is one of them. Although it has been demonstrated in many articles that negative μ-v slope can cause unstable vibration for systems with a single degree of freedom (d.o.f.), its effects on multi-d.o.f. brake systems are not yet well understood. Since almost all types of friction materials for automotive brakes exhibit negative μ-v slope under certain conditions, it is important to clarify its role in brake squeal. The current study incorporates the negative μ-v slope friction law into a Finite element model for disc brake systems. The rotor and pads are modeled by beam elements, and the caliper is represented by a rigid body with two degrees of freedom. The effects of negative μ-v slope on the vibration stability of a brake system are studied along with several parameters including friction level, lining compression modulus, and steelback thickness.

PSEUDO PROBABILISTIC APPROACH TO TEST ISOMORPHISM AMONG KINEMATIC CHAINS

1997 ◽  
Vol 21 (2) ◽  
pp. 65-83 ◽  
Author(s):  
S. Shubhashis ◽  
M. Choubey ◽  
A.C. Rao
Keyword(s):  
Numerical Scheme ◽  
Degrees Of Freedom ◽  
Probabilistic Approach ◽  
Kinematic Chain ◽  
Single Degree Of Freedom ◽  
Reliable Test ◽  
Kinematic Chains ◽  
Single Degree ◽  
Unique Method ◽  
P Matrix

There is no dearth of methods to test isomorphism amongst kinematic chains. Search for a computationally easier, logically simple and unique method is still on. Present work is in quest of a reliable test to detect isomorphism among kinematic chains. Work presented here is more versatile as it incorporates more features of the kinematic chain which were not included earlier such as number and type of links, their relative dispositions in the kinematic chain, nature of adjacent links etc. The method proposed is based on the concept of pseudo-probability (pseudo means it appears to be, but not exactly. The approach does not follow in-toto the principles of probability and considerable liberty has been taken in interpreting the word probability hence the word pseudo is used along with the probability schemes). Using the resemblance of different coloured balls in an urn for the number and type of links in a kinematic chain, a matrix (named P-Matrix) representing the kinematic chain in totality is generated. For the sake of comparison a numerical scheme named, pseudo probability scheme, P-Scheme, is developed from the above P-Matrix and is used for testing isomorphism. In fact the method is more powerful in the sense that each row of the proposed P-Matrix is capable of representing the respective kinematic chain distinctly and can be used to compare the kinematic chains with same link assortments, uniquely. The proposed method, besides possessing the potential of testing the isomorphism among simple-joint, single degree of freedom kinematic chains is also capable of multi degrees of freedom and multiple-joint kinematic chains.

scholarly journals Fluid-driven origami-inspired artificial muscles

2017 ◽  
Vol 114 (50) ◽  
pp. 13132-13137 ◽  
Author(s):  
Shuguang Li ◽  
Daniel M. Vogt ◽  
Daniela Rus ◽  
Robert J. Wood
Keyword(s):  
Peak Power ◽  
Degrees Of Freedom ◽  
Multiple Scales ◽  
Low Cost ◽  
Artificial Muscles ◽  
Fluid Medium ◽  
Single Degree Of Freedom ◽  
Flexible Skin ◽  
Actuation Systems ◽  
Power Densities

Artificial muscles hold promise for safe and powerful actuation for myriad common machines and robots. However, the design, fabrication, and implementation of artificial muscles are often limited by their material costs, operating principle, scalability, and single-degree-of-freedom contractile actuation motions. Here we propose an architecture for fluid-driven origami-inspired artificial muscles. This concept requires only a compressible skeleton, a flexible skin, and a fluid medium. A mechanical model is developed to explain the interaction of the three components. A fabrication method is introduced to rapidly manufacture low-cost artificial muscles using various materials and at multiple scales. The artificial muscles can be programed to achieve multiaxial motions including contraction, bending, and torsion. These motions can be aggregated into systems with multiple degrees of freedom, which are able to produce controllable motions at different rates. Our artificial muscles can be driven by fluids at negative pressures (relative to ambient). This feature makes actuation safer than most other fluidic artificial muscles that operate with positive pressures. Experiments reveal that these muscles can contract over 90% of their initial lengths, generate stresses of ∼600 kPa, and produce peak power densities over 2 kW/kg—all equal to, or in excess of, natural muscle. This architecture for artificial muscles opens the door to rapid design and low-cost fabrication of actuation systems for numerous applications at multiple scales, ranging from miniature medical devices to wearable robotic exoskeletons to large deployable structures for space exploration.

scholarly journals Symmetric waterbomb origami

2016 ◽  
Vol 472 (2190) ◽  
pp. 20150846 ◽  
Author(s):  
Yan Chen ◽  
Huijuan Feng ◽  
Jiayao Ma ◽  
Rui Peng ◽  
Zhong You
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Solar Panels ◽  
Deployable Structures ◽  
Single Degree Of Freedom ◽  
Folding Process ◽  
Multiple Degrees Of Freedom ◽  
Single Degree ◽  
Flat Roofs ◽  
Additional Constraints

The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.

On fluid motions induced by an electric current source

1971 ◽  
Vol 46 (1) ◽  
pp. 25-32 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Electromagnetic Field ◽  
Linear Problem ◽  
Flow Problem ◽  
Current Source ◽  
Inviscid Flow ◽  
Circular Cone ◽  
Infinite Plane ◽  
Half Angle ◽  
Whole Space ◽  
Electric Current Source

In this paper we consider the flow field induced in an incompressible viscous conducting fluid, occupying the interior of a right circular cone, by an electriccurrent source situated at the vertex of the cone. We assume that the velocity field is small and its effect on the electromagnetic field is negligible. A similarity solution is obtained for the non-linear problem. This solution is an adaptation of Slezkin's solution for the momentum transfer through a viscous jet and, apart from the numerical solution of a Riccati type of equation, is exact. In particular, we investigate the case when the half angle of the cone is ½π and the fluid occupies the whole space on one side of an infinite plane. We also consider the corresponding inviscid flow problem that was recently investigated by another author and suggest that the solution obtained is not physically realistic.

A guide to classical flutter

1988 ◽  
Vol 92 (919) ◽  
pp. 339-355 ◽  
Author(s):  
L. T. Niblett
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Structural Coupling ◽  
Two Degrees Of Freedom ◽  
Single Degree ◽  
Lifting Surface ◽  
Classical Flutter ◽  
Comprehensive Study

Summary First essentials of classical flutter are demonstrated by a comprehensive study of the behaviour of a lifting surface with two degrees of freedom under the action of airforces limited to those in phase with displacement. Structural coupling between the coordinates is eliminated by taking the normal modes to be the deflection coordinates, and this results in conditions for stability with particularly concise forms. It is shown that the flutter stability can be seen to be very much a matter of the relative amplitudes of heave and pitch in the normal modes. In-quadrature airforces are then introduced and it is shown that they have little effect when the flutter is severe. They are of more importance in the milder forms of flutter, the extreme of which are shown to be little different from instabilities in a single degree of freedom.

Localization Phenomena of Nonlinear Vibrations in Three-Blade Wind Turbines

2013 ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Hisashi Takahashi ◽  
Yukio Ishida
Keyword(s):  
Wind Turbines ◽  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Coupled System ◽  
Wind Pressure ◽  
Response Curves ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Frequency Responses ◽  
Time Histories

Vibration characteristics of three-blade wind turbines are investigated. The system is modeled by a coupled system of the flexible tower with two degrees of freedom and each blade with a single degree of freedom, and these blades are subjected to wind pressure which varies depending on the height from the ground. The vibrations of the three-blade wind turbines are theoretically analyzed to determine the natural frequency diagrams, frequency responses, stationary time histories and their FFT results. It is found that several peaks appear at the specific range of the rotational speed ω in the response curves because of both the wind pressure and the parametric excitation terms. In three-blade wind turbines, vibrations including predominant components of 3ω and its higher harmonics appear near these peaks. The response curves near the highest peak exhibit soft spring types due to the nonlinearities of the restoring moments of the blades. In the numerical simulations, “localization phenomena” in the blades, which vibrate at different amplitudes, are observed. The influence of an imperfection of the three blades is also examined.

Sign in / Sign up

Export Citation Format

Share Document