scholarly journals Stability of a flexible structure with destabilizing boundary conditions

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160109 ◽  
Author(s):  
M. Shubov ◽  
V. Shubov
Keyword(s):  
Boundary Conditions ◽  
Control Parameter ◽  
The Other ◽  
Mode Shapes ◽  
Beam Model ◽  
Control Parameters ◽  
The Stability ◽  
Dissipative Boundary ◽  
The Right ◽  
Observation Vector

The Euler–Bernoulli beam model with non-dissipative boundary conditions of feedback control type is investigated. Components of the two-dimensional input vector are shear and moment at the right end, and components of the observation vector are time derivatives of displacement and slope at the right end. The codiagonal matrix depending on two control parameters relates input and observation. The paper contains five results. First, asymptotic approximation for eigenmodes is derived. Second, ‘the main identity’ is established. It provides a relation between mode shapes of two systems: one with non-zero control parameters and the other one with zero control parameters. Third, when one control parameter is positive and the other one is zero, ‘the main identity’ yields stability of all eigenmodes (though the system is non-dissipative). Fourth, the stability of eigenmodes is extended to the case when one control parameter is positive, and the other one is sufficiently small. Finally, existence and properties of ‘deadbeat’ modes are investigated.

scholarly journals Location of eigenmodes of Euler–Bernoulli beam model under fully non-dissipative boundary conditions

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190544
Author(s):  
Marianna A. Shubov
Keyword(s):  
Boundary Conditions ◽  
Half Plane ◽  
Adjoint Problem ◽  
Beam Model ◽  
Control Parameters ◽  
Bernoulli Beam ◽  
Left Half ◽  
The Right ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

The Euler–Bernoulli beam model with non-conservative feedback-type boundary conditions is investigated. Components of the two-dimensional input vector are shear and moment at the right end, and components of the observation vector are time derivative of displacement and slope at the right end. The boundary matrix containing four control parameters relates input and observation. The following results are presented: (i) if one and only one of the control parameters is positive and the rest of them are equal to zero, then the set of the eigenmodes is located in the open left half-plane of the complex plane, which means that all eigenmodes are stable; (ii) if the diagonal elements of the boundary matrix are positive and off-diagonal elements are zeros, then the set of the eigenmodes is located in the open left half-plane, which implies stability of all eigenmodes; (iii) specific combinations of the diagonal and off-diagonal elements have been found to ensure the stability results. To prove the results, two special relations between the eigenmodes and mode shapes of the non-self-adjoint problem and clamped–free self-adjoint problem have been established.

Linear Stability of a Plasma Diode

1969 ◽  
Vol 24 (8) ◽  
pp. 1235-1243 ◽  
Author(s):  
M Dobrowolny ◽  
F Engelmann ◽  
A Sestero
Keyword(s):  
Boundary Conditions ◽  
Linear Stability ◽  
Plane Waves ◽  
The Other ◽  
Other Hand ◽  
Free Particles ◽  
Plasma Diode ◽  
The Stability

AbstractThe stability of a plasma diode with respect to longitudinal oscillations is investigated. If there are free particles emitted by the electrodes, the perturbations do not have the same dynamics as they would in an infinite plasma, contrary to the case where only particles trapped in the diode are present. This can be interpreted as due to a coupling of plane waves of different wave lengths, introduced by the boundary conditions at the electrodes. The occurrence of resonant-particle effects, on the other hand, is subjected to precisely the same conditions as in an infinite plasma.

FiniteElement Vibration Characteristics of Composite Hypar Shallow Shells with Various Edge Supports

2005 ◽  
Vol 11 (10) ◽  
pp. 1291-1309 ◽  
Author(s):  
S. Sahoo ◽  
D. Chakravorty
Keyword(s):  
Boundary Conditions ◽  
Numerical Experiments ◽  
Laminated Composite ◽  
Shell Element ◽  
Vibration Characteristics ◽  
The Other ◽  
Mode Shapes ◽  
Review Of The Literature ◽  
Shallow Shells ◽  
Fundamental Frequencies

A review of the literature reveals that information regarding fundamental frequencies and mode shapes of shallow laminated composite hypar shells with practical civil engineering boundary conditions is not available. The present investigation aims to fill this gap by applying an eight-noded isoparametric shell element as the tool. Numerical experiments are carried out for different parametric variations including boundary conditions and stacking orders to obtain the fundamental frequencies and mode shapes. Some of the results are used for validating the correctness of the present approach by comparing with the existing benchmark, while the other results are studied meticulously to extract a set of meaningful conclusions regarding the free vibration characteristics of composite shallow hypar shells.

Experimental Study of the Stability of a High-Speed Gas Jet Under the Influence of Liquid Cross-Flow

2007 ◽  
Author(s):  
Chris Weiland ◽  
Jon Yagla ◽  
Pavlos Vlachos
Keyword(s):  
Mach Number ◽  
Free Boundary ◽  
Boundary Conditions ◽  
High Speed ◽  
Cross Flow ◽  
Upper And Lower Bounds ◽  
Gas Jet ◽  
Mode Shapes ◽  
Free Boundary Conditions ◽  
The Stability

This paper reports on the interfacial character and deflection of a high-speed gas jet transverse to an aqueous cross-flow as a function of cross-flow speed and gas jet Mach number. Several gas exit velocities were tested including subsonic cases up to supersonic cases at cross-flow velocities from 0.3 m/s to 0.7 m/s. For the subsonic cases, it was found that the stability and resistance of the gas jet to deflect in the presence of cross-flow were increased with the jet Mach number. However, the Mach 1.6 jet was more stable than the Mach 1.9 jet, suggesting that there exists upper and lower bounds for jet stability which are Mach number dependent. Unstable gas jets were shown to pinch-off, meaning the interface of the gas jet in a plane parallel to the ejector exit collapsed to almost a point and an independent bubble rose to the free surface. The stagnation side gas/liquid interfaces were analyzed using the Proper Orthogonal Decomposition (POD) method to better understand the fundamental mode shapes contained in the interface waveforms. It was found that the subsonic jets shared many of the same characteristics in their first, second, and third mode shapes. The supersonic jets differed from the subsonic mode shapes. Interestingly, the mode shapes for the subsonic cases compared well to those of a beam in transverse vibration with sliding-free boundary conditions. The supersonic cases compared relatively well to pinned-free boundary conditions, owing to the more columnar nature of the gas jet as it exited the ejector.

Theoretical Determination of Natural Modes of Deck Vibrations

1966 ◽  
Vol 3 (01) ◽  
pp. 66-79
Author(s):  
Robert D. Short
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Maximum Error ◽  
Nodal Line ◽  
The Other ◽  
Mode Shapes ◽  
Theoretical Determination ◽  
Natural Modes

Six methods for calculating the natural frequency and mode shapes of cross-stiffened plating were examined particularly for their application to plating with a large number of small closely spaced stiffeners in one direction supported by a few deep girders in the other. The best method was able to predict at least 1 6 frequencies (all that were measured) of a model with a maximum error of less than 15 percent when proper boundary conditions were used. The maximum error in nodal-line locations for the best method was 5.2 percent of the span

scholarly journals Determination methodology for stable control domain of electric powertrain based on permanent magnet synchronous motor

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879305 ◽  
Author(s):  
Donghai Hu ◽  
Yanzhi Yan ◽  
Xiaoming Xu
Keyword(s):  
Nonlinear Dynamics ◽  
Working Conditions ◽  
Control Parameter ◽  
Equilibrium Points ◽  
Permanent Magnet Synchronous Motor ◽  
Field Oriented Control ◽  
Control Parameters ◽  
Proportional Control ◽  
Proportional Integral ◽  
The Stability

Oscillation of torque and speed occurs in the electric powertrain based on permanent magnet synchronous motor under field-oriented control when we set an unreasonable proportional control parameter of proportional–integral regulator. Thus, it influences the stability and reliability of electric powertrain. The objectives of this article are to study nonlinear dynamics of electric powertrain under various complex operating conditions and settle a minimum stable range of proportional control parameter of proportional–integral regulator. To achieve these goals, nonlinear dynamic model of electric powertrain was established. Then, we solved equilibrium points and analyzed the stability of equilibrium points. Finally, we set different control parameters of proportional–integral regulator and various complex working conditions of electric powertrain to simulate nonlinear dynamics of electric powertrain. The simulation results show the electric powertrain operates stably when the control parameter is set in the area where there is only one stable equilibrium point. Chaos do exist in the electric powertrain with field-oriented control under different working conditions. Our analysis reveals the dynamics of electric powertrain are dependent on proportional control parameters of proportional–integral regulator and electric powertrain performs unstably most likely under the operating condition with no-load and zero reference rotational speed.

Memory-type boundary control of a laminated Timoshenko beam

2020 ◽  
Vol 25 (8) ◽  
pp. 1568-1588 ◽  
Author(s):  
Baowei Feng ◽  
Abdelaziz Soufyane
Keyword(s):  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Stability Result ◽  
Kernel Functions ◽  
The Other ◽  
Interfacial Slip ◽  
Small Thickness ◽  
Memory Type ◽  
Type Boundary ◽  
The Stability

In this paper, we consider a laminated Timoshenko beam with boundary conditions of a memory type. This structure is given by two identical uniform layers, one on top of the other, taking into account that an adhesive of small thickness bonds the two surfaces and produces an interfacial slip. Under the assumptions of wider classes of kernel functions, we establish an optimal explicit energy decay result. The stability result is more general than previous works and hence improves earlier results in the literature.

A Pilot Study of a Dynamical Systems Approach to Examining Changes in Static Balance of Adolescents

2002 ◽  
Vol 95 (1) ◽  
pp. 267-278 ◽  
Author(s):  
Jason Wicke ◽  
Robert Jensen
Keyword(s):  
Pilot Study ◽  
Dynamical Systems ◽  
Control Parameter ◽  
Systems Approach ◽  
The Body ◽  
Static Balance ◽  
Control Parameters ◽  
Systems Model ◽  
Balance Task ◽  
The Stability

In a dynamical systems model, movement patterns are dictated by several variables, called control parameters. The goal of this pilot study was to assess whether changes on a static balance task can be described by a dynamical systems model with body inertial properties as one of the potential control parameters. Three aspects of a dynamic system were examined in relation to a 2-ft. static balance task: a relation between the changes in the balance pattern and the control parameter, a relation between the stability of the balance pattern and the stability under perturbed conditions (1-ft. balance task), and during the perturbation lack of relation between the balance pattern and the control parameters. Nine adolescent boys, 15.3 ± 1.0 yr. old were examined twice over a 14-wk. period. During each testing session, participants' body mass, moments of inertia, and radius from the ankle to the center of mass were calculated, after which 1- and 2-ft. balance tasks were performed. Center of pressure coordinates were recorded using a Kistler force plate. The body parameters were used to calculate the natural frequency of the body to represent the control parameter. Significant relations among all three aspects of a dynamic system examined in both the lateral and anterior-posterior axes were found. This investigation was designed for exploratory purposes and limited to correlational analysis; therefore, no concrete conclusions could be drawn. The results, however, suggest a dynamical systems approach to the study of static balance patterns may be possible.

On Asymptotic Approximations to Beam Model Shapes

1984 ◽  
Vol 51 (2) ◽  
pp. 439-439 ◽  
Author(s):  
E. H. Dowell
Keyword(s):  
Boundary Conditions ◽  
Mode Shapes ◽  
Asymptotic Approximations ◽  
General Interest ◽  
Beam Model ◽  
Asymptotic Character

Recently the author had occasion to investigate inter alia the asymptotic character of the mode shapes of uniform beams. These results do not seem to have been presented before in the literature and so are given here as they appear to be of general interest. Clamped-free and free-free beams are considered, although other beam boundary conditions may be treated in a similar manner.

scholarly journals Uniform exponential stabilisation of serially connected inhomogeneous Euler-Bernoulli beams

2020 ◽  
Vol 26 ◽  
pp. 110
Author(s):  
Björn Augner
Keyword(s):  
Boundary Conditions ◽  
Modulus Of Elasticity ◽  
Spatial Dependence ◽  
Mass Density ◽  
Coupled System ◽  
The Other ◽  
Exponential Energy Decay ◽  
A Chain ◽  
Dissipative Boundary ◽  
Dependent Mass

We consider a chain of Euler-Bernoulli beams with spatial dependent mass density, modulus of elasticity and area moment which are interconnected in dissipative or conservative ways and prove uniform exponential energy decay of the coupled system for suitable dissipative boundary conditions at one end and suitable conservative boundary conditions at the other end. We thereby generalise some results of G. Chen, M.C. Delfour, A.M. Krall and G. Payre from the 1980’s to the case of spatial dependence of the parameters.

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