Simultaneous Resonance and Anti-Resonance in Dynamical Systems Under Asynchronous Parametric Excitation

2019 ◽  
Author(s):  
Artem Karev ◽  
Peter Hagedorn
Keyword(s):  
Dynamical Systems ◽  
Parametric Excitation ◽  
Analytical Method ◽  
Normal Forms ◽  
High Sensitivity ◽  
Combination Resonance ◽  
Concurrent Study ◽  
The Stability ◽  
Analytical Expressions ◽  
Special Case

Abstract Since the discovery of parametric anti-resonance, parametric excitation has also become more prominent for its stabilizing properties. While resonance and anti-resonance are mostly studied individually, there are systems where both effects appear simultaneously at each combination resonance frequency. With a steep transition between them and a high sensitivity of their relative positions, there is a need for a concurrent study of resonance and anti-resonance. The semi-analytical method of normal forms is used to derive approximate analytical expressions describing the magnitude of the stability impact as well as the precise locations of stabilized and destabilized areas. The results reveal that the separate appearance of resonance and anti-resonance is only a special case with synchronous parametric excitation. In particular, in circulatory systems the simultaneous appearance is expected to be much more common.

Simultaneous Resonance and Anti-Resonance in Dynamical Systems Under Asynchronous Parametric Excitation

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Artem Karev ◽  
Peter Hagedorn
Keyword(s):  
Dynamical Systems ◽  
Parametric Excitation ◽  
Analytical Method ◽  
Normal Forms ◽  
High Sensitivity ◽  
Combination Resonance ◽  
Concurrent Study ◽  
The Stability ◽  
Analytical Expressions ◽  
Special Case

Abstract Since the discovery of parametric anti-resonance, parametric excitation has also become more prominent for its stabilizing properties. While resonance and anti-resonance are mostly studied individually, there are systems where both effects appear simultaneously at each combination resonance frequency. With a steep transition between them and a high sensitivity of their relative positions, there is a need for a concurrent study of resonance and anti-resonance. The semi-analytical method of normal forms is used to derive approximate analytical expressions describing the magnitude of the stability impact as well as the precise locations of stabilized and destabilized areas. The results reveal that the separate appearance of resonance and anti-resonance is only a special case occurring for synchronous parametric excitation. In particular, in circulatory systems the simultaneous appearance is expected to be much more common.

scholarly journals Parametrically Excited Nonlinear Two-Degree-of-Freedom Systems With Repeated Natural Frequencies

1993 ◽  
Author(s):  
A. H. Nayfeh ◽  
C. Chin ◽  
D. T. Mook
Keyword(s):  
Parametric Excitation ◽  
Nonlinear Response ◽  
Normal Forms ◽  
Natural Frequencies ◽  
Linear Part ◽  
Degree Of Freedom ◽  
Cubic Nonlinearity ◽  
Simply Supported ◽  
The Stability ◽  
Two Degree Of Freedom

Abstract The method of normal forms is used to study the nonlinear response of two-degree-of-freedom systems with repeated natural frequencies and cubic nonlinearity to a principal parametric excitation. The linear part of the system has a nonsemisimple one-to-one resonance. The character of the stability and various types of bifurcation are analyzed. The results are applied to the flutter of a simply-supported panel in a supersonic airstream.

A Generalization of Poincaré’s Theorem to Periodic Hybrid and Impulsive Dynamical Systems

2001 ◽  
Author(s):  
V. Chellaboina ◽  
S. G. Nersesov ◽  
W. M. Haddad
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Discrete Time ◽  
Discrete Time System ◽  
Time System ◽  
Stability Of Periodic Orbits ◽  
Poincaré Return Map ◽  
The Stability ◽  
Time Periodic ◽  
Special Case

Abstract Poincaré’s method is well known for analyzing the stability of continuous-time periodic dynamical systems by studying the stability properties of a fixed point as an equilibrium point of a discrete-time system. In this paper we generalize Poincaré’s method to dynamical systems possessing left-continuous flows to address the stability of limit cycles and periodic orbits of left-continuous, hybrid, and impulsive dynamical systems. It is shown that resetting manifold (which gives rise to the state discontinuities) provides a natural hyperplane for defining a Poincaré return map. In the special case of impulsive dynamical systems, we show the Poincaré map replaces an nth-order impulsive dynamical system by an (n − 1)th-order discrete-time system for analyzing the stability of periodic orbits.

Investigation of instability in ultrasonic welding under parametric excitation

2021 ◽  
pp. 002072092098350
Author(s):  
Yongqiang He ◽  
Lewei Zhao
Keyword(s):  
Parametric Excitation ◽  
High Frequency ◽  
Mathieu Equation ◽  
Ultrasonic Welding ◽  
Transition Curve ◽  
Time Varying ◽  
Combination Resonance ◽  
Bending Loads ◽  
Time Dependent Problem ◽  
The Stability

This paper develops a time-varying model for battery tabs based on the parametric excitation of Euler-Bernoulli beams. The instability caused by combination resonance under a high-frequency longitudinal load is considered. A Galerkin procedure is used to discretize the time-dependent problem into the Mathieu equation. The critical axial load is obtained from the transition curve of combination resonance. The effectiveness of the stability analysis was verified by numerical simulations involving longitudinal and bending loads.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

scholarly journals Development of TLC Chromatographic-Densitometric Procedure for Qualitative and Quantitative Analysis of Ceftobiprole

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 708
Author(s):  
Żaneta Binert-Kusztal ◽  
Małgorzata Starek ◽  
Joanna Żandarek ◽  
Monika Dąbrowska
Keyword(s):  
High Sensitivity ◽  
Biologically Active ◽  
Fifth Generation ◽  
Ich Guidelines ◽  
Relative Standard ◽  
Lipophilicity Parameter ◽  
Alkaline Environments ◽  
Acetic Acid Water ◽  
Cephalosporin Antibiotics ◽  
The Stability

Currently, there is still a need for broad-spectrum antibiotics. The new cephalosporin antibiotics include, among others, ceftobiprole, a fifth-generation gram-positive cephalosporin, active against Staphylococcus aureus methicillin agonist (MRSA). The main focus of the work was to optimize the conditions of ceftobiprole qualitative determination and to validate the developed procedure according to ICH guidelines. As a result of the optimization process, HPTLC Cellulose chromatographic plates as a stationary phase and a mixture consisting of ethanol:2-propanol: glacial acetic acid: water (4:4:1:3, v/v/v/v) as a mobile phase were chosen. The densitometric detection was carried out at maximum absorbance of ceftobiprole (λ = 232 nm). Next, the validation process of the developed procedure was carried out. The relative standard deviation (RSD) for precision was less than 1.65%, which proves the high compatibility of the results, as well as the LOD = 0.0257 µg/spot and LOQ = 0.0779 µg/spot values, which also confirm the high sensitivity of the procedure. The usefulness of the developed method for the stability studies of ceftobiprole was analyzed. Study was carried out under stress conditions, i.e., acid and alkaline environments, exposure to radiation imitating sunlight and high temperature (40–60 °C). It was found that cefotbiprole is unstable in an alkaline environment and during exposure to UV-VIS radiation. Moreover, the lipophilicity parameter, as a main physicochemical property of the biologically active compound, was determined using experimental and computational methods.

scholarly journals The Stability Criteria with Compound Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazhuo Zhang ◽  
Baodong Zheng
Keyword(s):  
Dynamical Systems ◽  
Spectral Property ◽  
Discrete Dynamical Systems ◽  
Asymptotical Stability ◽  
Hopf Bifurcations ◽  
Stability Criteria ◽  
Bifurcation Problem ◽  
Compound Matrices ◽  
The Stability ◽  
Schur Stability

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.

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