Shock and Vibration

Volume 2019, Article ID 7080941, 12 pages

https://doi.org/10.1155/2019/7080941

## The Spherical Shock Factor Theory of a FSP with an Underwater Added Structure

^{1}College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China^{2}Naval Research Academy, Beijing 100000, China

Correspondence should be addressed to Guo Jun; nc.ude.uebrh@nuj_oug

Received 11 September 2018; Revised 6 November 2018; Accepted 17 December 2018; Published 13 January 2019

Academic Editor: Chengzhi Shi

Copyright © 2019 Guo Jun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A floating shock platform (FSP) is important experimental equipment for the antishock assessment of large-scale shipborne equipment. Generally speaking, the FSP is a square barge structure with a flat bottom. In order to satisfy the key index of the horizontal-to-vertical ratio of the impact environment, a special added structure is mounted to the bottom of the platform, and the impact environment is more complicated due to the added structure. Therefore, the spherical shock factor theory is proposed to analyze the impact environment, and the validity of the theory is proved by numerical experiments. The results show that the average impact spectrum response of the platform is essentially consistent under the same shock factor. Meanwhile, the spherical shock factor builds a linear relationship between the input parameters and structural response, which is convenient for the prediction of impact response.

#### 1. Introduction

The antishock ability of shipborne equipment on a warship is directly related to a warship’s combat effectiveness and survivability. In order to reduce the possibility of shipborne equipment being damaged after it is subjected to an explosion, countries all over the world attach great importance to the impact resistance ability of shipborne equipment, and corresponding experimental methods have been developed. In terms of standard formulations, German standard BV043/85 [1] stipulates the equipment impact resistance standard from the point of the installation site, and US military standard MIL-S-901D [2] stipulates in detail the equipment impact resistance standard with 8 aspects that include weight, impact level, and category. At the same time, a special experimental device for shipborne equipment impact resistance has been designed by the US Navy. Fluid-structure coupling subject to an underwater explosion is a very complex problem. Therefore, in the study of fluid-structure coupling theory, the transient fluid-structure interaction mechanisms of a three-dimensional spherical shell and a ship’s stiffened plate were studied when subjected to an underwater explosion [3]. Through numerical simulation and experimentation, the fluid characteristics and fluid-structure coupling interactions of damaged ships in the process of submergence are analyzed [4]. Considering the complex input-output relationship of structure impact resistance subject to an underwater explosion, the KSF [5] (keel shock factor) is used to describe the severity of impact. The impact environment of a cylindrical shell subject to an underwater impact was compared and analyzed with different shock factors. It shows that, as a similarity parameter, the new shock factor can effectively reflect the response of an underwater explosion load, and the shock factor also has a certain feasibility for being used to describe the impact environment of a submarine [6]. The improved shock factor indicates that cylindrical and spherical shells have the same impact response [7]. Literature [8] uses the new shock factor to certify the impact environment similarity of a SWATH (small waterplane area twin hull) subject to an underwater explosion. When it comes to impact environment prediction, one author [9] uses the shock factor to predict the impact environment but does not take the difference of the hull and the equipment into account in the installation, and the shock factor has greater limitations itself. According to the type of ship and device, the position and the angle of incidence of the charge, and other factors, one researcher [10] summarizes the empirical formula of the impact environment, but the accuracy of the formula is not strictly checked, and the scope of application is not strictly defined.

In this paper, to satisfy the key index of the impact environment (shock spectrum [11, 12]) that the horizontal-to-vertical ratio of equipment antishock examination in UNDEX, the added structure is added to the bottom of the FSP, while the impact environment of the added structure is not considered. Since the added structure makes the impact environment of the FSP more complicated, the spherical shock factor theory is used to analyze the complex input-output relationship of the IFSP (irregular floating shock platform) impact environment, and the shock factor is used to predict the impact environment of the IFSP, which will guide the design, manufacture, and installation of the equipment.

#### 2. The Spherical Shock Factor Theory of the IFSP

When the structure is subject to UNDEX, for the sake of reflecting the impact environment characteristics, different regularities of shock spectrum change with the parameters such as conditions, geometric conditions, medium, and etcetera. One researcher [6] thoroughly illustrates the shock factors *C*_{1} and *C*_{2}. The keel shock factor *C*_{1} is difficult to use to correctly reflect the underwater explosion impact environment of the cylinder. *C*_{2} is based on the plane wave hypothesis and defined from the angle of energy shielded by the structure, which reflects the similarity of underwater explosion loads in the far field. However, the plane wave assumption cannot be held in the near field. Therefore, in this paper, a new shock factor *C*_{3} is considered to describe the shock energy absorbed by platform, namely, the impact strength received by platform.

##### 2.1. Basic Model and Theoretical Analysis of the Shock Factor

In an explosives experiment, charge weight, explosive distance, and structural characteristics are closely related to the impact environment. In order to study the similarity parameter which reflects the impact environment of the underwater explosion, one can assume that the shock wave is a spherical wave, so the energy born in an explosion can be expressed as follows [13]:where is the chemical energy per unit mass of charge, is the conversion of chemical energy to shock wave energy, and is the charge weight (kg).

In an infinite fluid field, the shock wave energy is considered to be distributed over the entire spherical shock wave surface. Thus, the spherical shock wave energy absorbed by the structure is given bywhere *E*_{s} is the shock wave energy absorbed by structure, *S*_{e} is the projection area of the structure on the wave surface, and *R* is the shortest distance from the charge to the hull.

The shock factor is defined as follows:where *S*_{e} is the area truncated by the solid angle and [14] is the solid angle.

It can be seen from formula (2) that is in proportion to , and the shock factor is the unique variable in the expression. *C*_{3} includes the information of the charge weight, the detonation distance, and the structural geometry characteristics of the platform. Therefore, if *C*_{3} is equal under different conditions when the charge is relative to different positions of the structure, the average shock spectrum response of the structure should be essentially consistent and *C*_{3} should fully reflect the characteristics of the impact environment. According to formula (3), the calculation method of under a spherical wave is explained as follows, using a simple rectangular plate.

Figure 1 shows the physical model and geometric relationship of a simple rectangular plate under a spherical shock wave. The vertex *Z*_{0} of the angle is located on the central axis of the rectangular plate. From the symmetry, we can calculate the angle of the whole rectangle using the quarter of the rectangle in the graph. The length of the rectangle is 2*a*, and the width is 2*b*. The length of the small rectangle is a, and the width is *b*. Arbitrarily taking the area microelement in the small rectangle, the angle of axis *Z* and the line between the area microelement and vertex *Z*_{0} is given by