# Thermal Buckling and Vibration Analysis of SMA Hybrid Composite Sandwich Beams
## 1 Introduction  
Today, sandwich structures are largely applied in many industrial applications, primarily in aerospace, marine, transportation, and civil applications due to their special properties, including lightweight, high stiffness, strength, and damping capability. Sandwich structures typically consist of two external layers and an internal core. The layer materials are usually made of metals [1], composites [2], or fiber-metal-laminate [3], whereas the core material includes foam [4], honeycomb [5], or Functionally-Graded materials (FGMs) [6]. The introduction of Shape Memory Alloys (SMAs) within the top/bottom layers is an efficient way to improve the sandwich properties. Intelligent materials such as SMAs, have some unique properties, such as a large recoverable strain field, together with a high flexibility shape memory effect and pseudo-elasticity [7]. On the other hand, a large recovery strain field and a certain flexibility of the SMAs for different load histories, temperatures, and stresses can be obtained for tunable thermal and mechanical properties [8]. In recent decades, different works from literature have shown an increased interest in the buckling and post-buckling behavior of composite plates, shells, and beams embedding SMAs [9; 10; 11; 12]. [PERSON] and [PERSON] [14] used a higher order shear deformation theory (HSDT) to study the buckling response of composite plates subjected to a uniform temperature distribution throughout the thickness. [PERSON] and [PERSON] [15] focused on an optimized buckling response of rectangular and skew composite plates in thermal environments by embedding different quantities of SMA wires. The authors applied the First Order Shear Deformation Theory (FSDT) and used a Generalized Differential Quadrature (GDQ) method to solve the governing equations of the problem. The Von Karman nonlineardisplacement-strain relationships were used by [PERSON] et al. [16] to investigate the thermal post buckling of shape memory alloy hybrid composite shell panels. In such work, it was shown that the snapping phenomenon of shells can be prevented by embedding SMA wires in a composite structure. Buckling and post-buckling phenomena are particularly important for structural beams in thermal conditions [17; 18]. One well-known method to increase the thermal buckling resistance of sandwich beams relies on the introduction of SMAs into these structures [19]. [PERSON] [20] studied the variation of the critical buckling temperature of cross-ply beams with various boundary conditions. The author also reported the effect of some parameters such as the length-to-thickness ratio and thermal expansion coefficients ratio on the critical buckling temperature. [PERSON] and [PERSON] [21] applied a Layer-Wise Theory (LWT) to explore the thermal buckling and post-buckling behavior of laminated composite beams reinforced with SMA wires. The authors studied the effect of some parameters on the mechanical response, including the symmetric and antisymmetric layouts, as well as the influence of the thickness/span ratio, SMA pre-strain, and volume fraction. The free vibration of composite structures is another important aspect to investigate, as extensively found in literature [8; 22; 23]. [PERSON] et al. [24] performed a vibration analysis of the composite plates embedded with shape memory alloy fibers by combining the FSDT basics with the Von Karman strain-displacement relations. Based on their results, the plates increased their stiffness for an increased volume fraction and initial strain of the SMA fibers; the authors also checked for the optimal design of fiber angle, stacking sequence, volume fraction, and initial strain of the SMAs. Similarly, [PERSON] and [PERSON] [25] studied the free vibration of SMA-embedded laminated composite shell panels, including spherical and cylindrical shell panels with TD material properties. The authors used a HSDT combined with the principle of virtual work and nonlinear von Karman strain displacement relations to handle the problem. [PERSON] et al.