# Slope Deflection Method in Nonlocal Axially Functionally Graded Tapered Beams
## 1 Introduction
In the studies conducted by the researchers, notably in the last few decades, it has been observed that the resistance of axially graded beams to buckling and dynamic behavior is better than that of isotropic beams. Researchers analyzed the vibration behavior of AFGM beams using a variation iteration approach [17]. The buckling behavior of a composite beam subjected to an axially varying load type was investigated using the Ritz method [18]. A group of researchers investigated the buckling and vibration behavior of axially graded GPL composite beams using the Ritz method. In this context, the mechanical behavior of Timoshenko beams for five different load types was examined and, at the end of the study, it was revealed that the grading pattern depends not only on the buckling load, but also on the grading type of the load (AVLs) [19]. The natural frequencies of a rotating AFGM beam are investigated within the scope of nonlocal elasticity theory [20]. At the end of the study, it was seen that the grading parameter has a significant effect on the free vibration behavior of the beams. Static analysis of an AFGM beam is numerically solved [21]. The mechanical behavior of axially graded metal-ceramic microbeams is studied with the help of a higher-order theory [22]. The vibration character of an AFGM beam reinforced by CNTs was investigated using a differential approximation method. The study revealed that the frequency value is very sensitive to the volume fraction of CNTs [23]. The vibration behavior of AFGM beams reinforced with GPLs has been investigated within the context of [PERSON]'s higher-order deformation theory [24]. The natural frequency values of AFGM beams reinforced with GPLs have been investigated in previous studies [25]. Many structural elements are exposed to mechanical effects such as bending, buckling, torsion, vibration, and thermal change due to external conditions. In order to minimize such effects, the geometry and specific properties of the building elements used should be thoroughly analyzed. The buckling behavior of sandwich beams subjected to axially variable load has been demonstrated by a series of studies [26]. The dynamic response of a laminated composite beam under axially varying loads (AVLs) is studied with the help of a higher-order deformation theory [27]. The effect of porosity shape on the buckling and free vibration behavior of a functionally graded beam was investigated [28]. The buckling and dynamic characteristics of porous beams reinforced with GPLs were investigated, and it was reported that porosity shape and axially varying loads have a sensitive effect on these behaviors [29]. A new approach is proposed for the free vibration behavior of a non-uniform AFGM beam [30]. The modal behavior of a three-dimensional FGM beam is obtained using the finite element method [31]. The natural frequencies of the exponential FGM beams are presented with an analytical solution method [32]. The free vibration behavior of AFGM beams under different boundary conditions has been demonstrated in studies [33]. Functionally graded materials were first introduced by a group of researchers in the Sendai region of Japan and have attracted the interest of researchers [34]. With their unique physical and mechanical properties, FGMs have significant potential in the field of mechanics in the analysis of building materials. Previous studies have demonstrated the mechanical behavior of FGM structures such as bending, buckling, vibration, and thermal stress. Investigations have clearly demonstrated the analysis of FGM structures under different loading conditions within many studies. In the study presented here, the subject was investigated with a different approach related to the work of the researchers and briefly discussed [35]. A study conducted by early researchers demonstrated the elasticity solution of Euler-Bernoulli beams made of FGM subjected to a transverse load [36].