## 1 Introduction  
Acoustic emission (AE) refers to the elastic wave generated by a material as a result of a sudden release of energy (other than heat) from localized sources within a solid. Material degradation related to deformation and fracture development is classified as the primary AE source, and is usually distinguished from secondary AE sources including leak and flow, chemical reactions, and the fabrication process. Crack formation and growth are the most important AE sources in practical non-destructive testing (NDT) investigations. The formation of a new crack face is accompanied by sudden changes in stress and displacement of the material in the vicinity of the crack. Consequently, an elastic wave is generated from the tip of the crack source [1]. AE testing has several unique advantages over other NDT methods, the most significant of which is its real-time monitoring capability; this allows for the detection of damage and degradation in various materials and structures [2; 3; 4; 5; 6]. AE data, refined with appropriate algorithms [7; 8; 9; 10; 11], provide useful information about the source of the emission and progression of crack growth; however, a quantitative interpretation of the AE signal is required to understand the physical processes underlying AE features. Analytical modeling of the AE signal is very important; however, in cylindrical structures, it is difficult to predict the AE generated from an internal crack. The point source, defined as a body force \(\mathbf{f}\) acting at a point, has been adapted as an AE excitation source in seismic displacements, crack formation and fracture, and concentrated vertical step force [12; 13; 14; 15; 16]. In the elastic field, the point source has been treated as a concentrated time harmonic source [17]. Although the AE generated by the point source is important for characterizing real signals observed in practical NDT investigations, theoretic modeling has been limited to spherical geometries with an infinite domain, given that a homogeneous solution is obtainable from the three-dimensional wave equation in spherical coordinates [12; 13; 17]. Most theoretical works on elastic wave propagation in cylindrical coordinates have focused on situations with or without external perturbations [18; 19; 20; 21; 22]. In cylindrical structures, the displacement field has been formulated in terms of one compression (P) potential, and two shear (vertically polarized, SV, and horizontally polarized, SH)potentials, by using the models proposed by [PERSON] and [PERSON] [23] and [PERSON] [24], respectively. The basic difference between the two models is that the compression and shear parts are separated in one model, but not the other. The two models have been examined comprehensively by [PERSON] et al. [18; 19] and [PERSON] et al. [21; 22]. In contrast to cases that are unperturbed or perturbed by external forces, the three potentials should be incorporated along with the concentrated force (CF) exerted by the internal defects [17; 25]. In this study, a \"concentrated force-incorporated potential\" (CFIP) is introduced into the displacement field on the basis of the model proposed by [PERSON] and [PERSON] [23], and the Navier-Lame (NL) equation is constructed (which involves the CF in a transversely isotropic cylinder [TIC]). The CFIP allows the NL equation to be separated into three partial differential equations (PDEs), representing the potentials for P, SV, and SH waves. As an internal defect, the CF has both spatial and temporal properties, represented by the delta function and harmonic oscillation of the point source, respectively. For solving the NL equation, determining [PERSON]'s function for the delta function in cylindrical coordinates is the first task. [PERSON] et al. proposed a Green's function for a closed cylinder, using \"the method of separation of variables\" [26]. We reconstructed [PERSON]'s function for the delta function by applying the continuity and discontinuity principles to the boundary around the point source.