205

1 INTRODUCTION

The development of a competitive environment

between individual sectors of the transport system

necessitates the development and implementation of

solutions aimed at maintaining the leading position of

railway transport in the segment of total freight

turnover [1-3]. One of the possible solutions to

achieve this goal is the introduction of combined

transport systems, in particular container systems, as

the most common and highly demanded for

international traffic [4, 5].

To increase the efficiency of container

transportation, it is important to create modern

container designs with improved technical properties.

When designing such containers, it is necessary to

take into account the loads that can act on them not

only during transportation by rail, road, air and sea,

but also during transportation as part of combined

trains by train ferries (Figure 1). This type of

combined transport was developed during the

commissioning of the New Silk Road transport

corridor, which connected Ukraine with China and

provided the possibility of transporting combined

transport by train ferries (Figure 2).

Therefore, the issue of creating new container

designs adapted to transportation by train ferries, as

part of combined trains requires further research.

Investigation Into the Dynamic Load of the Container

with Sandwich Panel Walls when Transported by Train

Ferry

G. Vatulia

, J. Gerlici

, A. Lovska

, Ye. Krasnokutskyi

, J. Harušinec

& P. Stastniak

O.M. Beketov National University of Urban Economy, Kharkiv, Ukraine

University of Zilina, Zilina, Slovak Republic

Joint stock company “Ukrainian railway”, Kyiv, Ukraine

ABSTRACT: The article presents the results of the study into the dynamic load of the container during its

transportation by the train ferry. The peculiarity of the container is that its walls are made of sandwich panels.

Such a solution will help to reduce the dynamic loads acting on the container at operating load modes,

including when transported by sea as part of combined trains.

To determine the dynamic loads acting on the container, a mathematical model was build that took into account

the angular displacements around the longitudinal axis of the system “train ferry – flat wagon – container –

freight”. The calculations were made for the train ferry Geroi Plevny. The mathematical model was solved in

MathCad. It was found that the value of acceleration acting on the container of the proposed design during

transportation by sea was 4.3% lower than that acting on the container of a typical design.

The acceleration value obtained, as a component of the dynamic load, was taken into account to determine the

stability coefficient of the container in a typical diagram of its interaction with the flat wagon. The roll angle of

the train ferry, at which the stability of the container placed on the flat wagon is ensured, was also calculated.

The results of the study will contribute to the database of recommendations for the design of modern container

structures and their safe operation in international rail and water traffic.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 18

Number 1

March 2024

DOI: 10.12716/1001.18.01.21

206

а)

Figure 1. Train ferries

a) Heroes of Shipka;

b) Heroes of Sevastopol and Heroes of Odessa

Figure 2. Transportation of containers by train ferries

a) Greifswald;

b) Heroes of Sevastopol

2 ANALYSIS OF RECENT RESEARCH AND

PUBLICATIONS

The issues of improving containers to increase their

efficiency are covered in the scientific works of many

Ukrainian and foreign scientists. For example, in [6]

the authors present the design features of ISO

containers. Possible load diagrams of their bearing

structures in operation are considered. A solution for

possible ways to improve containers to ensure their

durability in operation is proposed.

The study into the load of the 1АА high-capacity

container is covered in [7]. The stress state of the

container was analysed. The zones of concentration of

the highest load of its structure were determined. This

made it possible to formulate requirements aimed at

ensuring the safety of its operation.

At the same time, the authors of these works did

not investigate the strength of the proposed container

structures during transportation by train ferries.

The study of the dynamic load of the container is

carried out in [8]. The authors determined the inertial

loads acting on the container and calculated its

strength under the action of these loads. It was found

that the strength indicators of the container model

under study were provided. At the same time, the

authors did not propose measures to improve the

efficiency of containers.

Publication [9], which highlights the prospects for

the use of removable bodies that operate on the

principle of containers, is of scientific interest. It

presents the requirements that modern removable

body designs must meet. However, the authors did

not discuss the possibility of their transportation by

train ferries as part of combined trains.

The dynamic load of vehicles during

transportation by train ferries is determined in [10].

Mathematical models that allow estimating the

dynamic load acting on vehicles during the rolling

motion of the vessel are presented. However, the issue

of the dynamic load of containers during

transportation by sea was not studied in this work.

Article [11] proposes the design of a FLAT RACK

container, the peculiarity of which is the flexible

bonds in the fittings, as well as the fact that all the

components of its frame are made of rectangular

profiles. This solution helps to reduce its load in

operation in comparison with typical designs of

containers of this type.

The design features of the container for fruit and

vegetable products are highlighted in [12]. The

proposed design solutions were confirmed by the

corresponding strength calculations for the main

operational load schemes of the container.

At the same time, these container designs were not

tested for strength when transported by train ferries

as part of combined trains.

The analysis of literary sources [6 – 12] allows us to

conclude that the issues of improving containers in

order to enhance their operational properties are quite

relevant; at the same time they need further research

and development.

The objective of the study is to highlight the results

of determining the dynamic load of the container with

sandwich panel walls when transported by the train

ferry as part of the combined train. To achieve this

objective the following tasks were set:

207

− to conduct mathematical modelling of the dynamic

load of the container; and

− to determine the roll angle of the train ferry, which

ensures the container stability.

3 PRESENTATION OF THE MAIN MATERIAL OF

THE ARTICLE

To reduce the dynamic loads that act on the container

during operating modes, including when transported

by sea, it is proposed to manufacture its walls in the

form of sandwich panels. In this case, the sandwich

panel consists of two metal sheets with an energy-

absorbing layer between them (Figure 3).

Figure 3. Sandwich panel

To determine the possibility of transporting a

container of the proposed design as part of a

combined train by a train ferry, mathematical

modelling was carried out. The design scheme of the

container placed on the flat wagon and fixed on the

train ferry deck is shown in Figure 4.

It was taken into account that the system under

study has four degrees of freedom characterized by

angular movements around the longitudinal axis of

the train ferry, flat wagon, container and freight

placed in it, respectively. When making calculations,

the freight was considered as conditional, using the

full load capacity of the container. The energy-

absorbing material in the container walls was

modelled with an elastic-viscous connection with a

coefficient of viscous resistance of 20 kN·s/m and a

stiffness coefficient of 15 kN/m. These parameters

were determined on the basis of previous studies of

the authors.

Figure 4. Design diagram of the container placed on the flat

wagon

When building the mathematical model, the

friction forces between the following components of

the system were not taken into account: centre bowl –

centre plate, jack – bolster, freight – container, etc.

The mathematical model looked as follows

4 3 3

( ),









 +   =











 =  + +











 =  + +





 = −   −   +



FW FW FW FW

FW C

C C C C

I q q P t

I q p ММ

I q h q с h q М

(1)

( ) ( ),





=  +   

Р t p F t

(2)

where

ITF – the moment of inertia of the train ferry;

Δθ – the coefficient of resistance to oscillations;

В – the breadth of the train ferry;

h – the side height;

р'TF – the wind load on the above-water projection;

F(t) – the law of disturbing force (sea wave);

IFW

– the moment of inertia of the flat wagon;

hFW – the height of the side surface of the flat wagon;

p'ВПФ – the wind load on the side surface of the flat

wagon;

MFW

– the moment of forces arising between the flat

wagon and the train ferry deck;

MFW

– the moment of forces arising be-tween the flat

wagon and containers;

ІC

– the moment of inertia of the container;

hC – the height of the side surface of the container;

р'C – the wind load on the side surface of the

container;

– the moment of forces arising between the

container and the flat wagon;

– the moment of forces arising between the

container and the freight;

– the moment of inertia be-tween the freight and

the container;

M'C

– the moment of forces arising between the

freight and the container;

β – the coefficient of viscous resistance of the energy-

absorbing material;

c – the stiffness of the energy-absorbing material.

The motion of the wave was described by a

trochoidal curve. System of differential equations (1)

was solved in MathCad [13 – 16]. For this, the

transition from systems of second-order differential

equations to systems of first-order differential

equations was carried out, followed by the use of

standard algorithms for solving systems using the

rkfixed Mathcad function [17, 18].

The generalized accelerations were calculated in

the array ddqj,i:

208

()

2 2 2

( 4 )







 +    −  













h B B

p F t y

ddq

(3)





 + +

FW FW FW

p ММ

ddq

(4)





 + +

FW C

С С C

p ММ

ddq

(5)







−   −   +

С С С

hq с h q М

ddq

(6)

Based on the calculation, it was found that the

greatest acceleration values occur at the wave angles

relative to the train ferry body χ = 60° and χ = 120°. At

the same time, the maximum acceleration of the

container relative to the standard place on the deck

was about 2.3 m/s² (Figure 5). The numerical

acceleration value was indicated without the

component of free fall acceleration.

The total acceleration value was determined as

sin ,

  

= + 

tot a

(7)

where



– the acceleration that acts relative to the standard

place of the flat wagon with containers on the deck;

g – the free fall acceleration;

θ – the roll angle of the train ferry.

Figure 5. Accelerations on the container transported by the

train ferry

By taking into account the hydro-meteorological

characteristics of the sea and the above-water

projection of the train ferry, the roll angle value was

12.2°. The value of roll angle was calculated for the

case of static action of the wind on the above-water

projection of the train ferry. The calculation was made

for a train ferry of the Geroi Plevny type when

moving by the Black Sea.

Taking this into account, the total acceleration

acting on the container was 4.4 m/s

(0.45 g). The

resulting acceleration value was 4.3% lower than that

acting on the container of a typical design.

The accelerations were calculated for the other roll

angles of the train ferry (Figure 6).

Figure 6. Dependence of accelerations to the container on

the roll angle of the train ferry

The obtained accelerations were taken into account

when determining the stability coefficient of the

container placed on the flat wagon. The calculation

was made according to the methodology given in the

previous works of the authors. The results of the

calculation are given in Figure 7.

Figure 7. Dependence of the stability coefficient of the

container on the roll angle

By analysing the dependence shown in Fig. 7, it

can be concluded that the stability of the container is

ensured at roll angles up to 17°.

The results of the study will contribute to the

database of recommendations for the design of

modern container structures and their safe operation

in international traffic.

4 CONCLUSIONS

1. Mathematical modelling of the dynamic load of the

container with sandwich panel walls during

transportation as part of the combined train by the

train ferry was carried out. The largest acceleration

values occur at the wave angles relative to the train

ferry body χ = 60° and χ = 120°. The maximum

acceleration of the container relative to the

standard place on the deck is about 2.3 m/s². In this

case, the total acceleration that acts on the

container is 4.4 m/s2 (0.45 g). The resulting

acceleration value is 4.3% lower than that acting on

the container of a typical design.

2. The admissible roll angle of the train ferry in terms

of ensuring the stability of the container was

determined. The results of the calculations show

that the stability of the container is ensured at roll

angles up to 17°. At the same time, the stability

coefficient of the container is 1.

The results of the study will contribute to the

database of recommendations for the design of

209

modern container structures and their safe

operation in international rail and water traffic.

ACKNOWLEDGEMENTS

This contribution was elaborated within execution of the

projects VEGA 1/0513/22. Investigation of the properties of

railway brake components in simulated operating

conditions on a flywheel brake stand; KEGA 036ŽU-4/2021.

Implementation of modern methods of computer and

experimental analysis of the properties of vehicle

components in the education of designers of future means

of transport.

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