scholarly journals Effect of Parameters on the Design of a Suspension System with Four Oblique Springs

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Gianluca Gatti
Keyword(s):  
Frequency Response ◽  
Dynamic Performance ◽  
Excitation Amplitude ◽  
Suspension System ◽  
Closed Form Expression ◽  
Deflection Curve ◽  
Form Expression ◽  
Static And Dynamic Characteristics ◽  
System Parameters ◽  
Static Performance

This paper presents the fundamental static and dynamic characteristics of a suspension system consisting of four linear springs arranged in an X-shaped configuration to achieve geometric nonlinearity. The particular interest is towards the design of a softening spring geometry realizing a quasi-zero stiffness behaviour at large deflections, and the influence of the system parameters is investigated. The static performance is studied in terms of the force-deflection curve and the dynamic performance in terms of the frequency response curve. The softening-hardening behaviour of the suspension leads to a frequency response which bends to the lower frequencies reaching a well-defined minimum. It is found that both the static and dynamic behaviours may be described in terms of a single parameter, and a simple closed-form expression is determined which links the damping in the system to the excitation amplitude to achieve the lowest possible resonance frequency.

Design of 2-DOF Micro-Positional Stage Based on Parallel Structure Using Flexible Plate

2010 ◽  
Vol 37-38 ◽  
pp. 317-321
Author(s):  
Hua Chun ◽  
Yu Guo Cui ◽  
Yong Li ◽  
Lei Qiu
Keyword(s):  
Finite Element Method ◽  
Driving Force ◽  
Dynamic Performance ◽  
Parallel Structure ◽  
Flexible Plate ◽  
The Finite Element Method ◽  
Maximum Displacement ◽  
Compact Structure ◽  
Static And Dynamic Characteristics ◽  
Static Performance

A new prototype of 2-DOF micro-positional stage was designed based on parallel structure according to the following requirements of the stage, such as, symmetrical structures in X and Y directions, decoupling movement in X and Y directions, large operating surface, and more simple and compact structure. Using double flexible arched plate, the specified structure of the stage was designed by considering the realization of its movement. Static and dynamic characteristics of the stage have been analyzed by using the finite element method. For the static performance, there is a linear relationship between the displacement of the stage and its driving force. The maximum displacement of the stage is about 36 μm under the maximum force 650 N. For dynamic performance, the natural frequency and the response time of the stage are about 2.4 kHz and 1.4 ms, respectively.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

scholarly journals Impact of the Generation System Parameters on the Frequency Response of the Power System: A UK Grid Case Study

Electricity ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 143-157
Author(s):  
Jovi Atkinson ◽  
Ibrahim M. Albayati
Keyword(s):  
Power System ◽  
Frequency Response ◽  
Power Grid ◽  
Sudden Increase ◽  
Generation System ◽  
System Parameters ◽  
Primary Frequency ◽  
Primary Frequency Response ◽  
The Impact ◽  
System Inertia

The operation and the development of power system networks introduce new types of stability problems. The effect of the power generation and consumption on the frequency of the power system can be described as a demand/generation imbalance resulting from a sudden increase/decrease in the demand and/or generation. This paper investigates the impact of a loss of generation on the transient behaviour of the power grid frequency. A simplified power system model is proposed to examine the impact of change of the main generation system parameters (system inertia, governor droop setting, load damping constant, and the high-pressure steam turbine power fraction), on the primary frequency response in responding to the disturbance of a 1.32 GW generation loss on the UK power grid. Various rates of primary frequency responses are simulated via adjusting system parameters of the synchronous generators to enable the controlled generators providing a fast-reliable primary frequency response within 10 s after a loss of generation. It is concluded that a generation system inertia and a governor droop setting are the most dominant parameters that effect the system frequency response after a loss of generation. Therefore, for different levels of generation loss, the recovery rate will be dependent on the changes of the governor droop setting values. The proposed model offers a fundamental basis for a further investigation to be carried on how a power system will react during a secondary frequency response.

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

Analysis and Optimization of the Static and Dynamic Characteristics of Head Frame

2011 ◽  
Vol 418-420 ◽  
pp. 2055-2059 ◽  
Author(s):  
Yu Lin Wang ◽  
Na Jin ◽  
Kai Liao ◽  
Rui Jin Guo ◽  
Hu Tian Feng
Keyword(s):  
Machine Tool ◽  
Dynamic Characteristics ◽  
Maximum Stress ◽  
Dynamic Performance ◽  
Mode Shapes ◽  
Cnc Machine ◽  
Static And Dynamic Characteristics ◽  
Maximum Deformation ◽  
Improvement Measures ◽  
Optimal Measure

The head frame is a key component which plays a supportive and accommodative role in the spindle system of CNC machine tool. Improving the static and dynamic characteristics has profound significance to the development of machine tool and product performance. The simplified finite element modal is established with ANSYS to carry out the static and modal analysis. The results showed that the maximum deformation of the head frame was 0.0066mm, the maximum stress was 3.94Mpa, the deformation of most region was no more than 0.0007mm, which all verified that the head frame had a good stiffness and deforming resistance; several improvement measures for dynamic performance were also proposed by analyzing the mode shapes, and the 1st order natural frequency increased 7.33% while the head frame mass only increased 1.58% applying the optimal measure, which improved the dynamic characteristics of the head frame effectively.

Simple Closed-Form Expression to Estimate the Ring Ratio of 16-APSK to Compensate for Distortion in Nonlinear Systems

2017 ◽  
Author(s):  
M.J. Cañavate-Sánchez ◽  
A. Segneri ◽  
S. Godi ◽  
A. Georgiadis ◽  
S. Kosmopoulos ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression ◽  
Ring Ratio
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