# Shock Vibration Control of SDOF Systems with Tubular Linear Eddy Current Dampers
## 6 Conclusions  
This paper reports the dynamic characteristics of a tubular linear eddy current damper and its performance in reducing the transient response of a linear elastic SDOF system when subjected to shock loadings. The mechanical model of the TLECD is represented by the semi-empirical model proposed by [PERSON] [27], which is confirmed by electromagnetic finite element simulation in COMSOL. Response analyses have been carried out under the condition of three different types of shock excitation and various TLECD's mechanical parameters to validate the effectiveness of the TLECD in terms of shock vibration control of structures. The influence of the physical parameters of the TLECD on its mechanical parameters is discussed, and a simplified design flow chart and a design case for mechanical parameters are given. The following conclusions are obtained:  
(1) The dynamic characteristic of the TLECD can be well expressed by [PERSON]'s model, with approximately linearized characteristics in the low-velocity section and a nonlinear feature in the high-velocity section.  
(2) From the transient response analysis, TLECDs have been found effective in decreasing structural response and energy input. A larger maximum damping force and smaller critical relative velocity lead to smaller peak responses and a shorter time to reach peak responses.  
(3) Under the condition of achieving the target maximum displacement, there is an optimal dimensionless critical relative velocity that minimizes the dimensionless maximum damping force and the time of the maximum displacement. In addition, the dynamic characteristics of the system with the ECD subjected to half-cycle sine shock and the initial peak triangular shock are similar when the dimensionless critical relative velocity \(\gamma\) is between 0.2 and 1.  
(4) At the same maximum displacement and maximum damper force, the SDOF system with the TLECD takes more time to reach the maximum displacement and less time to reach one-third of the maximum displacement than the SDOF system with the FVD, and the former absorbs a little less energy from the external loading than the latter.  
(5) The SRS of the SDOF system and the design flowchart for the TLECD can be considered as a ready reference for the shock vibration control of an SDOF system with the nonlinear TLECD and the estimation of dimensions and costs of TLECDs.  
Overall, this paper focuses on the numerical analysis of TLECDs for SDOF systems. The conclusions are summarized according to the numerical calculations. In order to further confirm these conclusions, experimental tests are needed for the mechanical performance of TLECDs and their shock vibration control performance with structures. Moreover, further studies, such as applying TLECDs to MDOF systems and investigating the thermal effect of the TLECD, will be conducted in the future.  
Figure 14: Force-velocity relationship of the design example.  
Author Contributions: Y.P.: Validation, Investigation, Data Curation, Writing--Original Draft, Writing--Review & Editing, Visualization. Z.H.: Methodology, Formal analysis, Validation, Visualization, Writing--Reviewing and Editing. H.Z.: Validation, Investigation, Data Curation, Writing--Reviewing and Editing. X.H.: Conceptualization, Methodology, Formal analysis, Validation, Writing--Reviewing and Editing. Y.X.: Validation, Data Curation, Writing--Reviewing and Editing. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 51808210.  
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The authors declare no conflict of interest.