Stability and Hopf Bifurcation of Impact Dynamics Considering Delay in a Semi-Active Energy Absorbing Suspension System

2011 ◽  
Author(s):  
Xiaomin Dong ◽  
Wei Hu ◽  
Miao Yu ◽  
Norman M. Wereley
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Impact Velocity ◽  
Suspension System ◽  
Impact Dynamics ◽  
Ground Vehicles ◽  
Payload Mass ◽  
Energy Absorbers ◽  
Energy Absorbing ◽  
The Impact

In a crash event, such as the crash of an aircraft or the collision of two ground vehicles, the impact dynamics are a function of the impact velocity and payload mass. A typical bumper system on a ground vehicle has passive viscous energy absorbers (PVEAs) that are optimally designed for a specific impact velocity and payload, so that off-design performance may be suboptimal, and may even be unacceptable for large perturbations in sink rate and payload mass from the designed values. This is because the load-stroke profile of the energy absorbing suspension system (EASS) is passive in that spring stiffness and damping of the energy absorbers is fixed. Therefore, in this study, the PVEA in an EASS is replaced by an active or semi-active energy absorber (SAEA), and the effects of time delay in achieving controllable semi-active damping is analyzed in the context of impact dynamics. To accomplish this, a three degree-of-freedom dynamic model of an EASS is presented, and the effect of the time delay in commanding the controllable force of the EA is analyzed. The asymptotic stability and Hopf bifurcation of the trivial steady state response are analyzed for a range of time delay. A technique to stabilize the impact dynamic is developed, and it is shown that the impact dynamics can be stabilized using appropriate feedback control.

scholarly journals Lifting a sessile oil drop from a superamphiphobic surface with an impacting one

2020 ◽  
Vol 6 (34) ◽  
pp. eaba4330
Author(s):  
Olinka Ramírez-Soto ◽  
Vatsal Sanjay ◽  
Detlef Lohse ◽  
Jonathan T. Pham ◽  
Doris Vollmer
Keyword(s):  
Surface Tension ◽  
Energy Transfer ◽  
Impact Velocity ◽  
Sessile Drop ◽  
Cloud Formation ◽  
Impact Dynamics ◽  
Combustion Engines ◽  
Intrinsic Properties ◽  
Natural Processes ◽  
The Impact

Colliding drops are encountered in everyday technologies and natural processes, from combustion engines and commodity sprays to raindrops and cloud formation. The outcome of a collision depends on many factors, including the impact velocity and the degree of alignment, and intrinsic properties like surface tension. Yet, little is known on binary impact dynamics of low-surface-tension drops on a low-wetting surface. We investigate the dynamics of an oil drop impacting an identical sessile drop sitting on a superamphiphobic surface. We observe five rebound scenarios, four of which do not involve coalescence. We describe two previously unexplored cases for sessile drop liftoff, resulting from drop-on-drop impact. Numerical simulations quantitatively reproduce the rebound scenarios and enable quantification of velocity profiles, energy transfer, and viscous dissipation. Our results illustrate how varying the offset from head-on alignment and the impact velocity results in controllable rebound dynamics for oil drop collisions on superamphiphobic surfaces.

Drop-Induced Shock Mitigation Using Adaptive Magnetorheological Energy Absorbers Incorporating a Time Lag

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Young-Tai Choi ◽  
Norman M. Wereley
Keyword(s):  
Equations Of Motion ◽  
Time Lag ◽  
Soft Landing ◽  
Single Degree Of Freedom ◽  
Bingham Number ◽  
Shock Mitigation ◽  
Payload Mass ◽  
Energy Absorbers ◽  
Time Required ◽  
The Impact

This study addresses the nondimensional analysis of drop-induced shock mitigated using magnetorheological energy absorbers (MREAs) incorporating a time lag. This time lag arises from two sources: (1) the time required to generate magnetic field in the electromagnet once current has been applied and (2) the time required for the particles in the magnetorheological fluid to form chains. To this end, the governing equations of motion for a single degree-of-freedom (SDOF) system using an MREA with a time lag were derived. Based on these equations, nondimensional stroke, velocity, and acceleration of the payload were derived, where the MREA with a time lag was used to control payload deceleration after the impact. It is established that there exists an optimal Bingham number that allows the payload mass to achieve a soft landing, that is, the payload comes to rest after utilizing the available stroke of the MREA. Finally, the shock mitigation performance when using this optimal Bingham number control strategy is analyzed, and the effects of time lag are quantified.

Impact Response of Thin-Walled Tubes: A Prospective Review

2012 ◽  
Vol 165 ◽  
pp. 130-134 ◽  
Author(s):  
Fauziah Mat ◽  
K. Azwan Ismail ◽  
S. Yaacob ◽  
O. Inayatullah
Keyword(s):  
Compressive Loading ◽  
Axial Loading ◽  
Geometrical Parameters ◽  
Axial Deformation ◽  
Thin Walled Structures ◽  
Structural Applications ◽  
Thin Walled ◽  
Energy Absorbers ◽  
Energy Absorbing ◽  
The Impact

Thin-walled structures have been widely used in various structural applications asimpact energy absorbing devices. During an impact situation, thin-walled tubesdemonstrate excellent capability in absorbing greater energy through plastic deformation. In this paper, a review of thin-walled tubes as collapsible energy absorbers is presented.As a mean of improving the impact energy absorption of thin-walled tubes, the influence of geometrical parameters such as length, diameter and wall thickness on the response of thin-walled tubes under compression axial loading are briefly discussed. Several design improvements proposed by previous researchers are also presented. The scope of this review is mainly focus on axial deformation under quasi-static and dynamic compressive loading. Other deformations, such as lateral indentation, inversion and splitting are considered beyond the scope of this paper. This review is intended to assist the future development of thin-walled tubes as efficient energy absorbing elements.

Hopf Bifurcation in a Delayed Diffusive Leslie–Gower Predator–Prey Model with Herd Behavior

2019 ◽  
Vol 29 (04) ◽  
pp. 1950055
Author(s):  
Fengrong Zhang ◽  
Yan Li ◽  
Changpin Li
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Herd Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Stability ◽  
The Impact

In this paper, we consider a delayed diffusive predator–prey model with Leslie–Gower term and herd behavior subject to Neumann boundary conditions. We are mainly concerned with the impact of time delay on the stability of this model. First, for delayed differential equations and delayed-diffusive differential equations, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated respectively. It is observed that when time delay continues to increase and crosses through some critical values, a family of homogeneous and inhomogeneous periodic solutions emerge. Then, the explicit formula for determining the stability and direction of bifurcating periodic solutions are also derived by employing the normal form theory and center manifold theorem for partial functional differential equations. Finally, some numerical simulations are shown to support the analytical results.

scholarly journals Exploring droplet impact near a millimetre-sized hole: comparing a closed pit with an open-ended pore

2015 ◽  
Vol 772 ◽  
pp. 427-444 ◽  
Author(s):  
Rianne de Jong ◽  
Oscar R. Enríquez ◽  
Devaraj van der Meer
Keyword(s):  
Impact Velocity ◽  
Crucial Role ◽  
Drop Impact ◽  
Impact Dynamics ◽  
Air Bubbles ◽  
Air Bubble ◽  
Impact Location ◽  
Impact Phenomena ◽  
The Impact

We investigate drop impact dynamics near closed pits and open-ended pores experimentally. The resulting impact phenomena differ greatly in each case. For a pit, we observe three distinct phenomena, which we denote as a splash, a jet and an air bubble, whose appearance depends on the distance between impact location and pit. Furthermore, we found that splash velocities can reach up to seven times the impact velocity. Drop impact near a pore, however, results solely in splashing. Interestingly, two distinct and disconnected splashing regimes occur, with a region of planar spreading in between. For pores, splashes are less pronounced than in the pit case. We state that, for the pit case, the presence of air inside it plays the crucial role of promoting splashing and allowing for air bubbles to appear.

scholarly journals A fractional-order love dynamical model with time delay for synergic couple : Stability analysis and Hopf bifurcation

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
The Impact

We investigate the fractional order love dynamic model with time delay for synergic couples in this manuscript. The quantitative analysis of the model has been done where the asymptotic stability of the equilibrium points of the model have been analyzed. Under the impact of time delay, the Hopf bifurcation analysis of the model has been done. The stability analysis of the model has been studied with the reproduction number less than or greater than 1. By using Laplace transformation, the analysis of the model has been done. The analysis shows that the fractional order model with a time delay can sufficiently improve the components and invigorate the outcomes for either stable or unstable criteria. In this model, all unstable cases are converted to stable cases under neighbourhood points. For all parameters, the reproduction ranges have been described. Finally, to illustrate our derived results numerical simulations have been carried out by using MATLAB. Under the theoretical outcomes from parameter estimation, the love dynamical system is verified.

A Constant Stroking Load Regulator for Shock Absorption

2011 ◽  
Author(s):  
Gang Wang ◽  
Gregory Hiemenz ◽  
Wei Hu ◽  
Norman M. Wereley
Keyword(s):  
Impact Velocity ◽  
Input Parameter ◽  
Control Input ◽  
Soft Landing ◽  
Shock Absorption ◽  
Energy Absorber ◽  
Seat Suspension ◽  
Drop Tests ◽  
Payload Mass ◽  
The Impact

The goal of this study is to provide shock mitigation in an active (or semi-active) shock absorption system, typically comprising of a spring, and an adjustable stroking load element, such as an adaptive energy absorber (EA) or semiactive damper element, in which the stroking load can be electronically adjusted in real-time. Typically, there is a maximum limiting stroking load that can be accommodated by a payload. Thus, a Constant Stroking Load Regulator (CSLR) is developed that accepts sensor feedback, and then selects control gains that result in the energy absorber (EA) providing the required controllable stroking load. A key benefit of this regulator is that it is capable of adapting to a varying range of payload mass, impulse types, and impulse excitation levels. The payload mass is measured and used as a control input parameter. The measured impact velocity is used to determine the impulse acceleration level by assuming an impulse profile, which tends to be application-specific. Finally, the required constant stroking load is determined using a physics-based model. The CSLR is designed to achieve a “soft landing” such the payload comes to rest when the available stroke is used completely, in order to minimize the stroking load and thereby minimize the potential for payload damage. The CSLR methodology was then experimentally validated for a representative occupant protection system consisting of a seat suspension with an adaptive stroking element, which in this case was a magnetorheological energy absorber (MREA). A MREA was used as the stroking element because its stroking load can be adjusted electronically. To validate the CSLR strategy, experimental drop tests were conducted for two different payloads. The impact velocity was 10.3 ft/s (3.15 m/s) and the acceleration profile was a 50 ms duration half-sine pulse. The constant stroking load was pre-calculated as a function of payload mass and initial velocity. During each drop test, the required stroking load was supplied to the MREA in order to achieve a “soft landing.” The CSLR was successfully demonstrated under laboratory conditions. These tests demonstrated feasibility of using the CSLR, in conjunction with a MREA as the stroking element.

Experimental Study of Corrugated Tubes Under Lateral Loading

2010 ◽  
Author(s):  
A. Eyvazian ◽  
M. Shakeri ◽  
M. Zarei Mahmoudabadi
Keyword(s):  
Experimental Tests ◽  
Absorption Characteristic ◽  
Lateral Compression ◽  
Lateral Direction ◽  
Static Tests ◽  
Crushing Force ◽  
Innovative Solution ◽  
Energy Absorbers ◽  
Energy Absorbing ◽  
The Impact

The protection of structures under impact loading often necessitates the need for energy absorbers; devices designed to absorb the impact energy in a controlled manner and hence, protect the structure under consideration. Thin-walled tubes are widely used as energy absorbers in various vehicles and moving parts. The objective of the present study is to investigate the energy absorption characteristic of tubes with corrugations in different geometries, in lateral direction. In order to produce corrugations, an innovative solution is introduced. Corrugations can be very easily generated on the surface of cylindrical aluminum tubes by stamping method. Corrugations with different wavelengths and amplitudes can be produced by this method. Experimental tests are conducted to study the effect of changing corrugation geometry (type and amplitude). Quasi-static tests are carried out whose results for lateral compression show that tubes with corrugation have a higher mean crushing force and this force is directly proportional to number of corrugations and their amplitude. Moreover, it is observed that corrugated tubes can absorb approximately four times more energy than tubes without corrugations, in the same size and weight. Finally, considering the experimental tests, corrugated tubes are shown to be more effective in lateral direction as an energy absorber, and they also exhibit desirable force-deflection responses which are important in the design of energy absorbing devices.

scholarly journals A study on COVID-19 transmission dynamics: stability analysis of SEIR model with Hopf bifurcation for effect of time delay

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
M. Radha ◽  
S. Balamuralitharan
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Transmission Rate ◽  
Real Life ◽  
Least Square Method ◽  
Least Square ◽  
Transmission Dynamics ◽  
Seir Model ◽  
Sensitivity Indices ◽  
The Impact

Abstract This paper deals with a general SEIR model for the coronavirus disease 2019 (COVID-19) with the effect of time delay proposed. We get the stability theorems for the disease-free equilibrium and provide adequate situations of the COVID-19 transmission dynamics equilibrium of present and absent cases. A Hopf bifurcation parameter τ concerns the effects of time delay and we demonstrate that the locally asymptotic stability holds for the present equilibrium. The reproduction number is brief in less than or greater than one, and it effectively is controlling the COVID-19 infection outbreak and subsequently reveals insight into understanding the patterns of the flare-up. We have included eight parameters and the least square method allows us to estimate the initial values for the Indian COVID-19 pandemic from real-life data. It is one of India’s current pandemic models that have been studied for the time being. This Covid19 SEIR model can apply with or without delay to all country’s current pandemic region, after estimating parameter values from their data. The sensitivity of seven parameters has also been explored. The paper also examines the impact of immune response time delay and the importance of determining essential parameters such as the transmission rate using sensitivity indices analysis. The numerical experiment is calculated to illustrate the theoretical results.

scholarly journals The impact of time delay on the transmission of Japanese encephalitis model without vaccination

2021 ◽  
Author(s):  
Vinod Baniya ◽  
Ram Keval
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Japanese Encephalitis ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Normal Structure ◽  
Infected Mosquito ◽  
Human Populations ◽  
Delay Model ◽  
The Impact

In the manuscript, the influence of time delay on the transmission of Japanese encephalitis model without vaccination model has been studied. The time delay is because of the existence of an incubation period during which the JE virus reproduces enough in the mosquitoes with the goal that it tends to be transmitted by the mosquitoes to people. The motivation behind this manuscript is to assess the influence of the time delay it takes to infect susceptible human populations after interacting with infected mosquitoes. The steady-states and the threshold value R0 of the delay model were resolved. This value assists with setting up the circumstance that ensure the asymptotic stability of relating  equilibrium points. Utilizing the delay as a bifurcation parameter, we built up the circumstance for the presence of a ”Hopf bifurcation”. Moreover, we infer an express equation to decide the stability and direction of ”Hopf bifurcation” at endemic equilibrium by using center manifold theory and normal structure strategy. It has been seen that delay plays a vital role in stability exchanging. In addition, larger values of virus transmission rate from an infected mosquito to  susceptible individuals and the natural mortality of humans of a model affect the existence of ”Hopf bifurcation”. Finally, to understand some analytical outcomes, the delay framework is simulated numerically.

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