scholarly journals Nonlinear Dynamic Analysis of Axially Moving Laminated Shape Memory Alloy Beam with 1:3 Internal Resonance

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4022
Author(s):  
Ying Hao ◽  
Ming Gao ◽  
Yuda Hu ◽  
Yuehua Li
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Axial Velocity ◽  
Nonlinear Dynamic ◽  
Internal Resonance ◽  
Initial Conditions ◽  
Nonlinear Dynamic Analysis ◽  
Time History ◽  
Resonance Amplitude ◽  
Axially Moving

The remarkable properties of shape memory alloys (SMA) are attracting significant technological interest in many fields of science and engineering. In this paper, a nonlinear dynamic analytical model is developed for a laminated beam with a shape memory alloy layer. The model is derived based on Falk’s polynomial model for SMAs combined with Timoshenko beam theory. In addition, axial velocity, axial pressure, temperature, and complex boundary conditions are also parameters that have been taken into account in the creation of the SMA dynamical equation. The nonlinear vibration characteristics of SMA laminated beams under 1:3 internal resonance are studied. The multi-scale method is used to solve the discretized modal equation system, the characteristic equation of vibration modes coupled to each other in the case of internal resonance, as well as the time-history and phase diagrams of the common resonance amplitude in the system are obtained. The effects of axial velocity and initial conditions on the nonlinear internal resonance characteristics of the system were also studied.

Analysis On the In-Plane 2:2:1 Internal Resonance of a Complex Cable-Stayed Bridge System Under External Harmonic Excitation

2021 ◽  
Author(s):  
Houjun Kang ◽  
Tieding Guo ◽  
Weidong Zhu
Keyword(s):  
Nonlinear Dynamic ◽  
Internal Resonance ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Phenomena ◽  
Arch Model ◽  
Shallow Arch ◽  
Cable Stayed Bridge ◽  
Bridge System

Abstract Nonlinear dynamic analysis of a cable-stayed bridge has been a hot topic due to its structural flexibility. Based on integro-partial differential equations of a double-cable-stayed shallow-arch model, in-plane 2:2:1 internal resonance among three first in-plane modes of two cables and a shallow arch under external primary or subharmonic resonance is considered. Galerkin's method and the method of multiple scales are used to derive averaged equations of the cable-stayed bridge system. Nonlinear dynamic behaviours of the system are investigated via the numerical simulation. Results show rich nonlinear phenomena of the cable-stayed bridge system and some new phenomena are observed. Two identical cables that are symmetrically located above the shallow arch can have different dynamic behaviours even when initial conditions of the system are symmetrically given. Two cables with some differences between their parameters can exhibit either softening or hardening characteristics.

scholarly journals Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Bamadev Sahoo ◽  
L. N. Panda ◽  
G. Pohit
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Time History ◽  
Mean Value ◽  
Phase Portraits ◽  
Axially Moving Beam ◽  
Internal Resonances ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability

The nonlinear vibration of a travelling beam subjected to principal parametric resonance in presence of internal resonance is investigated. The beam velocity is assumed to be comprised of a constant mean value along with a harmonically varying component. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times that of first mode; a three-to-one internal resonance is possible. The method of multiple scales (MMS) is directly applied to the governing nonlinear equations and the associated boundary conditions. The nonlinear steady state response along with the stability and bifurcation of the beam is investigated. The system exhibits pitchfork, Hopf, and saddle node bifurcations under different control parameters. The dynamic solutions in the periodic, quasiperiodic, and chaotic forms are captured with the help of time history, phase portraits, and Poincare maps showing the influence of internal resonance.

Free and Forced Response of an Axially Moving String Transporting a Damped Linear Oscillator

1993 ◽  
Author(s):  
W. D. Zhu ◽  
C. D. Mote
Keyword(s):  
Initial Conditions ◽  
Numerical Algorithms ◽  
Time History ◽  
Coupled System ◽  
Interaction Force ◽  
Forced Response ◽  
Linear Oscillator ◽  
Response Analysis ◽  
History Of ◽  
Axially Moving

Abstract The transverse response of a cable transport system, which is modelled as an ideal, constant tension string travelling at constant speed between two supports with a damped linear oscillator attached to it, is predicted for arbitrary initial conditions, external forces and boundary excitations. The exact formulation of the coupled system reduces to a single integral equation of Volterra type governing the interaction force between the string and the payload oscillator. The time history of the interaction force is discontinuous for non-vanishing damping of the oscillator. These discontinuities occur at the instants when transverse waves propagating along the string interact with the oscillator. The discontinuities are treated using the theory of distributions. Numerical algorithms for computing the integrals involving generalized functions and for solution of the delay-integral-differential equation are developed. Response analysis shows a discontinuous velocity history of the payload attachment point. Special conditions leading to absence of the discontinuities above are given.

APPLICATION OF GLOBAL METHODS FOR ANALYZING DYNAMICAL SYSTEMS TO SHIP ROLLING MOTION AND CAPSIZING

1992 ◽  
Vol 02 (01) ◽  
pp. 101-115 ◽  
Author(s):  
JEFFREY M. FALZARANO ◽  
STEVEN W. SHAW ◽  
ARMIN W. TROESCH
Keyword(s):  
Nonlinear Dynamic ◽  
Invariant Manifolds ◽  
Initial Conditions ◽  
Global Analysis ◽  
Relative Size ◽  
Nonlinear Dynamic Analysis ◽  
Periodic Wave ◽  
Industry Standards ◽  
Highly Nonlinear ◽  
Lobe Dynamics

Ship capsizing is a highly nonlinear dynamic phenomenon where global system behavior is dominant. However the industry standards for analysis are limited to linear dynamics or nonlinear statics. Until recently, most nonlinear dynamic analysis relied upon perturbation methods which are severely restricted both with respect to the relative size of the nonlinearity and the region of consideration in the phase space (i.e., they are usually restricted to a small local region about a single equilibrium), or on numerical studies of idealized system models. In this work, recently developed global analysis techniques (e.g., those found in Guckenheimer and Holmes [1986], and Wiggins [1988, 1990]) are used to study transient rolling motions of a small ship which is subjected to a periodic wave excitation. This analysis is based on determining criteria which can predict the qualitative nature of the invariant manifolds which represent the boundary between safe and unsafe initial conditions, and how these depend on system parameters for a specific ship model. Of particular interest is the transition which this boundary makes from regular to fractal, implying a loss in predictability of the ship’s eventual state. In this paper, actual ship data is used in the development of the model and the effects of various ship and wave parameters on this transition are investigated. Finally, lobe dynamics are used to demonstrate how unpredictable capsizing can occur.

scholarly journals Route to Chaos and Bistability Analysis of Quasi-Periodically Excited Three-Leg Supporter with Shape Memory Alloy

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Manisekaran Varadharajan ◽  
Prakash Duraisamy ◽  
Anitha Karthikeyan
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Controller Design ◽  
Initial Conditions ◽  
Basin Of Attraction ◽  
Martensite Phase ◽  
Dynamical Response ◽  
Periodic Excitation ◽  
Strange Nonchaotic Attractors ◽  
Parameter Ranges

In this paper, the effect of quasi-periodic excitation on a three-leg supporter configured with shape memory alloy is investigated. We derived the equation of motion for the system using the supporter configuration and polynomial constitutive model of the shape memory alloys (SMAs) based on Falk model. Two sets of parameters and symmetric initial conditions are used to analyze the system. The system responded with a chaotic attractor and a strange nonchaotic attractor. Coexistence of these attractors is studied and discussed with corresponding phase portrait, bifurcation plot, and cross section of basin of attraction. We confirm the quasi-periodic excitation results with generation of strange nonchaotic attractors as discussed in the literature. The special properties like symmetricity and bistability are revealed and the parameter ranges of existence of such behaviors are discussed. The system is analyzed for different phases and the existence of bistability in martensite phase and transition phase is explained. While the system enters into austenite phase, the bistability behavior vanishes. The results provide insight knowledge into dynamical response of a quasi-periodically excited SMA leg support system and will be useful for design improvements and controller design.

Seismic analysis and evaluation of several recentering braced frame structures

2013 ◽  
Vol 228 (5) ◽  
pp. 781-798 ◽  
Author(s):  
Jong Wan Hu
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Seismic Analysis ◽  
Time History ◽  
Frame Structures ◽  
Braced Frames ◽  
Concentrically Braced Frames ◽  
Economic Point ◽  
Conventional Steel ◽  
Steel Bracing

After earthquakes, residual inter-story drifts greater than 0.5% in buildings may indicate a complete loss of the structure from an economic point of view. Recently, research efforts have been extended to the utilization of superelastic shape memory alloy materials for the smart control systems that can automatically reduce the plastic deformation of the structure subjected to strong seismic loading. Superelastic shape memory alloys are unique metallic alloys that undergo substantial inelastic deformations and regain their original conditions when applied loads are removed, thus alleviating the problem of permanent deformation. The frame structures make the best use of such shape memory alloy’s recentering capability if the superelastic shape memory alloy segments used to replace the steel segments are installed at the part where large deformation is likely to occur. The primary focus of this study is on the seismic response of special steel concentrically braced frames and buckling-restrained braced frames, utilizing superelastic shape memory alloy braces. In order to examine the comparative residual inter-story drift response of both braced frames, 3- and 6-story buildings were designed in accordance with current code specifications, and then nonlinear time-history analyses for two seismic hazard levels were conducted on 2D analytical frame models. The braced frames with superelastic shape memory alloy bracing systems were also compared to those with conventional steel bracing systems. Overall, analysis results show that the superelastic shape memory alloy bracing systems are more effective in decreasing residual inter-story drifts than the conventional steel bracing systems.

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