The unexpectedly small coefficient of restitution of a two-degree-of-freedom mass-spring system and its implications

2016 ◽  
Vol 88 ◽  
pp. 1-11 ◽  
Author(s):  
H.H. Ruan ◽  
T.X. Yu
Keyword(s):  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Small Coefficient ◽  
Spring System ◽  
Mass Spring ◽  
Two Degree Of Freedom

The Onset of Chaos in a Two-Degree-of-Freedom Impacting System

1989 ◽  
Vol 56 (1) ◽  
pp. 168-174 ◽  
Author(s):  
Jinsiang Shaw ◽  
Steven W. Shaw
Keyword(s):  
Piecewise Linear ◽  
Global Bifurcation ◽  
Degree Of Freedom ◽  
Chaotic Motions ◽  
Impact Damper ◽  
Onset Of Chaos ◽  
Spring System ◽  
Stability And Bifurcations ◽  
Mass Spring ◽  
Two Degree Of Freedom

The dynamic response of a two-degree-of-freedom impacting system is considered. The system consists of an inverted pendulum with motion limiting stops attached to a sinusoidally excited mass-spring system. Two types of periodic response for this system are analyzed in detail; existence, stability, and bifurcations of these motions can be explicitly computed using a piecewise linear model. The appearance and loss of stability of very long period subharmonics is shown to coincide with a global bifurcation in which chaotic motions, in the form of Smale horseshoes, arise. Application of this device as an impact damper is also briefly discussed.

Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System

2012 ◽  
Author(s):  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Fractal Boundary ◽  
Final State ◽  
Potential Wells ◽  
Mechanical Coupling ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.

scholarly journals Analysis of controllers in suppressing the structural building vibration

2019 ◽  
Vol 15 (1) ◽  
pp. 112-116
Author(s):  
Normaisharah Mamat ◽  
Fitri Yakub ◽  
Sheikh Ahmad Zaki Sheikh Salim
Keyword(s):  
Fuzzy Logic ◽  
Sliding Mode ◽  
Degree Of Freedom ◽  
Control Voltage ◽  
Sliding Mode Controller ◽  
Building Structure ◽  
Matlab Simulink ◽  
Mass Spring ◽  
Earthquake Vibration ◽  
Two Degree Of Freedom

Two degree of freedom (2 DOF) mass spring damper system is used in representing as building structure that dealing with the earthquake vibration. The real analytical input is used to the system that taken at El Centro earthquake that occurred in May 1940 with magnitude of 7.1 Mw. Two types of controller are presented in controlling the vibration which are fuzzy logic (FL) and sliding mode controller (SMC). The paper was aimed to improve the performance of building structure towards vibration based on proposed controllers. Fuzzy logic and sliding mode controller are widely known with robustness character. The mathematical model of two degree of freedom mass spring damper wasis derived to obtain the relationship between mass, spring, damper, force and actuator. Fuzzy logic and sliding mode controllers were implemented to 2 DOF system to suppress the earthquake vibration of two storeys building. Matlab/Simulink was used in designing the system and controllers to present the result of two storeys displacement time response and input control voltage for uncontrolled and controlled system. Then the data of earthquake disturbance was taken based on real seismic occurred at El Centro to make it as the force disturbance input to the building structure system. The controllers proposed would minimize the vibration that used in sample earthquake disturbance data. The simulation result was carried out by using Matlab/Simulink. The simulation result showed sliding mode controller was better controller than fuzzy logic. In specific, by using the controller, earthquake vibration can be reduced.

Variation in the Geometric Interpretation of the Eigenvalue Problem of a Structure Due to Damage

1999 ◽  
Author(s):  
Frederick A. Just Agosto ◽  
Scott L. Hendricks
Keyword(s):  
Eigenvalue Problem ◽  
Convex Hull ◽  
Convex Set ◽  
Conservative System ◽  
Geometric Interpretation ◽  
Degree Of Freedom ◽  
Damage Scenarios ◽  
Spring System ◽  
Two Degree Of Freedom

Abstract This paper studies the behavior of the geometric interpretation of the eigenvalue problem. An arbitrary two degree of freedom structure is modeled as a two mass, two spring system. The damage in the system is represented as a reduction in stiffness and the structure is assumed to be a natural conservative system. The geometric interpretation of the system is an ellipse which is examined under various damage conditions occurring on the structure. It is shown that this representation is a convex set and that damage produces a new set which is the convex hull of the existing condition. These results are graphed for several damage scenarios of the system.

Robust end point tracking control of a two-degree-of-freedom mass-spring-damper system

1994 ◽  
Vol 59 (5) ◽  
pp. 1309-1324
Author(s):  
M. M. BRIDGES ◽  
J. Y. ZHU ◽  
D. M. DAWSON ◽  
Z. QU
Keyword(s):  
Tracking Control ◽  
Degree Of Freedom ◽  
End Point ◽  
Point Tracking ◽  
Mass Spring ◽  
Two Degree Of Freedom

The Design of Modeled Cam Systems—Part I: Dynamic Synthesis and Chart Design For the Two-Degree-of-Freedom Model

1975 ◽  
Vol 97 (4) ◽  
pp. 1175-1180 ◽  
Author(s):  
G. K. Matthew ◽  
D. Tesar
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Dynamic Synthesis ◽  
Wide Range ◽  
Cam Follower ◽  
Chart Design ◽  
Mass Spring ◽  
Two Degree Of Freedom ◽  
Cam Systems ◽  
Made In

An extension of the dynamic synthesis philosophy given earlier [1] for cam follower systems is made in terms of a two-degree-of-freedom model. Three additional dimensionless parameters η, λ, γ for the distribution of mass, spring, and dashpot content are sufficient to describe this more complex system relative to the single degree-of-freedom coefficients. Charts in terms of η, λ, γ are presented to assist in choosing the best set of these values. Finally, “rules of thumb” are given which are applicable to a wide range of mechanical systems.

Modelling the Stiffness Element in the Multi-Degree of Freedom Mass-Spring System

2020 ◽  
Vol 899 ◽  
pp. 3-10
Author(s):  
Abdul Rahim Bahari ◽  
Mohd Azmi Yunus ◽  
Muhamad Norhisham Abdul Rani ◽  
Wan Imaan Izhan Wan Iskandar Mirza ◽  
Mohd Azam Shah Aziz Shah
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Finite Element Modelling ◽  
Degree Of Freedom ◽  
Mode Analysis ◽  
Modal Parameters ◽  
Stiffness Parameter ◽  
Element Modelling ◽  
Spring System ◽  
Mass Spring

Structural dynamics in structural engineering analysis involves the modal parameters (natural frequency, mode shape and damping ratio). The modal parameters of engineering structures is mainly influenced by the damping and stiffness properties. This research paper presents the reliability of CELAS element in the finite element modelling to represent the stiffness parameter. The simplified engineering structure considered in this study is a mass-spring system with multi-degree of freedom. Experimental modal testing is performed using an electro-magnetic vibration shaker as an exciter and an accelerometer to record the natural frequency of the system. HyperMesh normal mode analysis is used to compute the natural frequency of the mass-spring system. The comparative evaluation is performed in order to identify the accuracy of the natural frequencies obtained from the modelling analysis and the measured counterparts. Consequently, it is found that the element CELAS has a good capability to represent as the stiffness parameter in the finite element modelling.

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