Parametric Instability of a Beam Due to Axial Excitations and to Boundary Conditions

1998 ◽  
Vol 120 (2) ◽  
pp. 461-467 ◽  
Author(s):  
R. Dufour ◽  
A. Berlioz
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It is shown that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

Influence of Axial Excitations and of Boundary Conditions on the Parametric Instability of a Beam

1995 ◽  
Author(s):  
Régis Dufour ◽  
Alain Berlioz ◽  
Thomas Streule
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

Abstract In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It shows that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

scholarly journals Possible reasons for early artificial bone failure in biomechanical tests of ankle arthrodesis systems

2015 ◽  
Vol 1 (1) ◽  
pp. 507-509
Author(s):  
H. Martin ◽  
N. Gutteck ◽  
J.-B. Matthies ◽  
T. Hanke ◽  
G. Gradl ◽  
...  
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Experimental Tests ◽  
Element Model ◽  
Ankle Arthrodesis ◽  
Artificial Bone ◽  
Basic Model ◽  
Simplified Finite Element Model ◽  
Biomechanical Tests ◽  
Horizontal Displacements

AbstractIn order to demonstrate the influence of the boundary conditions in experimental biomechanical investigations of arthrodesis implants two different models were investigated. As basic model, a simplified finite element model of the cortical bone was used in order to compare the stress values with (Model 1) and without (Model 2) allowing horizontal displacements of the load application point. The model without constraints of horizontal displacements showed considerably higher stress values at the point of failure. Moreover, this investigation shows that the boundary conditions (e.g. constraints) have to be carefully considered, since simplifications of the reality with experimental tests cannot always be avoided.

Conditions of Parametric Resonance in Periodically Time-Variant Systems With Distributed Parameters

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Yong-Kwan Lee ◽  
Leonid S. Chechurin
Keyword(s):  
Parametric Resonance ◽  
Robot Manipulator ◽  
Synchronous Generator ◽  
Constant Current ◽  
Time Varying ◽  
Distributed Parameters ◽  
Time Varying Parameter ◽  
Manipulator Arm ◽  
The Stability ◽  
Systems With Distributed Parameters

Theoretical analysis of the stability problem for the control systems with distributed parameters shall be given. The approach to the analysis of such systems can be composed of two parts. First, the distributed parameter element is modeled by a frequency response function. Second, approximate conditions of parametric resonance are derived by a method of stationarization (describing functions of time-variant elements). The approach is illustrated by two examples. One is a robot-manipulator arm (distributed mechanical parameter system) controlled by a controller with a modulator/demodulator cascade (time-varying element). Another is an electromechanical transformer that consists of a constant current motor and a synchronous generator. Inductance between stator windings and the rotor of the synchronous generator serves as a periodical time-varying parameter, and a long electrical line plays the role of an element with distributed parameters. In both examples, dangerous (in terms of the first parametric resonance) regions for time-varying parameter are obtained theoretically and compared with simulation experiment.

scholarly journals Squeal Frequency of a Railway Disc Brake Evaluation by FE Analyses

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
F. Cascetta ◽  
F. Caputo ◽  
A. De Luca
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Experimental Tests ◽  
Numerical Approach ◽  
System Stability ◽  
Brake System ◽  
Physical Parameters ◽  
Disc Brake ◽  
Complex Eigenvalues ◽  
The Stability

This paper deals with the development of a numerical model, based on the Finite Element (FE) theory for the prediction of the squeal frequency of a railway disc brake. The analytical background has been discussed and presented, as well as the most efficient methods for evaluating the system stability; the attention has been paid particularly to the complex eigenvalues method, which has been adopted within this paper to investigate the railway disc brake system. Numerical results have been compared with measurements from experimental tests in order to validate the proposed numerical approach. At the end of this work, a sensitivity analysis, aimed at understanding the effects of some physical parameters influencing the stability of the brake system and the squeal propensity, has been carried out.

A Finite Element Investigation of a Bearing/Cartridge Interface for a Fretting Corrosion Study

1985 ◽  
Vol 107 (2) ◽  
pp. 157-163 ◽  
Author(s):  
R. J. Stover ◽  
H. H. Mabie ◽  
M. J. Furey
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Analytical Study ◽  
Experimental Tests ◽  
Tangential Direction ◽  
Rolling Element Bearings ◽  
Interface Conditions ◽  
Finite Element Technology ◽  
Rolling Element ◽  
Contact Pressures

The bearing/cartridge interfaces of a Ship Service Motor Generator Set (SSMG) were modeled by using finite element technology. The purpose of this analytical study was to verify the results of earlier experimental tests made on an actual SSMG unit. This research is part of a larger research project to examine the important parameters influencing the fretting of rolling element bearings. Models for the bearings at both ends of the unit were developed, and loads simulating the ball pass loads were applied to these models; the contact pressures, radial deformations, and relative displacements at the interface were calculated. The resulting data showed the interface conditions to be extremely complex with the contact pressures varying from zero to a maximum of 55.4 MPa (8030 psi) as the balls passed by. The maximum relative displacements occurred in the tangential direction (2.44 μm) and were independent of the axial boundary conditions.

The Influence of Different Restrained Boundary Conditions on the Stability of Steel-Concrete Composite Ribbed Shell

2011 ◽  
Vol 243-249 ◽  
pp. 7005-7008
Author(s):  
Yu Zhen Chang ◽  
Ling Ling Wang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Bearing Capacity ◽  
Ultimate Bearing Capacity ◽  
Element Analysis ◽  
Boundary Constraints ◽  
Ribbed Shell ◽  
Post Buckling ◽  
The Stability ◽  
Section Dimension

The steel-concrete composite ribbed shell is a new type of spatial structure. Different restrained boundary conditions have a considerably influence on the ultimate bearing capacity and stability. Based on the nonlinear finite element method, a numerical model is made by finite element analysis software ANSYS, in which material and geometrical nonlinear are considered. A spherical composite ribbed shell with 40m span, three different section dimensions and two different vector heights is used as an example, in which 4 different restrained boundary conditions are considered, including all fixed, all hinged, node fixed and node hinged. The results show that when the section dimension and span height are the same, the ultimate bearing capacity will be greater as the boundary becoming rigid, and when the section dimension is larger, the ratio of ultimate bearing capacity under different restrained boundary conditions is increasing, while as the span height is greater, the ratio is decreasing. To the instable shape, the influence of different restrained boundary is minor, all the instable modes are extreme point instability, but the trend of load-displacement curves are almost similar, and when the cross-section dimension of composite rib increases, the composite ribbed shell under different boundary constraints has shown higher post-buckling strength.

scholarly journals Stability of orthotropic plates

2020 ◽  
Vol 166 ◽  
pp. 06004
Author(s):  
Mykola Surianinov ◽  
Dina Lazarieva ◽  
Iryna Kurhan
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Boundary Conditions ◽  
Critical Loads ◽  
Orthotropic Plate ◽  
Algebraic Equations ◽  
Stability Equation ◽  
Element Analysis ◽  
Linear Algebraic Equations ◽  
The Stability

The solution to the problem of the stability of a rectangular orthotropic plate is described by the numerical-analytical method of boundary elements. As is known, the basis of this method is the analytical construction of the fundamental system of solutions and Green’s functions for the differential equation (or their system) for the problem under consideration. To account for certain boundary conditions, or contact conditions between the individual elements of the system, a small system of linear algebraic equations is compiled, which is then solved numerically. It is shown that four combinations of the roots of the characteristic equation corresponding to the differential equation of the problem are possible, which leads to the need to determine sixty-four analytical expressions of fundamental functions. The matrix of fundamental functions, which is the basis of the transcendental stability equation, is very sparse, which significantly improves the stability of numerical operations and ensures high accuracy of the results. An analysis of the numerical results obtained by the author’s method shows very good convergence with the results of finite element analysis. For both variants of the boundary conditions, the discrepancy for the corresponding critical loads is almost the same, and increases slightly with increasing critical load. Moreover, this discrepancy does not exceed one percent. It is noted that under both variants of the boundary conditions, the critical loads calculated by the boundary element method are less than in the finite element calculations. The obtained transcendental stability equation allows to determine critical forces both by the static method and by the dynamic one. From this equation it is possible to obtain a spectrum of critical forces for a fixed number of half-waves in the direction of one of the coordinate axes. The proposed approach allows us to obtain a solution to the stability problem of an orthotropic plate under any homogeneous and inhomogeneous boundary conditions.

scholarly journals Experimental Investigation of Vibration Response of a Flexible Coupler In a Four Bar Mechanism Due to Varying Crank Length and Crank Speed

2018 ◽  
Vol 248 ◽  
pp. 01008 ◽  
Author(s):  
Rizky Arman ◽  
Andi Isra Mahyuddin ◽  
Wenny Marthiana ◽  
Iman Satria
Keyword(s):  
Dynamic Behaviour ◽  
Parametric Instability ◽  
Excitation Frequency ◽  
Vibration Response ◽  
Time Varying ◽  
Dynamic Parameters ◽  
Inertial Effects ◽  
Time Varying Parameter ◽  
Increase Productivity ◽  
Crank Length

Effort to increase productivity calls for increasingly higher operating speed. Consequently, many part of a machinery are made as light as possible to avoid the detrimental inertial effects. This condition means several of the elements are no longer rigid and tend to experience elastic deformation in operation. The existence of the deformation yields element possessing position dependent dynamic parameters. Mechanisms with time-varying parameter have a phenomenon known as parametric instability where the mechanism could becomes dynamically unstable at several frequency bands, even at relatively low excitation frequency. This research investigates the dynamic behaviour of a flexible coupler on an experimental four-bar mechanism setup. The study examines the coupler vibration response due to varying crank length and crank speed.

Parametric Instability of a Rotating Axially Loaded FG Cylindrical Thin Shell Under Both Axial Disturbances and Thermal Effects

2018 ◽  
Vol 73 (12) ◽  
pp. 1105-1119
Author(s):  
X. Li ◽  
Q. Xu ◽  
Y.H. Li
Keyword(s):  
Boundary Conditions ◽  
Thin Shell ◽  
Thermal Environment ◽  
Parametric Instability ◽  
Rotation Velocity ◽  
Functionally Graded ◽  
Angular Rotation ◽  
Various Boundary Conditions ◽  
Love’S Thin Shell Theory ◽  
The Stability

AbstractParametric instability of a rotating functionally graded (FG) cylindrical thin shell with axial compression under various boundary conditions is studied in this article. In particular, the shell is subjected to both axial periodic displacement disturbances and a thermal environment. The initial hoop tension and Coriolis effects due to rotation are also considered. The coupled dynamic equations of the shell under multiple conditions are formulated based on Love’s thin-shell theory. The instability boundaries of the shell with different boundary conditions considering thermal factors, axial disturbances, and other system parameters are obtained analytically under the case of primary and combination resonance; numerical illustrations are also given. It is found that high temperature weakens the stability of the system, while axial disturbances show stronger influence on the instability regions of the shell compared to other parameters such as thermal factors and the angular rotation velocity.

scholarly journals Shock Tube Testing and Modelling of Annealed Float Glass

2018 ◽  
Vol 183 ◽  
pp. 01035
Author(s):  
Karoline Osnes ◽  
Tore Børvik ◽  
Odd Sture Hopperstad
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Prediction Model ◽  
Shock Tube ◽  
Fracture Strength ◽  
Blast Loading ◽  
Experimental Tests ◽  
Float Glass ◽  
Strength Prediction ◽  
Glass Strength

Failure of glass is dominantly brittle, and is caused by microscopic flaws randomly distributed on the surface. Fracture mainly initiates in these flaws, and this leads to a high variability in the glass strength, which depends on geometry, boundary conditions and loading situation. Consequently, the identification of the fracture strength, in e.g. finite element analyses, is not straightforward. For rapid loading conditions, as for blast loading situations, the glass strength is generally increased because flaws need time to grow into cracks. The current study aims to identify the probabilistic fracture strength of glass plates under blast loading as a function of the plate?s boundary conditions, geometry and loading by using a newly proposed strength prediction model. To validate this model in some measure, 12 blast tests on annealed float glass were performed in a shock tube. As expected, the tests showed a large scatter in fracture strength. The strength prediction model captured the main trends found in the experimental tests, but a closer investigation of the strain rate sensitivity of glass was deemed necessary. Finally, the results from the strength prediction model were used as input in a simulation of annealed float glass under blast pressure in the finite element program IMPETUS Afea Solver. By use of a node splitting technique, the simulations captured the behaviour displayed in the experimental tests to a great extent.

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