Stability analysis of two coupled pre-shaped beams in parallel

2017 ◽  
Vol 232 (13) ◽  
pp. 2482-2489 ◽  
Author(s):  
Wu Zhou ◽  
Huiju Yu ◽  
Lili Chen ◽  
Yu Chen ◽  
Bei Peng ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Analytical Methods ◽  
Nonlinear Phenomenon ◽  
Single Beam ◽  
Fabrication Errors ◽  
Coupled Beams ◽  
The Stability ◽  
Bistable Mechanism ◽  
Minimum Force ◽  
Good Agreement

Parallel bistable mechanism rather than single bistable beam is preferred in micro devices like relays and resonators due to its higher stability in insensitive axis and higher robustness to fabrication errors. Its stability characteristics including nonlinearity and bistability or snap-through, however, rarely appear in current publications. The coupled mechanism constructed by two pre-shaped beams in parallel is investigated analytically and numerically in this paper. Based on the quasi-linearization of the problem and analytical equation of force and displacement, the dimension combinations of coupled beams are categorized into three types according to the apex amplitudes of cosine-shaped beams. It is concluded that the appearance of snap-through behaviors in parallel coupled mechanism is sustained by both arranging two bistable beams and making the apex difference meet condition of Fmin < 0. The smallest values of minimum force only appears when the apexes are equal to each other, and any efforts to increase or decrease the apex of single beam will lead the nonlinear phenomenon from snap-through to constrained-snap-through and further to no snap-through. The numerical method is also introduced to observe the stability of coupled mechanism and shows a good agreement with analytical methods proposed by this paper.

Stability Analysis of Initially Curved Beams Mechanically Coupled in a Parallel Arrangement

2018 ◽  
Vol 18 (03) ◽  
pp. 1850041
Author(s):  
Hassen M. Ouakad
Keyword(s):  
Nonlinear Behavior ◽  
Coupled System ◽  
Curved Beams ◽  
Stable Mechanism ◽  
Coupled Beams ◽  
The Stability ◽  
Two Parameters ◽  
Force Displacement ◽  
Minimum Force ◽  
Good Agreement

This paper investigates the stability behavior of a mechanically coupled bi-stable mechanism made of two parallel and initially curved microbeams with focus on the influence of the coupled beams’ initial curvatures on the system. First, the nonlinear and coupled force–displacement equation is derived. Then, a parametric study of the coupled beams system is studied with the system categorized into different structural compartment types according to the initial curvature of the coupled beams. It is concluded that the snap-through of such a coupled bi-stable system is governed by the beams’ initial curvatures difference. The simulation results showed that these two parameters (the beams’ initial curvatures) essentially govern the structural behavior of the coupled system in satisfying the necessary structural stability condition. It is found that the smallest (critical) value of the minimum force amplitude occurs only when both initial beams’ mid-point elevations are equal to each other. Furthermore, it is shown that any probability to increase or decrease the curvature of any beam will alter the nonlinear behavior of the coupled beam system from a simple regular snap-through to a constrained-snap-through, and even to the disappearance of the snap-through. Finally, a finite element method is conducted to investigate the stability of the coupled mechanism, of which the results show a good agreement with the analytical results of this paper.

Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

2011 ◽  
Vol 137 ◽  
pp. 72-76
Author(s):  
Wei Zhang ◽  
Xian Wen ◽  
Yan Qun Jiang
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Global Stability ◽  
Dimensional Model ◽  
Global Stability Analysis ◽  
The Stability ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Calculated Amount ◽  
Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

Theoretical Prediction of Onset of Horizontal Slug Flow

1980 ◽  
Vol 102 (4) ◽  
pp. 441-445 ◽  
Author(s):  
Kaichiro Mishima ◽  
Mamoru Ishii
Keyword(s):  
Experimental Data ◽  
Stability Analysis ◽  
Slug Flow ◽  
Flow Analysis ◽  
Finite Amplitude ◽  
Empirical Correlations ◽  
Deformation Limit ◽  
Theoretical Criterion ◽  
The Stability ◽  
Good Agreement

A criterion for the onset of a slug flow in a horizontal duct is derived theoretically. A potential flow analysis is carried out by considering waves of finite amplitude. The stability criterion is obtained by introducing the wave deformation limit and the “most dangerous wave” concept in the stability analysis. The present theoretical criterion for slug formation shows very good agreement with a large number of experimental data and with some empirical correlations.

scholarly journals Stability Analysis of Dike to Impound Freshwater in Brackish Water Estuarine Environment

2020 ◽  
Vol 14 (1) ◽  
pp. 139-149
Author(s):  
Amala Krishnan ◽  
Sreevalsa Kolathayar
Keyword(s):  
Stability Analysis ◽  
Brackish Water ◽  
High Tide ◽  
Estuarine Environment ◽  
Water Demands ◽  
River Flood ◽  
The Stability ◽  
River Dike ◽  
Underlying Soil ◽  
Good Agreement

This paper presents the stability analysis of a dike proposed to impound the river flood waters within an estuary near the west coast of south India. The proposed dike will be located within Ashtamudi Lake, the second largest lake in the state of Kerala, India, separating fresh water from brackish water. Constructing a dike at Munro Island portion of Ashtamudi, which is about 9.23 km from Arabian Sea coast, can meet the water demands of the region as well as prevent the sinking of Island during high tide. The river dike is designed to construct artificially as rock filled structures. The stratigraphy in the top 2 m consists of clayey mud underlined by fine to medium sand up to 6 m followed by alternate layers of clay and sand up the investigated depth of 15 m. In this paper, the stability of the dike located in an estuarine environment has been investigated and the factor of safety values have been determined with varying water level conditions and varying properties of the underlying soil. A detailed parametric study using RocScience software is presented, considering all the design conditions. The expected settlement of the dike is estimated considering the soil profile at the location both manually as well as using software Geo5. Both were in good agreement and the maximum possible settlement was found to be less than half a meter.

scholarly journals Stability analysis of cylindrical shells subjected to complex loads

2001 ◽  
Vol 23 (4) ◽  
pp. 247-256
Author(s):  
Ngo Huong Nhu
Keyword(s):  
Cylindrical Shell ◽  
Stability Analysis ◽  
Composite Shell ◽  
Laminated Composite ◽  
Numerical Results ◽  
Load Pressure ◽  
Combined Loads ◽  
Analytical Result ◽  
The Stability ◽  
Good Agreement

The paper deals with stability analysis of shell on the basis FEM via Castem 2000. The numerical results of stability problems of cylinders subjected to different loads as compress load, pressure, concentrated and combined loads are compared with analytical result and give a good agreement. The influence of changing radius of the cylindrical shell on the unstable forms and the influence of angles of fibers on unstable behaviour of laminated composite shell are considered. Numerical results and corresponding programs by languages Gibian given in the paper to realize software Castem 2000 can be applied in the design and in the stability analysis of the shell with more complex conditions

The instability of the thin vortex ring of constant vorticity

1977 ◽  
Vol 287 (1344) ◽  
pp. 273-305 ◽  
Keyword(s):  
Stability Analysis ◽  
Vortex Ring ◽  
Mean Flow ◽  
Bending Waves ◽  
Constant Vorticity ◽  
Ring Radius ◽  
Amplification Rate ◽  
The Mean ◽  
The Stability ◽  
Good Agreement

A theoretical investigation of the instability of a vortex ring to short azimuthal bending waves is presented. The theory considers only the stability of a thin vortex ring with a core of constant vorticity (constant /r) in an ideal fluid. Both the mean flow and the disturbance flow are found as an asymptotic solution in e = a /R, the ratio of core radius to ring radius. Only terms linear in wave amplitude are retained in the stability analysis. The solution to 0 (e 2 ) is presented, although the details of the stability analysis are carried through completely only for a special class of bending waves that are known to be unstable on a line filament in the presence of strain (Tsai & Widnall 1976) and have been identified in the simple model of Widnall, Bliss & Tsai (1974) as a likely mode of instability for the vortex ring: these occur at certain critical wavenumbers for which waves on a line filament of the same vorticity distribution would not rotate (w 0 = 0). The ring is found to be always unstable for at least the lowest two critical wavenumbers ( ka = 2.5 and 4.35). The amplification rate and wavenumber predicted by the theory are found to be in good agreement with available experimental results.

Linear and Nonlinear PSE for Stability Analysis of the Blasius Boundary Layer Using Compact Scheme

2001 ◽  
Vol 123 (3) ◽  
pp. 545-550 ◽  
Author(s):  
V. Esfahanian ◽  
K. Hejranfar ◽  
F. Sabetghadam
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Nonlinear Effects ◽  
Numerical Investigations ◽  
Blasius Boundary Layer ◽  
Incompressible Boundary ◽  
Linear And Nonlinear ◽  
Tollmien Schlichting ◽  
The Stability ◽  
Good Agreement

A highly accurate finite-difference PSE code has been developed to investigate the stability analysis of incompressible boundary layers over a flat plate. The PSE equations are derived in terms of primitive variables and are solved numerically by using compact method. In these formulations, both nonparallel as well as nonlinear effects are accounted for. The validity of present numerical scheme is demonstrated using spatial simulations of two cases; two-dimensional (linear and nonlinear) Tollmien-Schlichting wave propagation and three-dimensional subharmonic instability breakdown. The PSE solutions have been compared with previous numerical investigations and experimental results and show good agreement.

scholarly journals Effect of Corner Radius in Stabilizing the Low-Re Flow Past a Cylinder

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Wei Zhang ◽  
Ravi Samtaney
Keyword(s):  
Sensitivity Analysis ◽  
Stability Analysis ◽  
New Physics ◽  
Flow Past ◽  
Corner Radius ◽  
Flow Past A Cylinder ◽  
The Stability ◽  
Variation Trends ◽  
Far Wake ◽  
Good Agreement

We perform global linear stability analysis on low-Re flow past an isolated cylinder with rounded corners. The objective of the present work is to investigate the effect of cylinder geometry (corner radius) on the stability characteristics of the flow. Our investigation sheds light on new physics that the flow can be stabilized by partially rounding the cylinder in the critical and weakly supercritical flow regimes. The flow is first stabilized and then gradually destabilized as the cylinder varies from square to circular geometry. The sensitivity analysis reveals that the variation of stability is attributed to the different spatial variation trends of the backflow velocity in the near- and far-wake regions for various cylinder geometries. The results from the stability analysis are also verified with those of the direct simulations, and very good agreement is achieved.

scholarly journals Undrained Stability Analysis of Shallow Tunnel and Sinkhole in Soft Clay: The Cavity Contraction Method

2021 ◽  
Vol 11 (19) ◽  
pp. 9059
Author(s):  
Hui Qi ◽  
Wenjie Cui ◽  
Huaijian Li ◽  
Junwei Cheng ◽  
Lingdi Kong ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Soft Clay ◽  
Field Tests ◽  
Model Tests ◽  
Shallow Tunnel ◽  
New Methods ◽  
The Stability ◽  
Contraction Theory ◽  
Good Agreement ◽  
Centrifuge Model Tests

This paper presents theoretical methods for the undrained stability analysis of shallow tunnels/sinkholes in clay based on the cavity contraction theory, with some assumptions and simplifications. To examine the accuracy and reliability of the new methods, a database was assembled, which consists of stability numbers of tunnel/sinkholes in clays from 22 centrifuge model tests, 10 field tests, and 62 FELA results. It is shown that the proposed methods give an average of 2.5% overestimation for the stability numbers from model tests and is in a good agreement with the FELA results. The cavity contraction theory-based methods are then discussed, which could provide useful guidance for designers to roughly assess shallow tunnel/sinkhole stability in clays.

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