scholarly journals Parametric Random Vibration Analysis of an Axially Moving Laminated Shape Memory Alloy Beam Based on Monte Carlo Simulation

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 562
Author(s):  
Ying Hao ◽  
Ming Gao ◽  
Jiajie Gong
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Random Vibration ◽  
Random Perturbation ◽  
Laminated Composite ◽  
Beam Theory ◽  
Axial Forces ◽  
Axially Moving

The study of the bifurcation, random vibration, chaotic dynamics, and control of laminated composite beams are research hotspots. In this paper, the parametric random vibration of an axially moving laminated shape memory alloy (SMA) beam was investigated. In light of the Timoshenko beam theory and taking into consideration axial motion effects and axial forces, a random dynamic equation of laminated SMA beams was deduced. The Falk’s polynomial constitutive model of SMA was used to simulate the nonlinear random dynamic behavior of the laminated beam. Additionally, the numerical of the probability density function and power spectral density curves was obtained through the Monte Carlo simulation. The results indicated that the large amplitude vibration character of the beam can be caused by random perturbation on axial velocity.

Bending theory for laminated composite cantilever beams with multiple embedded shape memory alloy layers

2019 ◽  
Vol 30 (10) ◽  
pp. 1549-1568 ◽  
Author(s):  
Nguyen Van Viet ◽  
Wael Zaki ◽  
Rehan Umer
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Numerical Solutions ◽  
Phase Distribution ◽  
Solid Phase ◽  
Axial Stress ◽  
Laminated Composite ◽  
Beam Theory ◽  
Cantilever Beams ◽  
Element Analysis

In this article, a new analytical model is proposed for laminated composite cantilever beams consisting of multiple alternating superelastic shape memory alloy and elastic layers. The model is based on the Zaki–Moumni model for shape memory alloys combined with Timoshenko’s beam theory. The Zaki–Moumni model accounts for solid phase transformation as well as detwinning and reorientation of martensite under multiaxial thermomechanical loading conditions. Mathematical formulas are first derived to characterize the evolution of the solid phase structure within the beam with a prescribed load at the tip during loading and unloading. Analytical moment–curvature and shear force–shear strain relations are then obtained following the strength of materials approach. The present work is the first to fully develop the nonlinear expressions of the axial stress in terms of the distance from the neutral plane and to allow the description of the phase distribution in both the longitudinal and the transverse directions in the beam as the load evolves. The proposed model is validated against finite element analysis and high-accuracy numerical solutions. The influence of temperature and the number of shape memory alloy layers on the superelastic behavior of the laminate is also investigated.

Dynamic analysis of a shape memory alloy beam with pseudoelastic behavior

2018 ◽  
Vol 29 (9) ◽  
pp. 1835-1849 ◽  
Author(s):  
Reza Razavilar ◽  
Alireza Fathi ◽  
Morteza Dardel ◽  
Jamal Arghavani Hadi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Frequency Response ◽  
Kinetic Equations ◽  
Elastic Beam ◽  
Beam Theory ◽  
Response Analysis ◽  
Interesting Phenomenon ◽  
Time Saving ◽  
Solution Approach

This article aims at developing a semi-analytic approach for studying the free and forced vibrations of a pseudoelastically behaving shape memory alloy beam. Based on the Euler–Bernoulli beam theory, equations of motion were derived through Hamilton principle, and the obtained partial differential equations were decomposed by applying the Galerkin approach and were solved using Newmark integration method. A three-dimensional phenomenological model of shape memory alloy, which is capable of identifying the main properties of the shape memory alloy, was employed to model the behavior of the shape memory alloy beam. A closed-form numerical algorithm was introduced to simulate the governing kinetic equations of the shape memory alloy beam coupled with transformation strain. The presented novel solution approach is simple, flexible, and time-saving. Stability analysis was performed using phase state trajectories to show dynamic characteristics of the shape memory alloy beam. Due to hysteric behavior of the shape memory alloy, energy dissipation was clearly observed in early stages of the free vibration and within the transient regions of the forced vibration. The numerical results showed that, due to the hysteric induced damping effect, the vibration amplitude is smaller in comparison to an equivalent elastic beam, and consequently, the shape memory alloy beam exhibits more stable behavior at the resonant frequencies. This property can potentially find applications in energy damping applications and vibration control. Moreover, an interesting phenomenon called jumping was observed in the results of frequency response analysis. At jumping frequency, the amplitude of the frequency response has two distinct levels. This jumping frequency is as a result of the hysteresis behavior of the shape memory alloy, and it is a function of the exciting amplitude.

scholarly journals Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads

2020 ◽  
Vol 8 (12) ◽  
pp. 1001
Author(s):  
Wei Lin ◽  
Cheng Su ◽  
Youhong Tang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Time Domain ◽  
Vibration Analysis ◽  
Random Vibration ◽  
Present Approach ◽  
Dynamic Responses ◽  
Wave Loads ◽  
Morison Equation ◽  
Random Vibration Analysis

This paper is devoted to the random vibration analysis of jacket platforms under wave loads using the explicit time-domain approach. The Morison equation is first used to obtain the nonlinear random wave loads, which are discretized into random loading vectors at a series of time instants. The Newmark-β integration scheme is then employed to construct the explicit expressions for dynamic responses of jacket platforms in terms of the random vectors at different time instants. On this basis, Monte Carlo simulation can further be conducted at high efficiency, which not only provides the statistical moments of the random responses, but also gives the mean peak values of responses. Compared with the traditional power spectrum method, nonlinear wave loads can be readily taken into consideration in the present approach rather than using the equivalent linearized Morison equation. Compared with the traditional Monte Carlo simulation, the response statistics can be obtained through the direct use of the explicit expressions of dynamic responses rather than repeatedly solving the equation of motion. An engineering example is analyzed to illustrate the accuracy and efficiency of the present approach.

scholarly journals Modeling the behavior of bilayer shape memory alloy/functionally graded material beams considering asymmetric shape memory alloy response

2019 ◽  
Vol 31 (1) ◽  
pp. 84-99 ◽  
Author(s):  
Nguyen Van Viet ◽  
Wael Zaki ◽  
Rehan Umer ◽  
Quan Wang
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Functionally Graded Material ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Alloy Layer ◽  
Functionally Graded ◽  
Tension And Compression ◽  
Graded Material ◽  
Asymmetric Shape

A new model is proposed to describe the response of laminated composite beams consisting of one shape memory alloy layer and one functionally graded material layer. The model accounts for asymmetry in tension and compression of the shape memory alloy behavior and successfully describes the dependence of the position of the neutral surface on phase transformation within the shape memory alloy and on the load direction. Moreover, the model is capable of describing the response of the composite beam to both loading and unloading cases. In particular, the derivation of the equations governing the behavior of the beam during unloading is presented for the first time. The effect of the functionally graded material gradient index and of temperature on the neutral axis deviation and on the overall behavior of the beam is also discussed. The results obtained using the model are shown to fit three-dimensional finite element simulations of the same beam.

scholarly journals Vibrational Analysis of Composite Beam Embedded with Nitinol Shape Memory Alloy Wires

2018 ◽  
Vol 7 (3.4) ◽  
pp. 143
Author(s):  
Omer Muwafaq Mohmmed Ali ◽  
Rawaa Hamid Mohammed Al-Kalali ◽  
Ethar Mohamed Mahdi Mubarak
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Frequency Response ◽  
Response Curve ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Vibrational Analysis ◽  
Laminated Composite ◽  
Vibration Modes ◽  
Frequency Response Curve

In this paper, laminated composite materials were hybridized with fibers (E-glass) and shape memory alloy wires which considered a smart material. The effect of changing frequency on the (acceleration- frequency) response curve, the damping ratio of the vibration modes, the natural frequencies of the vibration mode, the effect of shape memory alloy wires number on the damping characteristics were studied. Hand lay-up technique was used to prepare the specimens, epoxy resin type was used as a matrix reinforced by fiber, E-glass. The specimens were manufactured by stacking 2 layers of fibers. Shape memory alloy, type Nitinol (nickel-titanium) having a diameter (1 and 2mm), was used to manufacture the specimens by embedding (1,2 and 3) wires into epoxy. Experimentally, the acceleration- frequency response curve was plotted for the vibration modes, this curve was used to measure the natural frequencies of the vibration modes and calculate the damping ratio of the vibration modes. ANSYS 15- APDL was used to determine the mode shape and find the natural frequencies of the vibration modes then compared with the experimental results. The results illustrated that, for all specimens increasing the natural frequency leads to decreasing the damping ratio. Increasing the number of shape memory alloy wires leads to increase the values of the damping ratio of the vibration modes and the natural frequencies of the vibration modes at room temperature. 

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