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.

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.

General Models for Linear Damping

2010 ◽  
Author(s):  
H. G. D. Goyder
Keyword(s):  
Real Axis ◽  
Imaginary Axis ◽  
Negative Real Axis ◽  
Variable Theory ◽  
Complex Variable Theory ◽  
The Standard Model ◽  
Complete Set ◽  
Linear Damping ◽  
Branch Cuts ◽  
Damping Model

The standard model for damping is the linear viscous dashpot which produces a force proportional to velocity. Although other sources of linear damping are known to exist, such as that due to viscoelasticity, it is not clear what range of mathematical forms damping models can take. Here it is suggested that there are only three types of damping model. These models are deduced by examining three configurations of mechanical components. These configurations include combinations of springs and dashpots and, most significantly, a semi-infinite beam. It is found that these models are best examined in the Laplace or s-plane so that features of the damping models may be expressed in terms of complex variable theory. The three types of damping model revealed by this analysis correspond to poles lying off the imaginary axis, poles on the negative real axis and pole like forms on the negative real axis that give rise to branch cuts. It is conjectured that these are the complete set of mathematical models that describe damping.

Vibration of Heavy String Tethered to Mass–Spring System

2017 ◽  
Vol 17 (04) ◽  
pp. 1771002 ◽  
Author(s):  
C. Y. Wang ◽  
C. M. Wang ◽  
R. Freund
Keyword(s):  
Natural Frequencies ◽  
Equation Of Motion ◽  
Gantry Crane ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Tower Crane ◽  
Spring System ◽  
Mass Spring ◽  
First Time ◽  
Top Mass

This paper is concerned with the vibration of a heavy string tethered to a mass–spring system which is a model for tower crane or gantry crane. The governing equation of motion of the aforementioned problem is solved analytically and exact closed-form characteristic solutions for the natural frequencies are presented. These exact solutions would serve as benchmarks for models which may be more complex than the basic vibration problem considered. Moreover, we investigate the effect of the string-mass pendulum as a flexible dynamic vibration absorber. Such a problem is important in vibration control, and is investigated analytically for the first time. It is found that the effect of the bottom mass is to decrease the amplitude of the string in general. The effect of increased forcing frequency increases the number of nodal points on the string. In most cases, the amplitude of the top mass is reduced.

Simulation on Vertical Vibration of Six-Roller Cold Rolling Mill

2013 ◽  
Vol 441 ◽  
pp. 623-626
Author(s):  
Xu Ma ◽  
Xing Hui Zhu ◽  
Jian Wei Li ◽  
Jing Hong Yang ◽  
Quan Lu Yang ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Vertical Vibration ◽  
Prototype Model ◽  
Cold Rolling Mill ◽  
Spring System ◽  
Tandem Cold Mill ◽  
Mass Spring ◽  
Modal Coordinates ◽  
Cold Mill

According to the chatter phenomenon of 3rd stand of a steelworks six-roller tandem cold mill (TCM), vertical vibration of tandem cold mill was simplified to eight degrees of asymmetric freedom mass-spring system. Virtual prototype model on vertical vibration of tandem cold mill was established and natural frequencies and main vibration mode of mill were solved by using automatic dynamic analysis of mechanical systems in software ADAMS. The modal coordinates of main vibration mode of the mill were referred firstly and obtained; the maximal mode of vibration system was found and finally discovered the fifth-octave-mode chatter was the probable vibration of the mill.

scholarly journals The Complexity of Approximating the Matching Polynomial in the Complex Plane

2021 ◽  
Vol 13 (2) ◽  
pp. 1-37
Author(s):  
Ivona Bezáková ◽  
Andreas Galanis ◽  
Leslie Ann Goldberg ◽  
Daniel Štefankovič
Keyword(s):  
Real Axis ◽  
Complex Plane ◽  
Maximum Degree ◽  
Negative Real Axis ◽  
Positive Real ◽  
Bounded Degree ◽  
Matching Polynomial ◽  
Correlation Decay ◽  
Connective Constant ◽  
General Complex

We study the problem of approximating the value of the matching polynomial on graphs with edge parameter γ, where γ takes arbitrary values in the complex plane. When γ is a positive real, Jerrum and Sinclair showed that the problem admits an FPRAS on general graphs. For general complex values of γ, Patel and Regts, building on methods developed by Barvinok, showed that the problem admits an FPTAS on graphs of maximum degree Δ as long as γ is not a negative real number less than or equal to −1/(4(Δ −1)). Our first main result completes the picture for the approximability of the matching polynomial on bounded degree graphs. We show that for all Δ ≥ 3 and all real γ less than −1/(4(Δ −1)), the problem of approximating the value of the matching polynomial on graphs of maximum degree Δ with edge parameter γ is #P-hard. We then explore whether the maximum degree parameter can be replaced by the connective constant. Sinclair et al. showed that for positive real γ, it is possible to approximate the value of the matching polynomial using a correlation decay algorithm on graphs with bounded connective constant (and potentially unbounded maximum degree). We first show that this result does not extend in general in the complex plane; in particular, the problem is #P-hard on graphs with bounded connective constant for a dense set of γ values on the negative real axis. Nevertheless, we show that the result does extend for any complex value γ that does not lie on the negative real axis. Our analysis accounts for complex values of γ using geodesic distances in the complex plane in the metric defined by an appropriate density function.

Graphene-Based Resonant Sensors for Detection of Ultra-Fine Nanoparticles: Molecular Dynamics and Nonlocal Elasticity Investigations

NANO ◽  
2015 ◽  
Vol 10 (02) ◽  
pp. 1550024 ◽  
Author(s):  
S. Kamal Jalali ◽  
M. Hassan Naei ◽  
Nicola Maria Pugno
Keyword(s):  
Molecular Dynamics ◽  
Nonlocal Elasticity ◽  
Md Simulations ◽  
Small Scale ◽  
Frequency Shifts ◽  
Resonant Sensors ◽  
Embedded Atom ◽  
Metal Metal ◽  
Spring System ◽  
Mass Spring

Application of single layered graphene sheets (SLGSs) as resonant sensors in detection of ultra-fine nanoparticles (NPs) is investigated via molecular dynamics (MD) and nonlocal elasticity approaches. To take into consideration the effect of geometric nonlinearity, nonlocality and atomic interactions between SLGSs and NPs, a nonlinear nonlocal plate model carrying an attached mass-spring system is introduced and a combination of pseudo-spectral (PS) and integral quadrature (IQ) methods is proposed to numerically determine the frequency shifts caused by the attached metal NPs. In MD simulations, interactions between carbon–carbon, metal–metal and metal–carbon atoms are described by adaptive intermolecular reactive empirical bond order (AIREBO) potential, embedded atom method (EAM), and Lennard–Jones (L–J) potential, respectively. Nonlocal small-scale parameter is calibrated by matching frequency shifts obtained by nonlocal and MD simulation approaches with same vibration amplitude. The influence of nonlinearity, nonlocality and distribution of attached NPs on frequency shifts and sensitivity of the SLGS sensors are discussed in detail.

Anodic stripping voltammetry of anti-Vi antibody functionalized CdTe quantum dots for the specific monitoring of Salmonella enterica serovar Typhi

RSC Advances ◽  
2015 ◽  
Vol 5 (107) ◽  
pp. 88234-88240 ◽  
Author(s):  
Satish K. Pandey ◽  
Praveen Rishi ◽  
C. Raman Suri ◽  
Aaydha C. Vinayaka
Keyword(s):  
Quantum Dots ◽  
Capsular Polysaccharide ◽  
Anodic Stripping Voltammetry ◽  
Stripping Voltammetry ◽  
Cdte Quantum Dots ◽  
Salmonella Enterica Serovar Typhi ◽  
Novel Approach ◽  
Anodic Stripping ◽  
Vi Capsular Polysaccharide ◽  
Insight Into

CdTe QD based stripping voltammetry for Vi capsular polysaccharide detection. The technique has provided an insight into the competence of CdTe QD and GNP immuno-conjugates. This is a novel approach to characterize the efficiency of immuno-conjugates of QDs and GNPs.

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