Interlacing Properties for Mass-Dashpot-Spring Systems With Proportional Damping

2004 ◽  
Vol 126 (2) ◽  
pp. 426-430 ◽  
Author(s):  
Jong-Lick Lin ◽  
Kuo-Chin Chan ◽  
Jyh-Jong Sheen ◽  
Shin-Ju Chen
Keyword(s):  
Real Axis ◽  
Nonlinear Mapping ◽  
Root Locus ◽  
Input Matrix ◽  
Column Space ◽  
Transmission Zeros ◽  
Output Matrix ◽  
Spring System ◽  
Interlacing Property ◽  
Zeros And Poles

A mass-dashpot-spring system with proportional damping is considered in this paper. On the basis of an appropriate nonlinear mapping and the root-locus technique, the interlacing property of transmission zeros and poles is investigated if the columns of the input matrix are in the column space generated by the transpose of the output matrix. It is verified that transmission zeros interlace with poles on a specific circle and the nonpositive real axis segments for a proportional damping system. Finally, three examples are given to illustrate the property.

On Transmission Zeros of Mass-Dashpot-Spring Systems

1999 ◽  
Vol 121 (2) ◽  
pp. 179-183 ◽  
Author(s):  
Jong-Lick Lin
Keyword(s):  
Real Axis ◽  
Imaginary Axis ◽  
Natural Frequencies ◽  
Negative Real Axis ◽  
Transmission Zeros ◽  
Novel Approach ◽  
Spring System ◽  
Mass Spring ◽  
Insight Into ◽  
Interlacing Property

For a noncollocated mass-dashpot-spring system with B=CTΓ, a novel approach is proposed to gain a better insight into the fact that none of its transmission zeros lie in the open right-half of the complex plane. In addition, the transmission zeros have physical meanings and will simply be the natural frequencies of a substructure constrained in the equivalently transformed system. Moreover, it is also shown that transmission zeros interlace with poles along the imaginary axis for a mass-spring system with B=CTΓ. They also interlace with poles along the negative real axis for a mass-dashpot system with B=CTΓ. Finally, two examples are used to illustrate the interlacing property.

scholarly journals On the interlacing property and the Routh-Hurwitz criterion

2003 ◽  
Vol 2003 (12) ◽  
pp. 727-737 ◽  
Author(s):  
Ziad Zahreddine
Keyword(s):  
Simple Proof ◽  
Stability Theory ◽  
Mathematical Community ◽  
Interesting Property ◽  
Important Criterion ◽  
Stability Criteria ◽  
Root Locus ◽  
Nyquist Criterion ◽  
Interlacing Property

Unlike the Nyquist criterion, root locus, and many other stability criteria, the well-known Routh-Hurwitz criterion is usually introduced as a mechanical algorithm and no attempt is made whatsoever to explain why or how such an algorithm works. It is widely believed that simple derivations of this important criterion are highly requested by the mathematical community. In this paper, we address this problem and provide a simple proof of the Routh-Hurwitz criterion based on two generalizations of an interesting property known in stability theory as the interlacing property. Within the same context, the singularities that may arise in the Routh-Hurwitz criterion are also dealt with.

scholarly journals Complex-Damped Dynamic Systems in the Time and Frequency Domains

2004 ◽  
Vol 11 (3-4) ◽  
pp. 209-225 ◽  
Author(s):  
Elvio Bonisoli ◽  
John E. Mottershead
Keyword(s):  
Frequency Response ◽  
Structural Dynamics ◽  
Dynamic Systems ◽  
Dynamic Behaviour ◽  
Root Locus ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Frequency Domains ◽  
Spring System ◽  
Mass Spring

The fact that a complex-damped model may represent the dynamic behaviour of elasto-mechanical systems when acted upon by a magnetic field was brought to the attention of the structural dynamics community very recently by Professor Bruno A. D. Piombo and his colleagues at the Politecnico di Torino. In this paper a thorough analysis of the single degree-of-freedom complex-damped mass-spring system is presented. The analysis includes the root locus, the (non-causal) impulse response, the frequency response and the transmissibility. Regions of different behaviour in the frequency response and transmissibility are described in detail. The stiffening behaviour observed in Prof. Piombo's experiments and known as the "phantom effect" is demonstrated by the complex-damped model.

scholarly journals Акустооптическая коммутация волоконно-оптических каналов

2019 ◽  
Vol 89 (2) ◽  
pp. 274
Author(s):  
С.Н. Антонов
Keyword(s):  
Optical Radiation ◽  
Fiber Optic ◽  
Operating Mode ◽  
Input Matrix ◽  
Output Waveguide ◽  
Short Response Time ◽  
Single Output ◽  
Output Matrix ◽  
Insertion Losses ◽  
Simultaneous Transmission

AbstractAn acousto-optic commutator of fiber-optic channels based on a ТеО_2 two-coordinate deflector has been proposed and realized. The commutator yields switching of optical radiation from a single output waveguide into a two-dimensional input matrix of waveguides, or vice versa, switching from any matrix waveguide into a single output one. The main interrelated parameters have been obtained. It has been established that the commutator has a short response time of 2–10 μs, yields up to several hundreds of switching channels, low insertion losses of 2–5 dB, and a considerable inter-channel isolation from –35 to –60 dB. Experiments were performed for the output matrix containing 19 waveguides. The channel multiplexing operating mode of this commutator has been demonstrated, which is simultaneous transmission of a signal from the output waveguide into a given number of waveguides of the input matrix.

scholarly journals Root Locus Practical Sketching Rules for Fractional-Order Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
António M. Lopes ◽  
J. A. Tenreiro Machado
Keyword(s):  
System Dynamics ◽  
Fractional Order ◽  
Transfer Functions ◽  
Important Case ◽  
Fractional Order Systems ◽  
Root Locus ◽  
Order Problem ◽  
Integer Order ◽  
The Subject ◽  
Zeros And Poles

For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

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