scholarly journals A numerical survey of nonlinear dynamical responses of discrete pantographic beams

2021 ◽  
Author(s):  
Emilio Turco
Keyword(s):  
Dynamical Behavior ◽  
Integration Scheme ◽  
Dynamical Response ◽  
Static Case ◽  
Equilibrium Equations ◽  
Response Curves ◽  
Nonlinear Dynamical ◽  
Nonlinear Equilibrium ◽  
Standard Integration ◽  
Inertia Forces

AbstractMaterials and structures based on pantographic cells exhibit interesting mechanical peculiarities. They have been studied prevalently in the static case, both in linear and nonlinear regime. When the dynamical behavior is considered, available literature is scarce probably for the intrinsic difficulties in the solution of this kind of problems. The aim of this work is to contribute to filling of this gap by addressing the dynamical response of pantographic beams. Starting from a simple spring mechanical model for pantographic beams, the nonlinear equilibrium problem is formulated directly for such a discrete system also considering inertia forces. Successively, the solution of the system of equilibrium equations is sought by means of a stepwise strategy based on a non-standard integration scheme. Here, only harmonic excitations are considered and, for large displacements, frequency-response curves are thoroughly discussed for some significant cases.

scholarly journals Bistable dynamics beyond rotating wave approximation

2014 ◽  
Vol 23 (02) ◽  
pp. 1450019 ◽  
Author(s):  
Y. A. Sharaby ◽  
S. Lynch ◽  
A. Joshi ◽  
S. S. Hassan
Keyword(s):  
Ring Cavity ◽  
Dynamical Behavior ◽  
Single Mode ◽  
Unstable State ◽  
Nonlinear Dynamical ◽  
Rotating Wave Approximation ◽  
Wave Approximation ◽  
Atomic Medium ◽  
Bistable Dynamics ◽  
Rotating Wave

In this paper, we investigate the nonlinear dynamical behavior of dispersive optical bistability (OB) for a homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity without invoking the rotating wave approximation (RWA). The periodic oscillations (self-pulsing) and chaos of the unstable state of the OB curve is affected by the counter rotating terms through the appearance of spikes during its periods. Further, the bifurcation with atomic detuning, within and outside the RWA, shows that the OB system can be converted from a chaotic system to self-pulsing system and vice-versa.

Second Order Averaging Study of an Autoparametric System

1993 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Dynamical Behavior ◽  
Period Doubling ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Pitchfork Bifurcation ◽  
Second Order ◽  
System Response ◽  
Response Curves ◽  
Vibratory System ◽  
First Order

Abstract The autoparametric vibratory system consisting of a primary spring-mass-dashpot system coupled with a damped simple pendulum serves as an useful example of two degree-of-freedom nonlinear systems that exhibit complex dynamic behavior. It exhibits 1:2 internal resonance and amplitude modulated chaos under harmonic forcing conditions. First-order averaging studies of this system using AUTO and KAOS have yielded useful information about the amplitude dynamics of this system. Response curves of the system indicate saturation and the pitchfork bifurcation sets are found to be symmetric. The period-doubling route to chaotic solutions is observed. However questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid cannot be answered by a first-order study. Some observed dynamical behavior, like saturation, may not persist when higher-order nonlinear effects are taken into account. Second-order averaging of the system, using Mathematica (Maeder, 1991; Wolfram, 1991) is undertaken to address these questions. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. The dynamics of the system is found to be very sensitive to damping, with extremely complicated behavior arising for low values of damping. For large ε second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response.

Instability of Discrete Pseudo-Conservative Structural Systems

1991 ◽  
Vol 44 (11S) ◽  
pp. S194-S198 ◽  
Author(s):  
Anibal E. Mirasso ◽  
Luis A. Godoy
Keyword(s):  
Classical System ◽  
Potential Energy Function ◽  
Structural Systems ◽  
Equilibrium Path ◽  
Equilibrium Equations ◽  
Total Potential ◽  
Approximate Form ◽  
Nonlinear Equilibrium ◽  
Mechanical Models ◽  
New Formulation

Critical and postcritical states of pseudo-conservative discrete structural systems are studied by means of a new formulation leading to a classification of critical states and to an approximate form of the postcritical equilibrium path. The nonlinear equilibrium equations are derived from the total potential energy function of a classical system, but with the addition of at least one control parameter. The follower force effect is thus included by nonlinear constraints to the equilibrium equation. The nonlinear equations are solved by perturbation techniques. Finally the theory is applied to investigate the instability of some simple mechanical models.

scholarly journals Modeling the Biomechanical Influence of Epilaryngeal Stricture on the Vocal Folds: A Low-Dimensional Model of Vocal–Ventricular Fold Coupling

2014 ◽  
Vol 57 (2) ◽  
Author(s):  
Scott R. Moisik ◽  
John H. Esling
Keyword(s):  
Dynamical Behavior ◽  
Model Performance ◽  
Vocal Folds ◽  
Element Model ◽  
Dynamical Response ◽  
Lumped Element ◽  
Glottal Stop ◽  
Lumped Element Model ◽  
Low Dimensional ◽  
Ventricular Folds

Purpose Physiological and phonetic studies suggest that, at moderate levels of epilaryngeal stricture, the ventricular folds impinge upon the vocal folds and influence their dynamical behavior, which is thought to be responsible for constricted laryngeal sounds. In this work, the authors examine this hypothesis through biomechanical modeling. Method The dynamical response of a low-dimensional, lumped-element model of the vocal folds under the influence of vocal–ventricular fold coupling was evaluated. The model was assessed for F0 and cover-mass phase difference. Case studies of simulations of different constricted phonation types and of glottal stop illustrate various additional aspects of model performance. Results Simulated vocal–ventricular fold coupling lowers F0 and perturbs the mucosal wave. It also appears to reinforce irregular patterns of oscillation, and it can enhance laryngeal closure in glottal stop production. Conclusion The effects of simulated vocal–ventricular fold coupling are consistent with sounds, such as creaky voice, harsh voice, and glottal stop, that have been observed to involve epilaryngeal stricture and apparent contact between the vocal folds and ventricular folds. This supports the view that vocal–ventricular fold coupling is important in the vibratory dynamics of such sounds and, furthermore, suggests that these sounds may intrinsically require epilaryngeal stricture.

NONLINEAR GENERALIZED BEAM THEORY FOR COLD-FORMED STEEL MEMBERS

2003 ◽  
Vol 03 (04) ◽  
pp. 461-490 ◽  
Author(s):  
N. SILVESTRE ◽  
D. CAMOTIM
Keyword(s):  
Numerical Technique ◽  
Beam Theory ◽  
Equilibrium Equations ◽  
Steel Members ◽  
Mode Decomposition ◽  
Nonlinear Equilibrium ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Cold Formed Steel ◽  
Generalized Beam Theory

A geometrically nonlinear Generalized Beam Theory (GBT) is formulated and its application leads to a system of equilibrium equations which are valid in the large deformation range but still retain and take advantage of the unique GBT mode decomposition feature. The proposed GBT formulation, for the elastic post-buckling analysis of isotropic thin-walled members, is able to handle various types of loading and arbitrary initial geometrical imperfections and, in particular, it can be used to perform "exact" or "approximate" (i.e., including only a few deformation modes) analyses. Concerning the solution of the system of GBT nonlinear equilibrium equations, the finite element method (FEM) constitutes the most efficient and versatile numerical technique and, thus, a beam FE is specifically developed for this purpose. The FEM implementation of the GBT post-buckling formulation is reported in some detail and then employed to obtain numerical results, which validate and illustrate the application and capabilities of the theory.

Stable and Unstable Quasiperiodic Oscillations in Robot Dynamics

1993 ◽  
Author(s):  
G. Stépán ◽  
G. Haller
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Time Lag ◽  
Nonlinear Behavior ◽  
Degree Of Freedom ◽  
Robot Dynamics ◽  
Robot Arm ◽  
Delayed Systems ◽  
Nonlinear Dynamical ◽  
Quasiperiodic Oscillations

Abstract Delays in robot control may result in unexpectedly sophisticated nonlinear dynamical behavior. Experiments on force controlled robots frequently show periodic and quasiperiodic oscillations which cannot be explained without including the time lag and/or the sampling time of the system in our models. Delayed systems, even of low degree of freedom, can produce phenomena which are already well understood in the theory of nonlinear dynamical systems but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm. The analytical results show typical nonlinear behavior in the system which may go through a codimension two Hopf bifurcation for an infinite set of parameter values, leading to the creation of two-tori in the phase space. These results give a qualitative explanation for the existence of self-excited quasiperiodic oscillations in the dynamics of force controlled robots.

Generating Fully Bounded Chaotic Attractors

2013 ◽  
pp. 148-153
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

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