Floating raft vibration isolation systems in the ships or submarines have the requirement of low weight and small volume. To reduce the weight of floating raft vibration isolation systems and improve its vibration suppression effect，nonlinear energy sink cell （NES cell） is applied to the structural optimization of the floating raft vibration isolation system. NES cells are placed on all the substructures of the floating raft system. The mechanical model of the floating raft system with four degrees of freedom and the vibration damping system with NES cell are established. The modal analysis of the floating raft system is carried out. The approximate analytical expression of steady-state response for nonlinear system is derived by Harmonic balance method （HBM） and verified by Runge-Kutta （RK）. The vibration suppression effect under the different total weight and NES cell number is compared by force transitivity response，and the influence of the NES cell number and total weight of the system for the 1st-order mode is analyzed. The results show that NES cell can effectively improve the vibration suppression efficiency of the floating raft system for all the modes while reducing the total weight of the system and realize the structural optimization of the floating raft system effectively.

A novel vibration method，the master-slave distributed vibration test method，was proposed. Aiming at its control requirements，an online waveform replication technique for vibration loads was developed and an integrative prototype system with measuring and controlling functions was constructed. Therein，a signal processing method of frame segmentation and reconstruction was proposed for solve the problem that time waveform replication for long-duration continuous vibration loads. A method for dynamic transfer function estimation based on sample database construction and weighted average was proposed to reduce the influence of nonlinear property on control precision. A spectrum correction method was introduced to improve the frequency domain control accuracy. A test with 1 master vibrator and 2 slave vibrators was performed using the developed online vibration load replication control technique，and the results show that the technique has a high replication precision in both time domain and frequency domain，has a subsecond overall delay time，and has a subpercent overall root-mean-square error. The technique can provide a key technique for supporting online distributed vibration tests.

The time-varying mesh stiffness is a core parameter of gear systems，and the mesh stiffness identification is of great significance for the dynamic analysis and condition monitoring of gear transmission systems. Since it is difficult to directly measure the mesh stiffness，it is necessary to develop a data-driven time-varying mesh stiffness identification method. To deal with this problem，an alternating state-parameter optimization method is proposed to identify the time-varying mesh stiffness of gear systems. The Fourier series with the fundamental frequency of the mesh frequency is constructed to characterize the mesh stiffness. Furthermore，a Reproducing Kernel Hilbert Space （RKHS）-based de-noise method is further proposed to estimate the system state and parameter. The system state and stiffness parameter are alternately optimized with the joint constrains of dynamic model and data to realize the time-varying mesh stiffness identification of gear transmission systems. The simulation and experimental studies validate the effectiveness of the new mesh stiffness identification method for gear systems.

The dynamic method for identifying axial force is grounded in vibration theory，making the vibration equation of a bar member crucial for accurate axial force estimation. Traditionally，the Timoshenko beam is derived from the equilibrium of transverse forces and moments. In this paper，an energy-based approach is applied to derive a new vibration equation for the Timoshenko beam under axial loading. The Ressiner energy equation for a Timoshenko beam，incorporating displacement，stress and axial force，is established using a condensation hypothesis from an energy perspective. The motion equation and stress equilibrium are calculated using the extremum principle，leading to a new free vibration equation for the Timoshenko beam under axial force. Compared to classical textbooks，the proposed dynamics equation includes two additional terms related to axial forces and shear effects. The new equation is validated through numerical simulations and laboratory experiments to identify the axial force in bar members. The results demonstrate that the proposed equation significantly improves the accuracy of axial force identification，confirming its correctness and applicability.

The study of the influence of potential well parameters on the output of a nonlinear energy harvester system is conducive to the design of the high-performance energy harvester system. Meanwhile，the stochastic resonance phenomenon in the corresponding electromechanical coupling dynamics model of the energy harvester system can be used to enhance the characteristics of weak faults，so as to effectively identify weak faults. This paper proposes a decoupled saddle-point-degradation bistable potential function，and the electromechanical dynamic model is introduced. The bifurcation diagram under different excitation amplitudes is obtained to discuss the effect of the barrier width and the barrier height on the responses （periodic response and chaotic response）. According to the methods of the Poincaré map，the frequency spectrum analysis，and the Lyapunov exponent，the periodic response and the chaotic response are examined at a fixed excitation amplitude，which is consistent with that obtained from the bifurcation diagram. Based on the electromechanical dynamic model perturbed by the random noise，the stochastic-resonance-based method is proposed for fault diagnosis，which achieves the enhancement of the simulated and experimental bearing fault characteristics.

Sparse regularization has been proven to be effective in addressing the ill-posed problem in moving force identification （MFI）. However，existing methods often neglect frequency characteristic disparities between static and dynamic components in moving loads，thereby limiting the identification accuracy. Therefore，an MFI method integrating response prior information and weighted dictionary is proposed. A linear relationship between vehicle-induced bridge responses and moving vehicle loads is established in bridge-vehicle system. Once frequency domain analysis is separately performed on bending moment and acceleration responses，the obtained frequency prior information is then employed to construct weighted dictionaries that correspond to both static and dynamic load components. Subsequently，the static and dynamic components of moving loads are individually solved by alternating direction method of multipliers （ADMM）. The effectiveness of proposed method is demonstrated through numerical simulations on a real bridge，and a series of MFI experiments are conducted in laboratory. Results show that the weighted dictionaries considering response prior information significantly improves the accuracy of force identification and enhance its robustness to noise.

The problem of load identification denotes identifying loads based on the measurement of structural responses，which is the inverse problem in structural dynamics. A load identification method based on time-delay neural network is proposed in this paper，and numerical examples based on simulation and experiments are provided to show that the method overperforms normal back-propagation neural network in accuracy of identification. Additionally，statistic pooling is introduced on the basis of the method，and it is proved that the method performs well in noisy environment compared with BP neural networks. based on the load identification methods mentioned above，a sensor placement optimization based on particle swarm optimization algorithm is proposed，and the optimal sensor placement is able to reduce the error of identification by 90% compared with the random sensor placements，meanwhile the minimum spacing of installation among sensors is also ensured during the optimization.

Aircraft often operate in complex and variable dynamic load environment，and dynamic load localization is the primary problem that needs to be solved in this field. This paper focuses on the dynamic load localization requirements of common and prone to abnormal vibrations in aircraft structures. Combining deep neural network，a rapid dynamic load localization method for aircraft structures is developed. By using Long Short-Term Memory （LSTM） neural network，the inverse implicit function model which can accurately describe the corresponding relationship between the dynamic load location and vibration response of the structure is constructed. A dynamic load localization method based on the LSTM neural network classification model is proposed. A simplified finite element model of the entire aircraft structure is established to simulate several typical dynamic load conditions that the aircraft may encounter during actual flight. The noise resistance and robustness of the established deep neural network are also studied. The simulation results show that the proposed method can accurately identify the location of dynamic loads under various load conditions，and can still maintain high locating accuracy under the measurement noise level of 10 dB and the parameter perturbation of 2.8%.

Spinning cylindrical shells are critical components in practical engineering structures. The boundary conditions at the shell ends are diverse and significantly influence the vibration characteristics of the shell. To study these characteristics under various boundary conditions，a dynamic model of the spinning cylindrical shell is established using Lagrange equations and Novozhilov’s shell theory. The mathematical description of the boundary conditions for the cylindrical shell is combined with the discretized displacement functions，which are constructed based on a linear combination of Chebyshev polynomials. These functions satisfy the boundary conditions and are independent of the cylindrical shell's parameters. The vibration characteristics of stationary cylindrical shells are determined by solving the eigenvalue problems，revealing the influence of rotary inertia on the vibration characteristics. The applicability of different shell theories with respect to various geometrical parameters of the shell is discussed. Additionally，circumferential wave-dependent mode functions are identified and used to compute the natural frequencies of shell modes with the zero circumferential waves，as well as the travelling waves of the spinning cylindrical shell under different boundary conditions. The impact of structural parameters on the natural frequencies of the travelling waves is also analyzed.

Direct measurement of dynamic loads on engineering structures is challenging due to environmental constraints. Therefore，the indirect identification or reconstruction of dynamic loads，using dynamic response information，has emerged as a highly effective method. Over decades，dynamic load identification has evolved，resulting in a series of valid solutions. This paper begins by reviewing the research history and main achievements of dynamic load identification methods. It provides a systematic exposition of typical frequency domain and time domain methods，as well as dynamic load identification methods which are based on various approaches such as function fitting，regularization strategies，Bayesian frameworks，and data-driven techniques. The advantages and disadvantages ，as well as application scope of each method，are also discussed. Additionally，this paper summarizes common issues in the load identification process，including uncertainties in structural parameters and input conditions. Identifying the position of dynamic loads is also a crucial aspect of the dynamic load identification problem. This paper analyzes the methods currently available for position identification. This paper delves into the engineering applications of dynamic load identification methods and analyzes the limitations of current methods. Considering the current challenges in the field of dynamic load identification and the increasing demands in practical engineering applications，the paper anticipates the technical difficulties that need to be addressed. It also discusses potential future development directions and key areas in dynamic load identification.