An analytical model for the vibration of a composite plate containing an embedded periodic shape memory alloy structure

Abstract This paper explores the integration of a periodic repeating arrangement of shape memory alloy (SMAs) within a composite plate, with a view to active control of the vibrations of the plate by means of a controllable activation strategy for the SMA elements. The benefits of this configuration are that ‘antagonistic’ operation of SMAs on the plate allows the significantly longer cooling time constant of previously activated elements to be shortened by means of active elements working against them during that phase. This concept dramatically shortens the cooling time constant and brings it into the same order of magnitude of the heating phase. The paper examines the mathematical modelling of such a plate, and offers an approximate analytical solution by means of a hybrid WKB–Galerkin method. The antagonistic operation of the system is represented mathematically by terms in which the stiffness and damping are both time dependent. Therefore the equation of motion contains terms with time variant coefficients and is impossible to solve without recourse to specialised methods. Comparisons with numerical methods are given and it is shown that good similarity can be obtained for judicious choice of practical values for the time variant stiffness and damping functions.

[1]  Zdeněk P. Bažant,et al.  Three-dimensional constitutive model for shape memory alloys based on microplane model , 2002 .

[2]  Matthew P. Cartmell,et al.  One-dimensional shape memory alloy models for use with reinforced composite structures , 2003 .

[3]  D. Lagoudas,et al.  A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy , 1996 .

[4]  Victor Birman,et al.  Shape Memory Elastic Foundation and Supports for Passive Vibration Control of Composite Plates , 2008 .

[5]  Hyo Jik Lee,et al.  A simulation study on the thermal buckling behavior of laminated composite shells with embedded shape memory alloy (SMA) wires , 1999 .

[6]  Matthew P. Cartmell,et al.  A sensitivity analysis of the dynamic performance of a composite plate with shape memory alloy wires , 2003 .

[7]  C. M. Wayman,et al.  Shape-Memory Materials , 2018 .

[8]  W. Ostachowicz,et al.  Statics and dynamics of composite structures with embedded shape memory alloys , 2001 .

[9]  L. Brinson,et al.  A three-dimensional phenomenological model for martensite reorientation in shape memory alloys , 2007 .

[10]  Donatello Cardone,et al.  Mechanical behaviour of shape memory alloys for seismic applications 1. Martensite and austenite NiTi bars subjected to torsion , 2001 .

[11]  Craig A. Rogers,et al.  One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials , 1990 .

[12]  J. Loughlan,et al.  Enhancing the post-buckling response of a composite panel structure utilising shape memory alloy actuators – a smart structural concept , 2001 .

[13]  L. Demasi.  ∞6 Mixed plate theories based on the Generalized Unified Formulation. Part IV: Zig-zag theories , 2009 .

[14]  J. Loughlan,et al.  Adaptive post-buckling response of carbon fibre composite plates employing SMA actuators , 1997 .

[15]  A. W. Lees,et al.  Proposals for Controlling Flexible Rotor Vibrations by Means of an Antagonistic SMA/Composite Smart Bearing , 2006 .

[16]  O. Ganilova,et al.  A hybrid WKB Galerkin method applied to a piezoelectric sandwich plate vibration problem considering shear force effects , 2008 .

[17]  E. Carrera.  On the use of the Murakami's zig-zag function in the modeling of layered plates and shells , 2004 .

[18]  Toshiaki Natsuki,et al.  Mechanical properties of composites filled with SMA particles and short fibers , 2007 .

[19]  Matthew P. Cartmell,et al.  Dynamics of Multilayered Composite Plates With Shape Memory Alloy Wires , 2003 .

[20]  Guoqiang Li,et al.  Analysis of an adhesively bonded single-strap joint integrated with shape memory alloy (SMA) reinforced layers , 2007 .