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 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. 

scholarly journals Nonlinear Free and Forced Vibration Behavior of Shear-Deformable Composite Beams with Shape Memory Alloy Fibers

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Ren Yongsheng ◽  
Du Chenggang ◽  
Shi Yuyan
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Shear Deformation ◽  
Forced Vibration ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Composite Beams ◽  
Vibration Behavior ◽  
Shear Deformable

The nonlinear free and forced vibration of the composite beams embedded with shape memory alloy (SMA) fibers are investigated based on first-order shear deformation beam theory and the von Kármán type nonlinear strain-displacement equation. A thermomechanical constitutive equation of SMA proposed by Brinson is used to calculate the recovery stress of the constrained SMA fibers. The equations of motion are derived by using Hamilton’s principle. The approximate solution is obtained for vibration analysis of the composite beams based on the Galerkin approach. The parametric study is carried out to display the effect of the actuation temperature, the volume fraction, the initial strain of SMA fibers, and the length-to-thickness ratio. The shear deformation is shown to have a significant contribution to nonlinear vibration behavior of the composite beams with SMA fibers.

Thin Film NiTi Shape Memory Alloy Microactuator With Two-Way Effect

2000 ◽  
Author(s):  
John J. Gill ◽  
Gregory P. Carman
Keyword(s):  
Thin Film ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Frequency Response ◽  
Microelectromechanical Systems ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
Vacuum System ◽  
Niti Shape Memory Alloy ◽  
Maximum Deflection

Abstract Thin film SMA (Shape memory alloy) is a useful material for MEMS (Microelectromechanical Systems) actuator. This is because the thin film has an improved frequency response compared to bulk SMA, high work density, and produces large strain. A novel two-way thin film NiTi (Nickel Titanium) shape memory alloy actuator is presented in this paper. Thin film shape memory alloy is sputter-deposited onto a silicon wafer in an ultra high vacuum system. Transformation temperatures of the NiTi film are determined by measuring the residual stress as a function of temperature. Test results show that the Martensite-Temperature-Finish (Mf) is approximately 60° C, and the Austenite-Temperature-Finish (Af) is 110° C. A free standing NiTi membrane (12 mm × 12 mm and 2.5 μm thick) is fabricated using MEMS technology. We found that a mixture of HF (Hydro Fluoric Acid), HNO3 (Nitric Acid) and DI (Deionized) water with thick photo resist mask works best for the fabrication process. The membrane is hot-shaped into a dome shape. Results indicate that when the temperature of the NiTi film exceeds Af, the NiTi membrane transforms into the trained hot-shape. When the temperature cools down to room temperature, the membrane returns to the initial flat shape. The performance of the SMA micro actuator is characterized with a laser measurement system for deflection vs. input power and frequency response. The maximum deflection of SMA microactuator is 230 μm. The corresponding frequency responses at the maximum deflection are 30 Hz with Copper (Cu) block placed underneath the microactuator and less than 1 Hz when Plexi-glass is placed.

Passive Seismic Control Using Shape Memory Alloy Springs

2006 ◽  
Author(s):  
Yoshitaka Yamashita ◽  
Arata Masuda ◽  
Akira Sone
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Shaking Table ◽  
Scale Model ◽  
Response Analysis ◽  
Acceleration Response ◽  
Restoring Force ◽  
Seismic Control ◽  
Seismic Force ◽  
Sma Spring

In this paper, seismic response analysis is made both experimentally and numerically for a passive isolation device with pseudoelastic shape memory alloy (SMA) spring as a restoring force component. Thanks to the material nonliniarity and the geometrical nonliniarity, the SMA spring used in the device has well-defined softening, or “force limiting”, property that can suppress the acceleration response of the superstructure by limiting the seismic force transmitted from the ground. To illustrate how the presented device can suppress the acceleration response under the prescribed level, shaking table tests of a reduced-scale model of uniaxial isolator are carried out with seismic inputs appropriately scaled both in time and in amplitude. Then, a Preisach model of the SMA spring is constructed for the purpose of design study, and verified by comparing the simulated seismic responses with the experimental ones.

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.

Damping capacity in pseudo-elastic and ferro-elastic shape memory alloy-reinforced hybrid composite beam

2019 ◽  
Vol 38 (10) ◽  
pp. 467-477 ◽  
Author(s):  
Yahya Bayat ◽  
Hamid EkhteraeiToussi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Composite Beam ◽  
Volume Fraction ◽  
Hysteresis Loops ◽  
Beam Theory ◽  
Material Model ◽  
Resonance Phenomenon ◽  
Damping Capacity ◽  
Concentrated Load

Reinforcing a composite beam with shape memory alloy wires may have several benefits such as reduction of buckling risks or elimination of unwanted oscillations. In this paper, the vibration damping of a typical shape memory alloy-reinforced composite or hybrid beam is explored. To formulate the thermo-mechanical behavior of embedded shape memory alloy wires, three-dimensional Panico–Brinson model is employed and tailored to one-dimensional model. This material model can simulate pseudo-elastic and ferro-elastic forms of martensite transformations which occurs in cyclic loadings. Besides, unlike the former studies which rely on classical beam theories, the first-order shear deformation beam theory is used to obtain more accurate estimations of shape memory alloy-wire hysteresis loops and their decaying characteristics. In order to explore the effects of a transient concentrated load applied in the middle of a beam, the governing equations are developed and discretized by differential quadrature–integral quadrature combined method. Incremental time marching solution of the problem is accomplished using the Newmark technique. Results are assessed by comparing with available literature. Considering different types of boundary conditions, the influence of pseudo-elastic and ferro-elastic hysteresis loops on the material damping effects, shape memory alloy volume fraction, and resonance phenomenon is studied in detail.

Nonlinear Free Vibration of Hybrid Composite Moving Beams Embedded with Shape Memory Alloy Fibers

2016 ◽  
Vol 16 (07) ◽  
pp. 1550032 ◽  
Author(s):  
M. R. Ebrahimi ◽  
A. Moeinfar ◽  
M. Shakeri
Keyword(s):  
Shape Memory Alloy ◽  
Free Vibration ◽  
Shape Memory ◽  
Hybrid Composite ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parametric Studies ◽  
The One ◽  
Nonlinear Equations Of Motion

The aim of this paper is to investigate the free vibration of hybrid composite moving beams embedded with shape memory alloy (SMA) fibers. The nonlinear equations of motion are derived based on the Euler–Bernoulli beam theory in conjunction with the von Karman type of nonlinearity in strain–displacement relations via the extended Hamilton principle. Also, the recovery stress induced by the SMA fibers is computed by applying the one-dimensional Brinson model and Reuss scheme. Then, an analytical approach in used to solve the nonlinear equation of motion for the simply supported shape memory alloy hybrid composite (SMAHC) moving beams. Based on the analytical solution, several parametric studies are presented to show the effects of various parameters such as volume fraction, pre-strain in the SMA fibers, temperature rise and velocity on the fundamental frequency of the SMAHC moving beams. Due to the lack of similar results in the specialized literature on the subject of interest, this paper is likely to fill a gap in the state of the art of the related research.

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