This study establishes an integrated inverse-analysis framework for partially submerged rectangular thin plates, aimed at enabling non-destructive parameter estimation and impact monitoring in fluid–structure interaction systems. The framework couples closed-form analytical solutions with optimization algorithms to tackle three distinct inverse problems: simultaneous identification of material and geometric properties, impact source localization, and impact force history reconstruction.

regarding parameter identification, the Nelder–Mead simplex algorithm is employed to estimate multiple variables based on measured resonant frequencies. Through convergence tests with varied initial guesses and a rigorous sensitivity analysis, the inverse estimates for Poisson’s ratio, Young’s modulus, density, thickness, and fluid depth demonstrate excellent agreement with experimental measurements. For impact localization, a gradient-descent optimizer combined with the analytical model accurately retrieves impact positions from transient displacement records. Furthermore, a direct inversion scheme reconstructs the time history of impact forces; these reconstructed profiles align consistently with measurements from PVDF sensors.

Experimental validation confirms that the proposed methods exhibit fast convergence, robust localization using sparse sensor layouts, and accurate force recovery even under moderate noise. Consequently, this framework offers a practical and adaptable solution with significant potential for underwater detection, material assessment, and non-destructive testing of submerged structures.

Since the early 21st century, adjusting material parameters to design and control structural responses, and inversely identifying material coefficients from dynamic behavior, has become an important direction in material technology and a basis for structural non-destructive testing. Because vibration characteristics strongly influence acoustic systems, energy harvesters, and structural control, they are essential in aerospace, electronic packaging, energy, and transportation engineering. The Finite Element Method (FEM) remains the predominant tool for analyzing dynamic characteristics due to its capability to model complex geometries and obtain approximate solutions. However, FEM analyses of large structures require significant computational resources. Traditional theoretical approaches, meanwhile, are limited to simple geometries, restricting their practical use. Moreover, FEM often encounters numerical instability when analyzing structures with densely distributed point supports, resulting in poor convergence of frequency and mode shapes. To address this, the present study develops an extended superposition theory for orthotropic structures to derive analytical solutions for dynamic problems with multiple fixed points and mass attachments, demonstrating superior accuracy in predicting resonance frequencies and mode shapes for complex plate geometries.

This study adopts the dual-plane balancing method and introduces particle damping (PD) technology for the correction of eccentric rotors. The primary objective is to balance the inertial forces of the rotor system as effectively as possible while reducing vibration during mechanical rotation. The experimental settings include three operating speeds, three load torques, and three particle diameters. These parameters were varied to observe the dynamic behavior of the rotor system. In accordance with ISO 21940, the balance quality grade was set to G2.5. Two sets of engine rotor systems were sequentially subjected to dynamic balancing corrections. After balancing, the rotors were installed on the test rig for operation. Radial displacement and orbit of the rotor shaft were measured using eddy current displacement sensors, while the dynamic vibration acceleration behavior was monitored with two accelerometers respectively on the two bearings. System dynamic characteristics was quantitatively assessed using metrics such as the maximum radial displacement of the rotor shaft, root mean square (RMS) values, power spectral density (PSD), and response vibration energy. The experimental results demonstrate that the rotor system equipped with particle dampers (PD) exhibits significant vibration suppression compared to the equivalent mass (EM) system under all tested conditions. The study confirms that particle damping not only facilitates effective dynamic balancing correction but also provides substantial vibration reduction, thereby enhancing the stability and overall vibration mitigation performance of rotor systems.