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

• Published in: Composite structures Vol. 92; no. 1; pp. 39 - 47
• Main Authors: Ganilova, O.A., Cartmell, M.P.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2010; Elsevier
• Subjects: Analytical approach; Antagonistic approach; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Sandwich plate; Shape memory alloy; SMA/composite; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Sandwich plate; Shape memory alloy; Antagonistic approach; Analytical approach; SMA/composite; Cooling; Vibration; Equation of motion; Sandwich structure; Activation; Similarity solution; Modeling; Composite material; Periodic structure; Plate; Heat source; Time varying system; WKB approximation; Active system; Vibration control; Galerkin method; Embedded transducer; Structural analysis
• ISSN: 0263-8223; 1879-1085
• DOI: 10.1016/j.compstruct.2009.06.008

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.