Dynamics of a Continuous System With Clearance and Motion Limiting Stops

1999 ◽  
Author(s):  
P. Metallidis ◽  
S. Natsiavas
Keyword(s):  
Piecewise Linear ◽  
Research Work ◽  
Continuous System ◽  
Continuous Model ◽  
Equation Of Motion ◽  
Model System ◽  
Periodic Motions ◽  
System Parameters ◽  
Rigid Rods ◽  
The Stability

Abstract The present study generalises previous research work on the dynamics of discrete oscillators with piecewise linear characteristics and investigates the response of a continuous model system with clearance and motion-limiting constraints. More specifically, in the first part of this work, an analysis is presented for determining exact periodic response of a periodically excited deformable rod, whose motion is constrained by a flexible obstacle. This methodology is based on the exact solution form obtained within response intervals where the system parameters remain constant and its behavior is governed by a linear equation of motion. The unknowns of the problem are subsequently determined by imposing an appropriate set of periodicity and matching conditions. The analytical part is complemented by a suitable method for determining the stability properties of the located periodic motions. In the second part of the study, the analysis is applied to several cases in order to investigate the effect of the system parameters on its dynamics. Special emphasis is placed on comparing these results with results obtained for similar but rigid rods. Finally, direct integration of the equation of motion in selected areas reveals the existence of motions, which are more complicated than the periodic motions determined analytically.

Vibration of Harmonically Excited Oscillators With Asymmetric Constraints

1992 ◽  
Vol 59 (2S) ◽  
pp. S284-S290 ◽  
Author(s):  
S. Natsiavas ◽  
H. Gonzalez
Keyword(s):  
Piecewise Linear ◽  
Periodic Motions ◽  
Van Der Pol ◽  
System Parameters ◽  
State Response ◽  
Damping Coefficients ◽  
Restoring Forces ◽  
Van Der Pol Oscillators ◽  
The Stability ◽  
Stiffness And Damping

investigation is carried out for a class of piecewise linear oscillators with asymmetric characteristics. The damping and restoring forces are general trilinear functions of the system velocity and displacement, respectively, while the excitation is harmonic in time. First, an analysis is presented which determines harmonic and subharmonic steady-state response. Then, a special formulation is employed in examining the stability of located periodic motions. Finally, numerical results are presented for several representative sets of the system parameters. Effects of asymmetries in the response due to unequal gaps as well as unequal stiffness and damping coefficients are analyzed in detail. Asymmetric response of a system with symmetric technical characteristics is also investigated. The behavior of the systems examined resembles response of similar nonlinear systems with continuous characteristics, like the response of the Duffing and van der Pol oscillators. Complicated nonperiodic response is also encountered and analyzed.

Approximate Analytic Method of Piping Systems With Elasto-Plastic Damper

2002 ◽  
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Simple Procedure ◽  
Continuous System ◽  
Approximate Solutions ◽  
Continuous Model ◽  
Equation Of Motion ◽  
Forced Response ◽  
Mode Shapes ◽  
Piping System ◽  
Restoring Force ◽  
Approximate Methods

An elasto-plastic damper is one of the vibration absorbers in which energy is absorbed by elasto-plastic deformation of the hysteretic type damper. It is used for the piping system. The piping system is continuous system. Since it is difficult to find the analytical solution of the equation of motion for the system with elasto-plastic damper, the equation of motion is treated by various approximate methods in which the system is usually considered as a single- or a multiple-degree-of-freedom system, but not as a continuous system. In order to analyze the response of a nonlinear continuous system, however, it is necessary to consider the system as a continuous system. In this paper, the nonlinear steady-state response of the piping system with elasto-plastic damper is undertaken by approximate solutions, which are easily obtained by a simple procedure and are more practical than the exact solutions. As a continuous model of the piping system, a beam simply supported or clamped at one end, with elasto-plastic damper at the other end is used. The restoring force is modeled as hysteresis loop characteristics in order to consider the energy loss in the damper. In the analysis, the restoring force is expanded into the Fourier series, and only fundamental terms are considered. The resonance curves and mode shapes of the beam are obtained from the approximate solution. And effect of elasto-plastic damper on the forced response of continuous system is examined.

Periodic Motions of a Semi-Active Suspension System With MR Damping.

2006 ◽  
Author(s):  
Albert C. J. Luo ◽  
Arun Rajendran
Keyword(s):  
Piecewise Linear ◽  
Active Suspension ◽  
Suspension System ◽  
Mapping Technique ◽  
Periodic Motions ◽  
Mapping Structures ◽  
The Stability ◽  
Magneto Rheological ◽  
Mr Damping ◽  
Full Nonlinearity

Periodic motions in a hysteretically damped, semi-active suspension system are investigated. The Magneto-Rheological damping varying with relative velocity is modeled through a piecewise-linear model. The theory for discontinuous dynamical systems is employed to determine the grazing motions in such a system, and the mapping technique is used to develop the mapping structures of periodic motions. The periodic motions are predicted analytically and verified numerically. The stability and bifurcation analyses of such periodic motions are performed, and the parameters for all possible motions are developed. This model is applicable for the semi-active suspension system with the Magneto-Rheological damper in automobiles. The further investigation on the Magneto-Rheological damping with full nonlinearity should be completed.

Study of Static and Dynamic Stability of an Exponentially Tapered Circular Revolving Beam Exposed to a Variable Temperature Grade under Several Boundary Arrangements

2019 ◽  
Vol 24 (3) ◽  
pp. 504-510
Author(s):  
Rakesh Ranjan Chand Chand ◽  
Pravat Kumar Behera ◽  
Madhusmita Pradhan ◽  
Pusparaj Dash
Keyword(s):  
Dynamic Stability ◽  
Variable Temperature ◽  
Research Work ◽  
Equation Of Motion ◽  
Revolution Speed ◽  
Static And Dynamic Stability ◽  
End Conditions ◽  
Variation Parameter ◽  
Instability Regions ◽  
The Stability

This research work is concerned with the static and dynamic stability study of an exponentially tapered revolving beam having a circular cross-section exposed to an axial live excitation and a variable temperature grade. The stability is analysed for clamped-clamped, clamped-pinned, and pinned-pinned end arrangements. Hamilton’s principle is used to develop the equation of motion and accompanying end conditions. Then, the non-dimensional form of the equation of motion and the end conditions are found. Galerkin’s process is used to find a number of Hill’s equations from the non-dimensional equations. The parametric instability regions are acquired by means of the Saito-Otomi conditions. The consequences of the variation parameter, revolution speed, temperature grade, and hub radius on the instability regions are examined for both static and dynamic load case and represented by a number of plots. The legitimacy of the results is tested by plotting different graphs between displacement and time using the Runge-Kutta fourth-order method. The results divulge that the stability is increased by increasing the revolution speed; however, an increase in the variation parameter leads to destabilization in the system and for same parameters, the stability is less in the case of a variable temperature grade than that of a constant temperature grade condition.

scholarly journals Numerically Efficient Methods for Variational Fractional Wave Equations: An Explicit Four-Step Scheme

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1095
Author(s):  
Jorge E. Macías-Díaz
Keyword(s):  
Wave Equation ◽  
Anomalous Diffusion ◽  
Wave Equations ◽  
Continuous System ◽  
Continuous Model ◽  
Smooth Functions ◽  
Fractional Wave Equations ◽  
Functional Forms ◽  
Variational Form ◽  
The Stability

In this work, we investigate numerically a one-dimensional wave equation in generalized form. The system considers the presence of constant damping and functional anomalous diffusion of the Riesz type. Reaction terms are also considered, in such way that the mathematical model can be presented in variational form when damping is not present. As opposed to previous efforts available in the literature, the reaction terms are not only functions of the solution. Instead, we consider the presence of smooth functions that depend on fractional derivatives of the solution function. Using a finite-difference approach, we propose a numerical scheme to approximate the solutions of the fractional wave equation. Along with this integrator, we propose discrete forms of the local and the total energy operators. In a first stage, we show rigorously that the energy properties of the continuous system are mimicked by our discrete methodology. In particular, we prove that the discrete system is dissipative (respectively, conservative) when damping is present (respectively, absent), in agreement with the continuous model. The theoretical numerical analysis of this system is more complicated in light of the presence of the functional form of the anomalous diffusion. To solve this problem, some novel technical lemmas are proved and used to establish the stability and the quadratic convergence of the scheme. Finally, we provide some computer simulations to show the capability of the scheme to conserve/dissipate the energy. Various fractional problems with functional forms of the anomalous diffusion of the solution are considered to that effect.

Existence, Stability and Bifurcation of Periodic Motions in a Periodically Forced, Piecewise, Linear Oscillator With Impacts

2004 ◽  
Author(s):  
Albert C. J. Luo ◽  
Lidi Chen
Keyword(s):  
Nonlinear Dynamics ◽  
Periodic Motion ◽  
Piecewise Linear ◽  
Linear Oscillator ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Perfectly Plastic ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
The Stability

The nonlinear dynamics of a generalized, piecewise linear oscillator with perfectly plastic impacts is investigated. The generic mappings based on the discontinuous boundaries are constructed. Furthermore, the mapping structures are developed for the analytical prediction of periodic motions of such a system. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems.

Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

2003 ◽  
Vol 3 ◽  
pp. 297-307
Author(s):  
V.V. Denisov
Keyword(s):  
Fourier Transform ◽  
Control System ◽  
Automatic Control ◽  
Fast Fourier Transform ◽  
Automatic Control System ◽  
Resonance Phenomenon ◽  
Periodic Motions ◽  
Multiply Connected ◽  
Non Linear ◽  
The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

Stability and Folding of the Unusually Stable Hemoglobin from Synechocystis is Subtly Optimized and Dependent on the Key Heme Pocket Residues.

2020 ◽  
Vol 27 ◽  
Author(s):  
Sheetal Uppal ◽  
Mohd. Asim Khan ◽  
Suman Kundu
Keyword(s):  
Molten Globule ◽  
Life Forms ◽  
Model System ◽  
Heme Pocket ◽  
The Past ◽  
Specific Manner ◽  
Delivery Vehicles ◽  
The Stability ◽  
Key Residues ◽  
Synechocystis Sp

Aims: The aim of our study is to understand the biophysical traits that govern the stability and folding of Synechocystis hemoglobin, a unique cyanobacterial globin that displays unusual traits not observed in any of the other globins discovered so far. Background: For the past few decades, classical hemoglobins such as vertebrate hemoglobin and myoglobin have been extensively studied to unravel the stability and folding mechanisms of hemoglobins. However, the expanding wealth of hemoglobins identified in all life forms with novel properties, like heme coordination chemistry and globin fold, have added complexity and challenges to the understanding of hemoglobin stability, which has not been adequately addressed. Here, we explored the unique truncated and hexacoordinate hemoglobin from the freshwater cyanobacterium Synechocystis sp. PCC 6803 known as “Synechocystis hemoglobin (SynHb)”. The “three histidines” linkages to heme are novel to this cyanobacterial hemoglobin. Objective: Mutational studies were employed to decipher the residues within the heme pocket that dictate the stability and folding of SynHb. Methods: Site-directed mutants of SynHb were generated and analyzed using a repertoire of spectroscopic and calorimetric tools. Result: The results revealed that the heme was stably associated to the protein under all denaturing conditions with His117 playing the anchoring role. The studies also highlighted the possibility of existence of a “molten globule” like intermediate at acidic pH in this exceptionally thermostable globin. His117 and other key residues in the heme pocket play an indispensable role in imparting significant polypeptide stability. Conclusion: Synechocystis hemoglobin presents an important model system for investigations of protein folding and stability in general. The heme pocket residues influenced the folding and stability of SynHb in a very subtle and specific manner and may have been optimized to make this Hb the most stable known as of date. Other: The knowledge gained hereby about the influence of heme pocket amino acid side chains on stability and expression is currently being utilized to improve the stability of recombinant human Hbs for efficient use as oxygen delivery vehicles.

scholarly journals Dynamical study of infochemical influences on tropic interaction of diffusive plankton system

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Satish Kumar Tiwari ◽  
Ravikant Singh ◽  
Nilesh Kumar Thakur
Keyword(s):  
Dimethyl Sulfide ◽  
Algal Bloom ◽  
Turing Instability ◽  
Model System ◽  
Ode Model ◽  
Estuarine Ecosystem ◽  
Dynamical Study ◽  
Oscillatory Dynamics ◽  
The Stability ◽  
Microzooplankton Grazing

AbstractWe propose a model for tropic interaction among the infochemical-producing phytoplankton and non-info chemical-producing phytoplankton and microzooplankton. Volatile information-conveying chemicals (infochemicals) released by phytoplankton play an important role in the food webs of marine ecosystems. Microzooplankton is an ecologically important grazer of phytoplankton for coexistence of a large number of phytoplankton species. Here, we discuss how information transferred by dimethyl sulfide shapes the interaction of phytoplankton. Phytoplankton deterrents may lead to propagation of IPP bloom. The interaction between IPP and microzooplankton follows the Beddington–DeAngelis-type functional response. Analytically, we discuss boundedness, stability and Turing instability of the model system. We perform numerical simulation for temporal (ODE model) as well as a spatial model system. Our numerical investigation shows that microzooplankton grazing refuse of IPP leads to oscillatory dynamics. Increasing diffusion coefficient of microzooplankton shows Turing instability. Time evolution also plays an important role in the stability of system dynamics. The results obtained in this paper are useful to understand the dominance of algal bloom in coastal and estuarine ecosystem.

scholarly journals Model system parameters influence the sodium hypochlorite susceptibility of endodontic biofilms

2021 ◽  
Author(s):  
R.C.D. Swimberghe ◽  
A. Crabbé ◽  
R.J.G. De Moor ◽  
T. Coenye ◽  
M.A. Meire
Keyword(s):  
Sodium Hypochlorite ◽  
Model System ◽  
System Parameters
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