Nonlinear Vibration of Beams Using a Form-Function Approximation

1975 ◽  
Vol 42 (1) ◽  
pp. 209-214 ◽  
Author(s):  
C. L. Lou ◽  
D. L. Sikarskie
Keyword(s):  
Function Approximation ◽  
Unknown Parameter ◽  
Nonlinear Response ◽  
System Behavior ◽  
Form Parameter ◽  
System Parameters ◽  
Forcing Function ◽  
Buckled Beam ◽  
Form Function ◽  
Insight Into

The nonlinear response and stability of a vibrating, buckled beam is analyzed using a form-function approximation. Such an approximation differs from the usual linear series approximations in that the unknown parameter appears nonlinearly. This new approximation has two major advantages. Since all harmonics (in both space and time) are represented, the dominant harmonics are “singled out” in the solution, thus making it very efficient. The form-function representation also permits an insight into system behavior not found in other methods. Knowledge of the form parameter shows explicitly how the form of the response changes with the system parameters, e.g., forcing function magnitude and frequency, material constants, etc.

Sequences of Global Bifurcations and the Related Outcomes after Crisis of the Resonant Attractor in a Nonlinear Oscillator

1997 ◽  
Vol 07 (11) ◽  
pp. 2437-2457 ◽  
Author(s):  
W. Szemplińska-Stupnicka ◽  
E. Tyrkiel
Keyword(s):  
Nonlinear Oscillator ◽  
Duffing Oscillator ◽  
Nonlinear Resonance ◽  
Basins Of Attraction ◽  
Global Bifurcations ◽  
System Behavior ◽  
Coexisting Attractors ◽  
System Parameters

The problem of the system behavior after annihilation of the resonant attractor in the region of the nonlinear resonance hysteresis is considered. The sequences of global bifurcations, in connection with the associated metamorphoses of basins of attraction of coexisting attractors, are examined. The study allows one to reveal the mechanism that governs the phenomenon of the post crisis ensuing transient trajectory to settle onto one or another remote attractor. The problem is studied in detail for the twin-well potential Duffing oscillator. The boundary which splits the considered region of system parameters into two subdomains, where the outcome is unique or the two outcomes are possible, is defined.

Suction-Controlled Detachment of Mushroom-Shaped Adhesive Structures

2021 ◽  
Vol 88 (3) ◽  
Author(s):  
Marcela Areyano ◽  
Jamie A. Booth ◽  
Dane Brouwer ◽  
Luke F. Gockowski ◽  
Megan T. Valentine ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Critical Stress ◽  
Design Space ◽  
Asymptotic Result ◽  
Length Scale ◽  
System Parameters ◽  
Trapped Air ◽  
Attachment Strength ◽  
Remote Stress ◽  
Insight Into

Abstract Experimental evidence suggests that suction may play a role in the attachment strength of mushroom-tipped adhesive structures, but the system parameters which control this effect are not well established. A fracture mechanics-based model is introduced to determine the critical stress for defect propagation at the interface in the presence of trapped air. These results are compared with an experimental investigation of millimeter-scale elastomeric structures. These structures are found to exhibit a greater increase in strength due to suction than is typical in the literature, as they have a large tip diameter relative to the stalk. The model additionally provides insight into differences in expected behavior across the design space of mushroom-shaped structures. For example, the model reveals that the suction contribution is length-scale dependent. It is enhanced for larger structures due to increased volume change, and thus the attainment of lower pressures, inside of the defect. This scaling effect is shown to be less pronounced if the tip is made wider relative to the stalk. An asymptotic result is also provided in the limit that the defect is far outside of the stalk, showing that the critical stress is lower by a factor of 1/2 than the result often used in the literature to estimate the effect of suction. This discrepancy arises as the latter considers only the balance of remote stress and pressure inside the defect and neglects the influence of compressive tractions outside of the defect.

Effects of shape of the neck of classical acoustical resonators on the sound absorption quality for large amplitudes: Experimental results

2020 ◽  
Vol 27 (2) ◽  
pp. 169-181
Author(s):  
Emmanuel Gourdon ◽  
Alireza Ture Savadkoohi ◽  
Bertrand Cauvin
Keyword(s):  
Sound Absorption ◽  
Nonlinear Response ◽  
Experimental Results ◽  
Resonant Frequencies ◽  
Helmholtz Resonators ◽  
Forcing Function ◽  
Amplitude Dependency ◽  
Broadband Frequency

This article presents some experimental results on Helmholtz resonators for large sound amplitudes with two general geometries of their necks: the resonators with classical (cylindrical) and quadratic nonlinear necks. Obtained results for large amplitudes show accelerated amplitude dependency of resonant frequencies of the resonators with modified shape of the neck compared to classical ones. This nonlinear response can be used as a passive controller system with nonlinear restoring forcing function for having broadband frequency absorption.

Creating Faultable Network Models of Complex Engineered Systems

2014 ◽  
Author(s):  
Brandon M. Haley ◽  
Andy Dong ◽  
Irem Y. Tumer
Keyword(s):  
Failure Analysis ◽  
Network Models ◽  
System Behavior ◽  
Levels Of Abstraction ◽  
Complex Engineered Systems ◽  
System A ◽  
Topological Configuration ◽  
Engineered Systems ◽  
Types Of Faults ◽  
Insight Into

This paper presents a new methodology for modeling complex engineered systems using complex networks for failure analysis. Many existing network-based modeling approaches for complex engineered systems “abstract away” the functional details to focus on the topological configuration of the system and thus do not provide adequate insight into system behavior. To model failures more adequately, we present two types of network representations of a complex engineered system: a uni-partite architectural network and a weighted bi-partite behavioral network. Whereas the architectural network describes physical inter-connectivity, the behavioral network represents the interaction between functions and variables in mathematical models of the system and its constituent components. The levels of abstraction for nodes in both network types affords the evaluation of failures involving morphology or behavior, respectively. The approach is shown with respect to a drivetrain model. Architectural and behavioral networks are compared with respect to the types of faults that can be described. We conclude with considerations that should be employed when modeling complex engineered systems as networks for the purpose of failure analysis.

scholarly journals Snap-jaw morphology is specialized for high-speed power amplification in the Dracula ant, Mystrium camillae

2018 ◽  
Vol 5 (12) ◽  
pp. 181447 ◽  
Author(s):  
Fredrick J. Larabee ◽  
Adrian A. Smith ◽  
Andrew V. Suarez
Keyword(s):  
High Speed ◽  
Muscle Power ◽  
Element Analysis ◽  
Predator Prey ◽  
Mantis Shrimp ◽  
Power Amplification ◽  
Form Function ◽  
Function Relationship ◽  
Relationship Of ◽  
Insight Into

What is the limit of animal speed and what mechanisms produce the fastest movements? More than natural history trivia, the answer provides key insight into the form–function relationship of musculoskeletal movement and can determine the outcome of predator–prey interactions. The fastest known animal movements belong to arthropods, including trap-jaw ants, mantis shrimp and froghoppers, that have incorporated latches and springs into their appendage systems to overcome the limits of muscle power. In contrast to these examples of power amplification, where separate structures act as latch and spring to accelerate an appendage, some animals use a ‘snap-jaw’ mechanism that incorporates the latch and spring on the accelerating appendage itself. We examined the kinematics and functional morphology of the Dracula ant, Mystrium camillae , who use a snap-jaw mechanism to quickly slide their mandibles across each other similar to a finger snap. Kinematic analysis of high-speed video revealed that snap-jaw ant mandibles complete their strike in as little as 23 µsec and reach peak velocities of 90 m s −1 , making them the fastest known animal appendage. Finite-element analysis demonstrated that snap-jaw mandibles were less stiff than biting non-power-amplified mandibles, consistent with their use as a flexible spring. These results extend our understanding of animal speed and demonstrate how small changes in morphology can result in dramatic differences in performance.

Hydrostatic Transmission for Wind Turbines: An Old Concept, New Dynamics

2013 ◽  
Author(s):  
Johannes Schmitz ◽  
Milos Vukovic ◽  
Hubertus Murrenhoff
Keyword(s):  
Wind Turbines ◽  
Mobile Applications ◽  
Test Bench ◽  
System Behavior ◽  
Hydrostatic Transmission ◽  
System Parameters ◽  
Standard Application ◽  
Mobile Machinery ◽  
Drive Systems ◽  
Theoretical Results

Hydrostatic drives are commonly used in mobile machinery. A new application for this technology is the renewable energy sector, especially wind power. Despite using the same basic components the dynamics of these new drive systems are somewhat different compared to those used in mobile applications. In order to design an appropriate control system for a wind turbine it is necessary to understand these differences and how they affect the system. In this paper, the system behavior of a hydrostatic transmission for wind turbines is compared to commonly used hydrostatic drives in mobile machinery. The analysis begins by explaining that the characteristics of the loading acting on a turbine are fundamentally different to the load torque present in a standard application. Using mathematical models of both systems these differences are highlighted and discussed with special reference to how changes in system parameters can affect stability and lead to non-minimum phase behavior. These theoretical results are validated using measurements of a 1 MW hydrostatic transmission installed on a test bench.

Methods of chaos and self-organization in psychophysiology

10.12737/3394 ◽  
2014 ◽  
Vol 3 (1) ◽  
pp. 13-28
Author(s):  
Поскина ◽  
T. Poskina ◽  
Филатова ◽  
D. Filatova ◽  
Филатов ◽  
...  
Keyword(s):  
Phase Space ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Self Organization ◽  
Deterministic Approach ◽  
System Behavior ◽  
System Parameters ◽  
A Value ◽  
Identification Theory

. All the H. Haken’s postulates (1970-2013) emphasize deterministic approach and level a value of trajectory of behavior of biological dynamic system in phase space of states. The significance of the latter theory is hard to overestimate, because according to phase space of states the new identification theory is being created and behavioral descriptions of biological dynamic systems are given. This new theory is based on measures of biological dynamic system parameters in phase space of states and does not need any concrete equations, it can be based on detection of quasi-attractors’ parameters of biological dynamic system behavior in phase space of states and characters are quasi-attractor parameters.

Empirical Analysis Using Advanced Similarity Methods

2002 ◽  
Author(s):  
John J. Wood ◽  
Kristin L. Wood ◽  
Wade O. Troxell
Keyword(s):  
Heat Transfer ◽  
Solid Mechanics ◽  
Large Range ◽  
System Parameters ◽  
Analysis Techniques ◽  
Domain Of Applicability ◽  
Development Cycle ◽  
Material Tests ◽  
Insight Into ◽  
Parameters Of Interest

Traditional dimensional analysis techniques for predicting the performance characteristics of a product can be greatly improved in both accuracy and domain of applicability by the infusion of empirical data, derived from material tests, into the equations that characterize the system parameters of interest. Advanced similarity methods are investigated which overcome the constraints associated with the traditional methods and provide increased analysis capability and improved insight into the phenomenon governing the problem. Such capability greatly increases the design toolbox available to product developers, across a large range of scale and application. It also significantly enhances a developer’s choices for prototype portioning during a development cycle. Solid mechanics and heat transfer applications are used to illustrate the basic utility of the methods.

A Complex-Systems Approach to Organizations

2000 ◽  
Vol 9 (2) ◽  
pp. 69-74 ◽  
Author(s):  
Daniel J. Svyantek ◽  
Linda L. Brown
Keyword(s):  
Complex Systems ◽  
Organizational Behavior ◽  
Systems Approach ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
System Behavior ◽  
Physical Sciences ◽  
Systems Research ◽  
Context Specific ◽  
Insight Into

The physical sciences have developed new theories of nonlinear behavior of complex systems. Defining characteristics of complex systems include (a) being composed of many variables that interact strongly to determine system behavior, (b) sensitivity to initial conditions, and (c) stability across time. Two complex-system concepts, phase spaces and attractors, provide insight into the evolution of system behavior and make prediction of future behavior possible. It is proposed that complex-systems research has application to the study of organizations and social behavior. Organizational attractors exist and seem to be both sensitive to initial conditions and stable. The discussion of concepts from complex systems, and their application to organizations, provides insight into how organizational research should be conducted. If organizations are assumed to exhibit nonlinear behavior, more historical, longitudinal, and qualitative research methods should be used to provide context-specific descriptions of organizational behavior.

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