## 1 Introduction  
A plate represents a structural component characterized by its three-dimensional solid geometry with a significantly thin thickness in relation to its other dimensions [1]. In various engineering applications [2; 3; 4], plates serve to offer structural reinforcement and assist in the distribution of loads and stresses throughout the construction [5].  
Over time, plates are subject to extreme events, persistent ambient oscillations, and natural incidents like earthquakes, corrosion, traffic-induced pressures, and material degradation, which cause damage to their microstructure [6]. Cracks can seriously damage structural effectiveness. Even minor damages can disrupt a plate's function, potentially resulting in structural breakdowns [7]. As a result, the consistent evaluation of the plates' performance has become vital to ensure structural robustness and safety [8; 9]. In other words, developing methods for early crack detection and accurate localization has become essential for the continuous operation and longevity of machinery and infrastructure [10].  
Over the years, SHM and methodologies for identifying damage in plate structures have grown prominently in disciplines such as aerospace, civil, and mechanical engineering [11; 12; 13]. Specialists in damage identification have made efforts to develop cost-effective and reliable monitoring methods. Emphasis in their research has been placed on utilizing the DR to determine plate deterioration [14; 15; 16; 17; 18]. This technique is effective for detecting hidden damage in a plate's interior, as evidenced by variations in characteristics such as stiffness detectable through vibration analyses. Additionally, this approach allows for inspections during active operations, reducing the potential downtime and associated expenses [19; 20].  
Numerous scholarly articles and reviews have been written to explain the phenomenon and significance of using the DR to predict the damages in UT plates [19; 21; 22; 23; 24; 25; 26]. Nevertheless, despite the significant progress achieved, a research gap still exists in the context of damage detection in VT plates. Plates characterized by a VT hold substantial significance, as they find application in critical components such as aircraft wings, automobile chassis, vessels, buildings, and more, where the optimization of weight, aerodynamics, and dimensions is essential to meet specific design specifications [27].  
Additionally, the critical review showed that the current research studies and their findings are insufficient in describing how to identify the crack path. Researchers have rarely studied the crack path in beams in the literature [28; 29], and for plates, they only predict the size or potential location of the crack [30; 31; 32; 33; 34; 35]. Identifying the crack path direction is crucial for several reasons such as preventing catastrophic failures because it may move in a direction where the size of the plate is critical, helping engineers to design structures that are more resistant to cracking, and can be used to develop methods for repairing and monitoring structures that have cracked.  
Addressing these research gaps, therefore, represents an opportunity for further investigation. By doing so, a comprehensive understanding of the challenges and prospects associated with monitoring techniques for detecting damage in VT plates and crack paths can be obtained, which will streamline the processes associated with the inspection of engineering structures, thereby reducing the time, effort, and associated costs.  
The subsequent sections of this paper are structured as follows. A general background and the fundamentals of the vibration of plates are presented in Section 2. In Section 3, vibration-based damage identification for cracked plates in forward and inverse research is discussed and reviewed. A general discussion of all sections is presented in Section 4. Conclusions are drawn, and gaps are listed in Section 5.