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Shuffling a deck of cards is normally used for randomization. An imperfect shuffle would not produce the desired randomization, since there would be residual correlation with the original order. On the other hand, from the classical card magic literature it is known that eight successive perfect riffle shuffles returns the deck to the original order. The question addressed here is whether this observation is in fact unusual and surprising. Although a general closed‐form analytical solution does not appear to be possible, a simple program could be written to determine deck sizes and numbers of shuffles for which eventual reordering occurs. This computational approach correctly predicts the original observation of eight shuffles for a deck of 52 cards; in fact if the trivial solutions of integral multiples of eight shuffles are discarded, eight shuffles appears to be the unique solution for a 52 card deck.

It is common practice in structural engineering to assume floor diaphragms infinitely stiff in their own plane. But, most of the code provisions lack clarity and unity in categorising floor diaphragms and discussing their behaviour based on the seismic response of the structures. Besides, although many of these code provisions have presented simple techniques and formulations for determining the level of flexibility in floor diaphragms, the implementation of these techniques on more complex floor systems such as the steel-deck composite floors is still under question. The paper aims to discuss these issues.

In this study, an equivalent concrete floor is employed as a representative of in-plane diaphragm action of steel-deck composite floor, using simple modelling techniques in SAP2000 and the results are validated by complex structural models developed in ABAQUS. Afterwards, the equivalent floor is inserted to 3, 5 and 7 storey steel structures with 2, 3 and 5 plan aspect ratios in two categories of structures with rigid diaphragms and analogous structures with flexible diaphragms and the responses are compared to each other.

The results show that the proposed technique is an effective method for evaluating the diaphragm action of steel-deck composite floors. Additionally, it is concluded that, the boundary values of plan aspect ratio equal to 3 and λ coefficient equal to 0.5 in steel-deck composite floors, mentioned in code provisions for categorising diaphragms, are not always conservative and need to be scrutinised.

The proposed methodology provides simple framework for assessing the effects of in-plane flexibility of steel-deck composite on seismic response of steel structures.

Although ground penetrating radar (GPR) technology is commonly used to assess the condition of reinforced-concrete (RC) bridge decks, the GPR data interpretation is not straightforward. Further, the thresholds that define the severity of deterioration are selected arbitrarily. This paper aims to solve a problem associated with GPR results generated by using a numerical amplitude method to assess corrosiveness of bridge decks.

Data, for more than 50 different bridge decks, were collected using a ground-coupled antenna. Depth-correction was performed for the collected data to normalize the reflected amplitude. Using k-means clustering technique, the amplitude values of each bridge deck were classified into four categories. Later, statistical analysis was performed where the threshold values of different categories of corrosion and deterioration are chosen. Monte-Carlo simulation technique was used to validate the value of these thresholds. Moreover, a sensitivity analysis was performed to realize the effect of changing the thresholds in the areas of corrosion.

The final result of this research is a four-category (good, fair, poor and critical) GPR scale with three fixed numerical thresholds (−7.71 dB, −10.04 dB and −14.63 dB) that define these categories. Besides, deterioration curves have been modeled using Weibull function and based on GPR outputs and corrosion areas.

The developed numerical GPR-based scale and deterioration models are expected to help the decision-makers in assessing the corrosiveness of bridge decks accurately and objectively. Hence, they will be able to take the right intervention decision for managing these decks.

The purpose of this paper is to provide a variety of viewpoints to illustrate the mechanism of the deck-stay interaction with the appropriate initial shapes of cable-stayed bridges, which is validated by a symmetrical structure.

Based on the smooth and convergent bridge shapes obtained by the initial shape analysis, the one-element cable system (OECS) and multi-element cable system (MECS) models of the symmetric harp cable-stayed bridge are developed to verify the applicability of the analytical model and numerical formulation from the field observations in the authors’ previous work. For this purpose, the modal analyses of the two finite element models are conducted to calculate the natural frequency and normalized mode shape of the individual modes of the bridge. The modal coupling assessment is also performed to obtain the generalized mass ratios among the structural components for each mode of the bridge.

The findings indicate that the coupled modes are attributed to the frequency loci veering and mode localization when the “pure” deck-tower frequency and the “pure” stay cable frequency approach one another, implying that the mode shapes of such coupled modes are simply different from those of the deck-tower system or stay cables alone. The distribution of the generalized mass ratios between the deck-tower system and stay cables are useful indices for quantitatively assessing the degree of coupling for each mode. For each identical group of stay cables in the MECS model, the local modes with similar natural frequencies and normalized mode shapes consist of the participation of one or more stay cables. These results are demonstrated to fully understand the mechanism of the deck-stay interaction with the appropriate initial shapes of cable-stayed bridges.

It is important to investigate the deck-stay interaction with the appropriate initial shape of a cable-stayed bridge. This is because such initial shape not only reasonably provides the geometric configuration as well as the prestress distribution of the bridge under the weight of the deck-tower system and the pretension forces in the stay cables, but also definitely ensures the satisfaction of the relations for the equilibrium conditions, boundary conditions and architectural design requirements. However, few researchers have studied the deck-stay interaction considering the initial shape effect. The objective of this paper is to fully understand the mechanism of the deck-stay interaction with the appropriate initial shapes of cable-stayed bridges, which is validated by a symmetrical structure. The modal coupling assessment is also performed for quantitatively assessing the degree of coupling for each mode of the bridge.

This paper aims to introduce physics-informed neural networks (PINN) applied to the two-dimensional steady-state laminar Navier–Stokes equations over a flat plate with roughness elements and specified local heating. The method bridges the gap between asymptotics theory and three-dimensional turbulent flow analyses, characterized by high costs in analysis setups and prohibitive computing times. The results indicate the possibility of using surface heating or wavy surface to control the incoming flow field.

The understanding of the flow control mechanism is normally caused by the unsteady interactions between the aircraft structure and the turbulent flows as well as some studies have shown, surface roughness can significantly influence the fluid dynamics by inducing perturbations in the velocity profile.

The description of the boundary-layer flow, based upon a triple-deck structure, shows how a wavy surface and a local surface heating generate an interaction between the inviscid region and the viscous region near the flat plate.

To the best of the authors’ knowledge, the presented approach is especially original in relation to the innovative concept of PINN as a solver of the asymptotic triple-deck method applied to the viscous–inviscid boundary layer interaction.

The purpose of this study is to test the performance of the designed automatic control system based on the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) algorithms during landing of the helicopter on the ship deck. This paper is a further development of the series based on Topczewski et al. (2020).

The system consists of two automatic control algorithms based on LQR and the LQG. It is integrated with the ship motion prediction system based on autoregressive algorithm with parameters calculated using Burg’s method. It is assumed that the source of necessary navigation data is integrated Inertial Navigation System with Global Positioning System. Landing of the helicopter on the ship deck is performed in automatic way, based on the preselected procedure. Performance of the control system is analyzed when all necessary navigation data is available for the system and in case when one of the parameters is unavailable during performing the procedure.

In this paper, description of the designed control system developed for performing the approach and landing of the helicopter using selected procedure is presented. Helicopter dynamic model is validated using the manufacturer data and by test pilots, overview is presented. Necessary information about ship motion model is also included. Tests showing mission performance while using LQR and LQG algorithms applied to the control system are presented and analyzed, taking into account both situations when full navigation data is available/unavailable for the control system.

Results of the system performance analyses can be used for selection of the proper control methodology for prospective helicopters autopilots. Furthermore, the system can be used to analyze the mission safety when information about one of the navigation parameters is identified by the navigation system as unavailable or incorrect and therefore unavailable during landing on the ship deck.

In this paper, control system dedicated for the automatic landing of the helicopter on the ship deck, based on two different control algorithms is presented. Influence of lack of information about one of the navigation parameters on the mission performance is analyzed.

FOR a number of years now it has been evident that a successor to the well‐tried Vickers Viscount and Convoir 240/340/440 series was required. However, the big problem was to design an aircraft such that its economics and passengerappealweresub‐stantially better than the machines it would ultimately replace. Other important factors which had to be con‐sidered were improved reliability, easier and cheaper maintenance, higher standards of safety and means of reducing ramp times. Furthermore, the difficult choice of passenger capacity and cruising speed had to be made. Probably the easiest decision was to employ the twin‐engine configuration with the power plants placed in the now familiar rear position, one on cither side of the fuselage.

The helicopter has been in existence, in its present form for over 50 years and it possesses a wide variety of operational use. This paper focuses on the development of the shipborne helicopter which requires controlled flight in a very complex and potentially dangerous atmospheric environment surrounding a ship's flight deck. This type of helicopter requires dedicated design features to enable appropriate missions to be successfully achieved. It is an interesting feature of the shipborne helicopter that operational problems are as important with the aircraft in contact with the deck as to flight above it. Also there are problems, which begin with extracting the aircraft to the hangar to its eventual reinsertion. The avoidance of unfavourable characteristics has, over the years, resulted in an air vehicle where the aeroelastic properties of the rotor blades govern the operation. The magnitude of the wind speeds over a ship's deck, coupled with the varying rotor speed during the engage and disengage parts of a sortie, expose the rotors to dangerous blade deflections which have, in the past, resulted in damage to the aircraft and, in severe cases, fatalities.

The purpose of this paper is to test the performance of the control system developed for the helicopter automatic approach and landing on the moving vessel deck, when different values of backlashes are applied to the four control actuators.

The system consists of automatic control algorithm based on the linear quadratic regulator and the vessel motion prediction algorithm based on autoregressive method with parameters calculated using Burg’s method. Necessary navigation data is provided by on-board inertial navigation system/Global Positioning System. Calculated control commands are executed by four electromechanical actuators. Performance of the mission, which is based on selected procedure of approach and landing of the helicopter on the moving vessel deck, is analyzed taking into account different values of backlashes applied to the actuators.

In this paper, a description of the control system dedicated for automatic approach and landing of the helicopter on the moving vessel deck is shown. Necessary information about helicopter dynamic model, control system and vessel motion model is included. Tests showing influence of actuator backlashes on the mission performance are presented.

The developed control methodology can be adapted for selected helicopter and used in prospective development of an automatic flight control system (AFCS) or in a simulator. The system can be used to define in which conditions helicopter can perform safe and successful automatic approach and landing on a moving vessel deck.

In this paper, an integrated control system is presented; influence of the control actuator backlashes on the mission performance is analyzed.