تجزیه و تحلیل حساسیت عملکرد دینامیکی یک صفحه کامپوزیت همراه با سیم های آلیاژی حافظه دار

In this paper the dynamic performance of a multi-layered composite plate with embedded shape memory alloy (SMA) wires has been investigated in terms of the changes in its relative fundamental natural frequency. A sensitivity analysis has been carried out on the influence of various geometrical parameters and material properties on the plate’s dynamic performance, as well as the influence of the form of boundary condition. The use of the active property tuning (APT) method and the active strain energy tuning (ASET) method has also been discussed within the paper. The finite element method has been used for the analysis, and a new element has been exploited for modelling multi-layered composite plates. It has been found that the dynamic performance of the multi-layered composite plate with embedded SMA wires strongly depends on the plate geometry and the form of boundary condition, however, the dynamics can be successfully controlled and influenced by an optimal selection of the geometrical parameters and material properties.

Over the past few decades various types of composite material have been extensively used in many fields of civil and mechanical engineering. This can be particularly clearly seen in the case of the civil and military aircraft industries, where numerous structural elements made of composite materials are now in common use [1], [2] and [3]. Because of their extensive use the guarantee of high durability and long-term performance of structural elements made of composite materials is a very important issue. One of many methods used to achieve this objective could be the integration of composite materials with another class of high performance material, such as one of the various alloys exhibiting the shape memory effect [4]. It has been found that under certain conditions selected material properties of such alloys can be precisely controlled; for example their Young’s modulus [4] and [5] and damping coefficient [4], [6] and [7]. Moreover, the shape memory alloys (SMAs) also possess two unique abilities for recovering large non-linear strains [4], and for generation of large internal forces [8] during their activation. These arise from the superelastic and shape memory effects, respectively. Due to their exceptional properties components made of SMAs in the form of wires, strips, or tubes, integrated within, or bonded to, the composite material element offer great capabilities for active control of the static and dynamic behaviour of the overall integrated structures [8] and [9]. The principal static and dynamic characteristics of structural components made from composite materials can be manipulated and enhanced by the introduction of embedded SMA wires or strips. The results presented in the literature report changes in deflection and shape [10], [11], [12], [13], [14], [15], [16] and [17], natural frequencies [17], [18], [19], [20] and [21], forced vibration amplitude [22] and [23], buckling load [20], [24], [25] and [26], and damping behaviour [27] and [28] in such installations. However, despite the fact that the use of SMA components has been extensively exploited in the literature, as shown above, very little information can be found regarding sensitivity studies in which the different influences on the performance of the composite structural elements with the embedded SMA components are considered. In many studies SMA-embedded composite components are characterised by very low thickness-to-length ratios [10], [13], [15], [18], [21], [24] and [27]. Although such structures can have very good performance characteristics their engineering applications are very limited due to their low stiffness and low critical loads. Many researchers have considered structural composite elements with embedded SMA components for which the ratio of the composite material Young’s modulus to the Young’s modulus of the SMA components is very low. As a consequence generally high performance of these structural elements has been widely reported [10], [14], [15], [18] and [21]. Furthermore, in certain cases the performance of such structures is enhanced by the high assumed relative volume fraction of the SMA components [10] and [15], or by the very high level of recovery stresses arising from activation of the SMA components [24]. As can be seen from the above literature review the performance of various composite structural elements with embedded SMA components is determined by a number of different factors. One such factor is the ratio of the SMA Young’s modulus to that of the composite material reinforcing fibres (glass, kevlar, graphite, boron, etc.), as well as the relative volume fraction of the SMA components. In addition the relative volume fraction of the reinforcing fibres, the structural geometry, the location and the orientation of the SMA components within the host structures, temperature, moisture, etc. are also of great importance. It should be emphasised here that the high relative volume fraction of the SMA components is in many cases not desirable. Since the SMA components are temperature activated to undergo their phase transformation considerable amounts of heat can be released at that time. Although this could easily result in the softening of the composite material, the effect can be avoided by appropriate selection of the SMA transformation temperatures, which can be adjusted accurately over a wide range (refer to Shape Memory Application, Inc. at http://www.sma-inc.com). In this paper certain results have been presented for a sensitivity analysis of the dynamic performance of a multi-layered composite plate with embedded SMA wires. The performance criterion is based on calculating relative changes in the fundamental natural frequency of the plate. For this analysis the finite element method has been chosen and a new finite element for modelling multi-layered composite plates has been applied. The use of the active property tuning (APT) method and the active strain energy tuning method (ASET) [9], [15], [17] and [21] have also been investigated in this work. The influences of the plate geometry on the relative fundamental frequency, as well as various material properties and the form of boundary condition, have been all investigated. It should be emphasised here that the results presented for the APT method have been obtained under the assumption that activation of the SMA wires leads only to changes in the plate’s stiffness matrix, due to changes in the Young’s modulus of the SMA wires. In the case of the ASET method the in-plane loads produced by recovery stresses resulting from the activation of the SMA wires have also been included within the plate’s geometrical stiffness matrix [19] and [20]. Selected properties of the SMA wires, as well as appropriate values of recovery stress levels have been taken from Dynalloy, Inc. and are summarised in Table 1––for more details see http://www.dynaloy.com. Table 1. Selected properties of the Flexinol™ actuator wires Property Value Wire diameter 0.025–0.4 mm Recovery stress 135.5–180 MPa Wire resistancea 1780–7.87 Ω/m Contraction 4% Activation currentb 20–2750 mA Contraction timeb 1 s Off time 0.06–10 s a For martensitic phase. b At room temperature. Table options It should also be noted that in this study, thermal and hygrothermal effects have not been taken into account due to limited data available in the literature as required for such a complex analysis. However, it should also be emphasised that these effects could have a great influence on dynamic performance in specific conditions, and cannot therefore be arbitrarily neglected.

Greater dynamic performance of the plate (i.e. greater relative changes in the fundamental natural frequency of the plate, for example) has generally been observed for the ASET method than for the APT method in all the cases considered in the paper. It has been shown that the number of constraints imposed by different types of boundary conditions has a major influence on the plate performance. The changes in the relative fundamental natural frequency of the plate observed are maximum for the cantilever plate, and minimum for the fully clamped plate. It has also been found that for different types of boundary condition the plate performance is a function of the plate dimensions. In the case of the APT method for the cantilever plate and the two-sided-clamped plate the plate performance is greater for a longer and narrower plate. For the simply-supported plate and the fully clamped plate the observed behaviour is opposite to this, and the plate performance increases for a wider and shorter plate. It can be summarised that in all the cases considered, regardless of the type of boundary condition, optimal performance is observed for beam-like structures. Contrary to this, when the dimensions of the plate are large the performance observed is strongly reduced. In the case of the ASET method in general, high plate performance can be observed for both a wider and longer plate. However, it should be emphasised here that this behaviour can additionally be influenced by changes in the orientation angle of the SMA wires. Furthermore, plate performance can be enhanced by an appropriate selection of the orientation angle of the SMA wires, as well as by the orientation angle of the reinforcing fibres. In addition to this, even greater plate performance can be achieved when various materials for the plate reinforcement, and various compositions, are considered, thereby influencing the stiffness ratio of the active layers with the SMA wires to the reinforcing layers. Also the location of the SMA wires within the plate is very important for plate performance. It has been found that the relative fundamental natural frequency of the plate increases when the SMA wires are located closer to the most extreme outer layers of the plate. This effect can also be manipulated by changes in the relative volume fraction of the SMA wires. It has also been clearly shown that the same, or greater, plate performance can be obtained in the case of smaller volume fractions of the SMA wires in those cases, when the SMA wires are located closer to the most extreme outer layers of the plate. Finally, it should be emphasised that for higher modes of plate vibration, as well as for other types of boundary conditions not considered in this paper, very similar results can be obtained, but an analogous sensitivity analysis must be repeated in order guarantee the correctness of such results.