Dynamics of a Free Play Type of Nonlinearity System Under Deterministic and Random Excitations

1995 ◽  
Author(s):  
Ismail I. Orabi
Keyword(s):  
Gaussian White Noise ◽  
Harmonic Excitation ◽  
Free Play ◽  
Nonlinear Structures ◽  
Single Degree Of Freedom ◽  
Linearization Technique ◽  
Single Degree ◽  
Nonlinear Responses ◽  
Digital Simulations ◽  
Good Agreement

Abstract The dynamics of nonlinear structures under harmonic and random excitations is studied. The harmonic excitation is modeled by periodic loadings while the random excitations is modeled by segments of stationary Gaussian white noise processes. Transient responses of a single-degree-of-freedom model is studied to illustrate the characteristic of nonlinear responses. A free play type of nonlinearity is considered. The effects of nonlinearities on the overall dynamics of structure is investigated. The linearization technique is used to calculate the response statistics. To check the accuracy of the linearization technique, the results are compared with Monte-Carlo digital simulations and good agreement are observed.

scholarly journals Development of n-DoF Preloaded Structures for Impact Mitigation in Cobots

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
S. Seriani ◽  
P. Gallina ◽  
L. Scalera ◽  
V. Lughi
Keyword(s):  
Three Dimensional ◽  
Impact Loads ◽  
Single Degree Of Freedom ◽  
Impact Mitigation ◽  
Single Degree ◽  
Future Developments ◽  
Core Issue ◽  
Comprehensive Framework ◽  
Peculiar Behavior ◽  
Good Agreement

A core issue in collaborative robotics is that of impact mitigation, especially when collisions happen with operators. Passively compliant structures can be used as the frame of the cobot, although, usually, they are implemented by means of a single-degree-of-freedom (DoF). However, n-DoF preloaded structures offer a number of advantages in terms of flexibility in designing their behavior. In this work, we propose a comprehensive framework for classifying n-DoF preloaded structures, including one-, two-, and three-dimensional arrays. Furthermore, we investigate the implications of the peculiar behavior of these structures—which present sharp stiff-to-compliant transitions at design-determined load thresholds—on impact mitigation. To this regard, an analytical n-DoF dynamic model was developed and numerically implemented. A prototype of a 10DoF structure was tested under static and impact loads, showing a very good agreement with the model. Future developments will see the application of n-DoF preloaded structures to impact-mitigation on cobots and in the field of mobile robots, as well as to the field of novel architected materials.

scholarly journals Blast Simulator Testing of Structures: Methodology and Validation

2011 ◽  
Vol 18 (4) ◽  
pp. 579-592 ◽  
Author(s):  
T. Rodriguez-Nikl ◽  
G.A. Hegemier ◽  
F. Seible
Keyword(s):  
High Speed ◽  
Field Tests ◽  
Detailed Model ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Explosive Materials ◽  
Blast Effects ◽  
Resistance Function ◽  
The University ◽  
Good Agreement

The blast simulator at the University of California, San Diego is a unique tool for conducting full-scale testing of blast effects on structures without the use of explosive materials. This blast simulator uses high speed hydraulic actuators to launch specially designed modules toward the specimen, thereby imparting impulse in a blast-like manner. This method of testing offers numerous advantages over field tests with actual explosives, including cost, turn-around time, repeatability, and a clear view of the progression of damage in the specimen. The viability of this method is established by comparing results obtained in the blast simulator with results obtained with actual explosives. The process by which the impulse is imparted to the specimen is then described by a detailed model based on the equivalent single degree of freedom method. Impulse calculated by the model is found to be in good agreement with the experimentally recorded values. Calculated impulse is found to be relatively insensitive to assumptions made about the specimen's resistance function (often not well known before a test) implying that the model can be used with confidence in designing an experimental study.

The Dynamic Response of a System With Preloaded Compliance

1988 ◽  
Vol 110 (3) ◽  
pp. 278-283 ◽  
Author(s):  
S. W. Shaw ◽  
P. C. Tung
Keyword(s):  
Dynamic Response ◽  
Piecewise Linear ◽  
Harmonic Excitation ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Linear Features ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Periodic ◽  
Model Equations

We consider the dynamic response of a single degree of freedom system with preloaded, or “setup,” springs. This is a simple model for systems where preload is used to suppress vibrations. The springs are taken to be linear and harmonic excitation is applied; damping is assumed to be of linear viscous type. Using the piecewise linear features of the model equations we determine the amplitude and stability of the periodic responses and carry out a bifurcation analysis for these motions. Some parameter regions which contain no simple stable periodic motions are shown to possess chaotic motions.

scholarly journals Shock Performance of Different Semiactive Damping Strategies

2010 ◽  
Vol 8 (02) ◽  
Author(s):  
D. F. Ledezma-Ramirez ◽  
N. Ferguson ◽  
M. Brennan
Keyword(s):  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Harmonic Vibration ◽  
Passive Stiffness ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Variable Damping ◽  
Stiffness And Damping ◽  
Shock Pulses

The problem of shock generated vibration is presented and analyzed. The fundamental background is explained based on the analysis of a single degree-of-freedom model with passive stiffness and damping. The advantages and limitations of such a shock mount are discussed. Afterwards, different semi-active strategies involving variable damping are presented. These strategies have been used for harmonic excitation but it is not clear how they will perform during a shock. This paper analyzes the different variable damping schemes already used for harmonic vibration in order to find any potential advantages or issues for theoretical shock pulses.

Periodic Motions in a Single-Degree-of-Freedom System Under Both an Aerodynamic Force and a Harmonic Excitation

2019 ◽  
Author(s):  
Bo Yu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Aerodynamic Force ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Period

Abstract In this paper, a semi-analytical approach was used to predict periodic motions in a single-degree-of-freedom system under both aerodynamic force and harmonic excitation. Using the implicit mappings, the predictions of period-1 motions varying with excitation frequency are obtained. Stability of the period-1 motions are discussed, and the corresponding eigenvalues of period-1 motions are presented. Finally, numerical simulations of stable period-1 motions are illustrated.

Passive, Transitioning Mounts for Simultaneous Shock and Vibration Isolation

2012 ◽  
Author(s):  
Emad Shahid ◽  
Al Ferri
Keyword(s):  
Vibration Isolation ◽  
Sliding Friction ◽  
Design Strategy ◽  
Harmonic Excitation ◽  
Viscous Damper ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
In Series ◽  
Velocity Input ◽  
Tradeoff Curve

A design strategy to simultaneously mitigate the effects of both shock and vibration is introduced. The proposed isolation mount is a passive, transitioning mount and consists of sliding friction elements in series connection with springs and dampers. A linear and a displacement dependent viscous damper are considered, while linear, hardening and softening springs, are considered. The isolation mount’s response is determined by numerical simulation. For a single-degree-of-freedom system, the tradeoff curve for a half-sine velocity input is determined, as is the nonlinear transmissibility for harmonic excitation. The method is found to achieve satisfactory isolation against shock events as well as persistent harmonic inputs. The suggested mount configuration was also found to have good performance against a ‘combined’ input with both resonant and transient content.

FOLDING OF A TYPE OF DEPLOYABLE ORIGAMI STRUCTURES

2012 ◽  
Vol 12 (06) ◽  
pp. 1250054 ◽  
Author(s):  
YAO CHEN ◽  
JIAN FENG
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Jacobian Matrix ◽  
Element Analysis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Element Simulation ◽  
Rigid Plane ◽  
Configuration Changes ◽  
Good Agreement

Some types of rigid origami possess specific geometric properties. They have a single degree of freedom, and can experience large configuration changes without cut or being stretched. This study presents a numerical analysis and finite element simulation on the folding behavior of deployable origami structures. Equivalent pin-jointed structures were established, and a Jacobian matrix was formed to constrain the internal mechanisms in each rigid plane. A nonlinear iterative algorithm was formulated for predicting the folding behavior. The augmented compatibility matrix was updated at each step for correcting the incompatible strains. Subsequently, finite element simulations on the deployable origami structures were carried out. Specifically, two types of generalized deployable origami structures combined by basic parts were studied, with some key parameters considered. It is concluded that, compared with the theoretical values, both the solutions obtained by the nonlinear algorithm and finite element analysis are in good agreement, the proposed method can well predict the folding behavior of the origami structures, and the error of the numerical results increases with the increase of the primary angle.

A First-Passage Approximation in Random Vibration

1971 ◽  
Vol 38 (1) ◽  
pp. 143-147 ◽  
Author(s):  
Ronald L. Racicot ◽  
Fred Moses
Keyword(s):  
Random Vibration ◽  
Numerical Technique ◽  
Joint Probability ◽  
Poisson Processes ◽  
Joint Probability Distribution ◽  
First Passage ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Average Size ◽  
Good Agreement

A numerical technique is described for computing approximate first-passage probabilities for single-degree-of-freedom systems. It is applicable to cases where the joint probability distribution of response at two times can be found. From these distributions, the average size of a clump of consecutive failure crossings is computed. Results are compared to previously published simulation first-passage probabilities and good agreement is found. Examples illustrate applications to Gaussian and filtered Poisson processes.

scholarly journals Sliding-vibrating responses of elastic structures

1988 ◽  
Vol 21 (3) ◽  
pp. 190-197
Author(s):  
Yu-An Fu
Keyword(s):  
Rigid Body ◽  
Harmonic Excitation ◽  
Body Motion ◽  
Shake Table ◽  
Reciprocating Motion ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Analytical Expressions ◽  
Vibrating Response

By using simulated friction forces, analytical expressions were derived from the sliding-vibrating response of a single degree of freedom system under harmonic excitation or the "disadvantageous period reciprocating motion", taking the mass of the sliding base into consideration. Some of the general laws were studied and some new characteristics determined which had previously been ignored by assuming rigid body motion. The analysis methods adopted in this paper have been confirmed in comparison with the results of model tests on a shake table.

Categorization of Dynamic Loading Into Force-Controlled Loading and Displacement-Controlled Loading

2018 ◽  
Author(s):  
Ichiro Tamura ◽  
Shinichi Matsuura ◽  
Ryuya Shimazu ◽  
Koji Kimura
Keyword(s):  
Dynamic Loading ◽  
Kinematic Hardening ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Skeleton Curve ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Dynamic Loadings ◽  
Restoring Forces

To investigate the behavior of inelastic single-degree-of-freedom systems, the maximum restoring forces and maximum deformations of the systems due to a harmonic excitation are calculated and drawn as a diagram. These systems have restoring forces characterized by bilinear skeleton curve of the kinematic hardening type. The diagram shows two types of characteristics, and the dynamic loadings can be categorized into force-controlled loading and displacement-controlled loading.

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