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Aircraft and helicopter often fly above open waters and thus have to observe regulations to ensure safe water landing under emergency conditions. This practice is also referred to as ditching - one of several types of slamming problems that are under review by the current regulations of the Federal Aviation Administration (FAA) and the European Aviation Safety Agency (EASA). Ditching is related to the controlled landing on water, with distinctive features such as hydrodynamic slamming loads, complex hydromechanics at tremendous forward speeds, as well as the interaction of multiphase fluid dynamics (air, water, and vapor). This paper presents the knowledge on system mechanics during helicopter ditching. The discussion begins with the fundamental kinetics of the rigid body, and then delves into dynamic relations to describe the effect of forces on motions. In the end, the paper discusses several relevant theories to further contribute to the understanding of the problem of impact.

Jointed structures are ubiquitous constituents of engineering systems; however, their dynamic properties (e.g., natural frequencies and damping ratios) are challenging to identify correctly due to the complex, nonlinear nature of interfaces. This research seeks to extend the efficacy of traditional experimental methods for linear system identification (such as impact testing, shaker ringdown testing, random excitation, and force or amplitude-control stepped sine testing) on nonlinear jointed systems, e.g., the half Brake–Reußbeam, by augmenting them with full-field data collected by high-speed videography. The full-field response is acquired using high-speed cameras combined with Digital Image Correlation (DIC), which enables studying the spatial–temporal dynamic characteristics of the system. As this is a video-based experiment, additional constraints are attached to the beam at the node points to remove the rigid body motion, which ensures that the beam is in the view of the camera during the entire test. The use of a video-based method introduces new sources of experimental error, such as noise from the high-speed camera's fan and electrical noise, and so the measurement accuracy of DIC is validated using accelerometer data. After validating the DIC data, the measurements are recorded for several types of excitation, including hammer testing, shaker ringdown testing, fixed sine testing, and stepped sine testing. Using the DIC data to augment standard nonlinear system identification techniques, modal coupling and the mode shapes’ evolution are investigated. The suitability of videography methods for nonlinear system identification of nonlinear beams is explored for the first time in this paper, and recommendations for techniques to facilitate this process are made. This article focuses on developing an accurate data collection methodology as well as recommendations for nonlinear testing with DIC, which paves the way for video-based investigation of nonlinear system identification. In Part-II (Jin et al., 2021) of this work, the same data set is used for a rigorous assessment of nonlinear system identification with full-field DIC data. ISSN:0888-3270 ISSN:1096-1216

Blast resistant modular steel (BRMS) buildings are prefabricated cost-effective and explosion-proof structures used to shelter personal near hazardous-material handling or storage facilities, in facilities handling high-pressure processes, and within designed blast zones in mining, petrochemical, and military industries. Typically, BRMS buildings are designed to be fixed (anchored) to their foundation. However, this design approach can result in very large anchorage and foundation reactions, which result in very large and high-cost foundations. Therefore, an alternative foundation approach which minimize foundation reactions and known as unanchored or free-to-slide foundation has recently attracted much attention for BRMS buildings. In this study, dynamic behavior of a typical BRMS building under blast loading with unanchored foundation was determined using 3D nonlinear dynamic finite element and a simplified numerical analysis method. The developed numerical analysis method is based on nonlinear numerical integration scheme, and it was verified using the finite element results. Applicability of the proposed numerical analysis method was evaluated using finite element results for a typical unachored BRMS building subjected to blast loads. Several values of coefficient of friction between the foundation and BRMS building were considered. The computed building sliding, horizontal velocity, acceleration, and horizontal foundation reaction histories were used to evaluate applicability of the proposed numerical method. The overall results show that the proposed simple numerical analysis method based on rigid-body dynamics is suitable to predict building sliding and sliding velocity, but unconservative in terms of foundation vertical reaction and horizontal acceleration.

Application of the principle of energy balance to a rigid indenter in contact with a thin elastic layer on a flat rigid substrate provides a very simple derivation of the detachment criterion which earlier has been obtained by much more complicated asymptotic analysis. The simple criterion is additionally confirmed by the fully three-dimensional simulations of contact with a coated rigid substrate using the recently developed formulation of the boundary element method for coated media. The found detachment criterion is applied to contact of indenters of various shape. In the case of flat-ended indenters, the adhesive strength occurs to be proportional to the area of the face of the indenter (independently of the shape). The asymptotic criterion is also used for calculation of the adhesion strength of indenters having arbitrary shape and is illustrated with a case study of a contact of a rough indenter with a coated substrate.

Significance Knots, knits, and weaves have been technologically essential across civilizations, and their significance remains undiminished today. In these systems, it is challenging to understand the equilibria of the deformable filaments with their tight contacts due to the intricate geometry of touching tubular volumes of small, but nonvanishing, radius. This article considers a specific canonical context for filaments in contact: the orthogonal clasp. We quantify the significant mismatches between the physical reality of orthogonal clasps and the simplifying assumptions underpinning conventional descriptive models, such as the classic capstan equation. Nevertheless, we show that a simple, geometric model qualitatively captures the striking localization patterns in the observed contact-pressure fields., Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple, yet canonical, problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (μCT) and mechanical testing experiments are in excellent agreement with finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibit strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact-pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the μCT and FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small, but nonzero, tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.

We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes, allows bodies with vertices and edges, we assume the bodies to be convex and take care not to assume more regularity than that implied by convexity. One main result is the (Liapunoff) stability of equilibria satisfying a condition equivalent to the standard 'metacentric' criterion., Comment: 22 pages

International audience; The speed profile of a train plays an important role in energy consumption and resulting costs. The industrial objective of this work is thus to develop a method to reduce the energy consumed by a train over a journey by playing on the driver commands (traction and braking forces) while respecting punctuality constraints. A coupling between measured data and simulation is proposed to solve this optimization problem. First, a rigid body approach (Lagrangian formalism) is introduced to characterize the dynamics of each element of the train and their interactions with their environment. In particular, the aerodynamic (including the wind effect), traction, and braking forces are taken into account, and a special attention is paid to the vertical and lateral characteristics of the track as they play a key role on the train dynamics. Secondly, a model for energy consumption and recovery (thanks to dynamic braking) is introduced. Experimental measurements of a high-speed line are then used to estimate the parameters on which the two previous models are based and to validate their predictive capacities. The optimization problem under constraints is finally solved using an evolutionary algorithm where the constraints are implemented using an augmented Lagrangian formalism. The performance of the proposed method in terms of speed optimization and energy consumption reduction is compared to measurements associated with commercial trains.

Finding a solution for Euler's equations is a classic mechanics problem. This study revisits the problem with numerical approaches. For ease of teaching and research, a Maple code comprising 2 lines is written to find a numerical solution for the problem. The study's results are validated by comparing these with previous studies. Our results confirm the correctness of the principle of maximum moment of inertia of the rotating body, which is verified by thermodynamics. As an essential part of this study, the Maple code is provided.

Tippe top is an example of simple moving system of rigid body with non-holonomic constraint, but the analysis of this system is not simple. A tippe top equation has been derived with Routhian reduction method and Poincaré equation, and physics computation in finding numeric solution of the dynamics of the tippe top has also been utilized by using Maple program. However, the Poincaré equation required that quasi-coordinate of the quasi-velocity is found, while in the case of the dynamics of tippe top, there is not any exact solution of the quasi-coordinate of the quasi-velocity was found. Therefore, the tippe top equation should be reduced to solve the problem. In this research, Routhian reduction was employed so that the Routhian reduction-based Poincaré equation was used to derive the tippe top equation. The method was able to derive a tippe top equation on a flat plane and tube inner surface clearly represented differential equations.

Hydroelastic phenomena play a critical role on the dynamics of lightweight marine vessels, but a comprehensive understanding of their potential benefits and drawbacks in water impact remains elusive. In contrast with the literature on hydroelastic impact that focuses on plane strain deformations and two-dimensional fluid flows, we address the water entry of compliant slender bodies. We propose a mathematically-tractable framework to predict the rigid body motion and elastic deformation of a beam impacting the water surface in free fall. At each location on the beam, the hydrodynamic loading is determined from the level of submersion of the cross-section and its local velocity and acceleration. Slamming, added mass, and drag are all included in the model and cogently weighted based on the level of submersion of the cross-section. Edge effects are incorporated in the model through a shape function that modulates the hydrodynamic loading as a function of the distance from the edges. Model predictions are validated through experiments on compliant beams of circular cross-section, which detail both the structural response and the resulting flow physics, through the integration of high-speed imaging, direct acceleration measurement, and particle image velocimetry. Results of this study are expected to aid in the design of lightweight ship hulls, experiencing dynamic bending deformations during sailing and maneuvering.

This paper aims to extend the implementation of DualSPHysics-Project Chrono coupling to hydroelasticity problems involving free-surface flows and deformable elastic boundaries. In the present model, the fluid sub-domain of the phenomenon is based on the WCSPH model of DualSPHysics. The solid sub-domain, simulated by the Project Chrono engine, is modeled using the set of rigid bodies attached by hinges with torsional and damping stiffness. An analytical solution of Euler-Bernoulli beam theory is employed to adapt the rigid-multibody system to the mechanical characteristics of the elastic sub-domain via the torsional stiffness values of hinges. The stability and accuracy of the present model are tested by three cases with different flow characteristics and mechanical properties for solid sub-domain, involving a newly-designed experimental setup and two benchmark cases in the literature. Obtained results show reasonable accuracy with experimental measurements and other numerical model computations.

The paper deals with the problem of heat conduction in a nonhomogeneous rigid body which is a homogeneous conductive layer with a periodic composite coating. The coating layer is a composite in which every unit cell in general case is composed of four rigid beams with rectangular cross-sections. The assumed structure permits to analyse some special cases of coatings: laminated composites with layer parallel or perpendicular to the boundary, composites with periodically distributed inclusions with rectangular cross-section and a homogeneous layer. The distributions of temperature and heat flux distributions on the interface between the coating and the homogenous layer are investigated.

Passive control of structures to sustain blast loads is extremely important; however, the current research literature and existing technologies are rather limited. The major challenge lies in the fact that the control system should operate rapidly during a very short period of time. In this work it is proposed to overcome this difficulty by changing the structure into a mechanism and by using shear and moment passive control devices attached to the structural members in a sophisticated manner to form “Passive controlled structural mechanism (PCSM)”. The friction devices are located at the joints of the structural members, they are designed so that under mundane loading they are locked and fully transfer the forces and moments acting between the members, while in the case of blast loadings, they transfer predetermined force Fr and moment Mr between the members. Thus, the blast response of the structure is defined by the forces and moments induced by the friction devices. These forces and moments are designed so that they do not exceed the elastic capacity of the structural members, and no damage or collapse will occur. The blast energy is absorbed mainly by the rigid body movement of the structural members and not by the structural members’ flexure. The blast response of a PCSM reinforced concrete (RC) column and frame are investigated by using an analytical model and a finite elements method (FEM) model. It is shown that the PCSM structure remains intact in the elastic regime while regular structures are losing their stability for the same impact.

A multi-system coupled closed-form dynamic model for controller design of hard rock Tunnel Boring Machine (TBM) is presented with consideration of the closed chain structure and interactions with rocks. Based on the analysis of closed chain structure, the motion equations of each rigid body in the TBM system are derived in terms of generalized coordinates. To obtain the mathematical model for controller design, the nonholonomic constraints are novelly proposed to describe the complex interactions between the TBM shield body and rocks instead of the traditional finite element method. With the nonholonomic constraints assumption, a closed-form mathematical model with Lagrangian multiplier is obtained by applying the Lagrangian approach. The interactions between the cutter-head and rocks as the main load acting on the TBM during excavation are described by the widely used Colorado School of Mines (CSM) model. The simulations of excavation performance of TBM in different distribution conditions of rocks with various UCS and TS are compared and discussed.

Three-dimensional Digital Image Correlation (3D-DIC) is a non-contact optical-numerical technique for evaluating the dynamic mechanical behavior at the surface of structures and materials, including biological tissues. 3D-DIC can be used to extract shape and full-?eld displacements and strains with high resolution, at various length scales. While various commercial and academic 3D-DIC software exist, the field lacks 3D-DIC packages which offer straightforward calibration and data-merging solutions for multi-view analysis, which is particularly desirable in biomedical applications. To address these limitations, we present MultiDIC, an open-source MATLAB toolbox, featuring the first 3D-DIC software specifically dedicated to multi-view setups. MultiDIC integrates robust two-dimensional subset-based DIC software with specially tailored calibration procedures, to reconstruct the dynamic behavior of surfaces from multiple stereo-pairs. MultiDIC contains novel algorithms to automatically merge meshes from multiple stereopairs, and to compute and visualize 3D shape and full-?eld motion, deformation, and strain. User interfaces provide capabilities to perform 3D-DIC analyses without interacting with MATLAB syntax, while standalone functions also allow proficient MATLAB users to write custom scripts for specific experimental requirements. This paper discusses the challenges underlying multi-view 3D-DIC, details the proposed solutions, and describes the algorithms implemented in MultiDIC. The performance of MultiDIC is tested using a low-cost experimental system featuring a 360-deg 12-camera setup. The software and system are evaluated using measurement of a cylindrical object with known geometry subjected to rigid body motion and measurement of the lower limb of a human subject. The findings confirm that shape, motion, and full-field deformations and strains can be accurately measured, and demonstrate the feasibility of MultiDIC in multi-view in-vivo biomedical applications.

This paper proposes a dual lifting and its cooperative control system with two different kinds of floating cranes. The Mega-erection and Giga-erection in the ship building are used to handle heavier and wider blocks and modules as ships and off-shore platforms are enlarged. However, there is no equipment to handle such Tera-blocks. In order to overcome the limit on performance of existing floating cranes, the dual lifting is proposed in this research. In the dual lifting, two floating cranes are well-coordinated to add up the lift capabilities of both cranes without any loss such that virtually a single crane is lifting, maneuvering and unloading. Two main constraints for the dual lifting are as follows: First, two barges of floating cranes should be constrained as a rigid body not to cause a relative motion between two barges and main hooks of the two cranes should be controlled as main hooks of a single crane. In order words, it is necessary to develop the cooperative control of two floating cranes in order to sustain a center of gravity of the module and minimize the tilting angle during the lifting and unloading by the two floating cranes. Two floating cranes are handled as a master-slave system. The master crane is able to gather information about all working conditions and make a decision to control the individual hook speed, which communicates the slave crane by TCP/IP. The developed control system has been embedded in the real floating crane systems and the dual lifting has been demonstrated five times at SHI shipyard in 2015. The moving angles of the lifting module are analyzed and verified to be suitable for hoisting control. It is verified that the dual lifting can be applied for many heavier and wider blocks and modules to shorten the construction time of ships and off-shore platforms.

International audience; Generally, when marine vessels encounter the water surface on entry and subsequently re-enter the water at high speed, this can subject the bottom section of the vessels to high hydrodynamic loads, especially over very short durations. This phenomenon generates high hydrodynamic loads, which can cause a catastrophic failure in the structure. In contrast, the interaction between deformable structures and free water surface can be modified the fluid flow and changed the estimated hydrodynamic loads comparing with rigid body, due to appearance of hydroelastic effects. These effects are considered active challenge areas in structural ship design. This work presents an experimental study of the water impact for composite laminate wedge at different constant entry velocities. The aim of this study is to investigate the dynamic structural response of panels and predicts the hydrodynamic loads to meet the specific requirements of marine vessels. In order to better describe hydroelastic influence, two composite panels with different thicknesses namely 8 mm and 13 mm are subjected under constant impact velocities of 4, 6 and 8 m/s with the deadrise angle of 10 degrees. The obtained experimental results were indicated that more flexible panels had a higher peak force and significant dynamic noise compared with higher stiffness panels. In addition, the maximum deformation occurred in the centre and close to the chine edge of the panel due to changes in local velocity and local deadrise angle. For this reason, special attention requires in both design phase and operation phase.

The axisymmetric torsional fretting contact between a rigid conducting spherical punch and a functionally graded piezoelectric material (FGPM) coating is studied in this paper. The exponential model is used to simulate the inhomogeneous electro-mechanical properties of the FGPMs coating. The conducting spherical punch with a constant surface electric potential is considered in the contact. A normal force and a cyclic torque are applied to the two contact bodies. The applied torque produces an outer annular slip area and an inner stick area. The torsion angle is produced within the inner stick area as a rigid body. With the aid of the Hankel integral transform technique, we can reduce the contact problem to the singular integral equations of the Cauchy type. Then the unknown electro-mechanical fields and stick/slip area can be obtained numerically. The effect of the gradient index on the surface electro-mechanical fields is discussed at loading and unloading phases. The Mises stress and principal stress at the contact surface are also discussed to predict the possible location of fretting damage and failure.

A go-kart structure is the small four wheeled vehicle that usually used in sports and recreation. The frame of go-kart chassis structure usually consists of joints such as welded joints. In d~sign process, finite element analysis is always used in order to predict the behavior of the designed structure under different kind of loading or force before fabricating the actual structure. Joints in structure are usually difficult to model because of inaccuracy in assuming the properties of joints. Therefore, it is come to agreement that finite element analysis is not always accurate. In this work, attempts to correlate several methods of modeling in order to find the best method to model the welded joint available on the go-kart structure is presented. Natural frequencies obtained through finite element analysis are compared to the benchmark data which is the experimental value of natural frequencies. Comparison is made between rigid body element, beam element (CBEAM and CBAR), rod element (CTUBE) and nodes equivalence strategy. By using the data gathered experimentally, the findings suggested that in general that the beam element (CBAR and CBEAM) is the most suitable element to be used in modeling welded joints in structures apart from other rigid elements.

Group tower-related interference is one of the major causes of wind-induced damage of large cooling towers. The four-tower arrangements are the most common forms of the layout of group towers. In engineering practice, five arrangements are generally used, namely, single row, rectangular, rhombic, L-shaped, and oblique L-shaped. We performed wind tunnel tests on the rigid body to study the static, dynamic and extreme interference effects under these five arrangements. Then the computation formulas of interference factor that accounted for the wind directions under the five arrangements were proposed. The effects of four-tower arrangement on the distribution patterns of mean and pulsating wind pressures were discussed. The wind pressure signals at the typical measurement points of the cooling towers were subjected to decomposition and joint time-frequency analysis using mathematical statistics technique and Hilbert-Huang transform (HHT). The study shows that the maximum interference factors under the five arrangements were all higher than those under the layout of two towers. It is reasonable to use the extreme interference factor as the measure of the interference effects. The maximum positive pressure of the cooling towers was less affected by the interference effects related to four-towers, and the mean wind pressure were affected greatly in the regions of minimum negative wind pressure and leeward regions. The distribution patterns and values of pulsating wind pressures at the bottom and top of the cooling towers were significantly affected by the five arrangements of the cooling towers. Finally, based on comprehensive assessment of the interference effects of overall wind loads, arranging the four towers in a row was the best scheme, which was followed by the arrangements in oblique L-shaped pattern, L-shaped pattern, rhombic pattern and rectangular pattern successively.

Traditional Velocity Prediction Programs (VPPs) for sailing yachts rely on empirical relations, while modern techniques include CFD. Normally a multi-dimensional matrix of CFD results is pre-computed and forces and moments obtained by interpolation during a VPP execution. A more exact technique is to use the CFD code itself as a VPP, i.e. to simultaneously integrate the flow and rigid body equations in time. In the present paper a technique of this coupled type is introduced. An initial guess is required for speed and attitude, and by time integration in six degrees of freedom this guess is corrected to a steady state solution. Three phases are identified. First the attitude is kept constant over a period of time to stabilize the flow. Thereafter the different degrees of freedom are released successively and the rudder activated to achieve yaw balance. Finally, in the converged phase, the net forces and moments are zero in all degrees of freedom and the results reported. The performance prediction is carried out for a dinghy and a large high-performance racing yacht. Convergence of all variables is demonstrated and the results used for finding the optimum speed to windward and downwind. Details of the numerical setup are reported.

Overturning of rigid blocks on rigid foundations subjected to earthquakes in principle can be analyzed by simple replacement signals. The effect of a signal is generally characterized by its overturning curve. In this paper a new approach is presented, which is based on the overturning acceleration spectra (OAS). It is shown that an earthquake can be reasonably well represented for overturning by two parameters: the peak ground acceleration and the replacement impulse duration. In the paper the OAS of rigid blocks is presented for 100 different earthquake records. Based on the replacement impulse duration a simple design method is presented to predict the safety of rocking blocks.

Summary The concept of input-to-state stability (ISS) is important in robust control, as the state of an ISS system subject to disturbances can be stably regulated to a small region around the origin. In this study, the ISS property of the rigid-body attitude system with quaternion representation is thoroughly investigated. It has been known that the closed loop with continuous controllers is not ISS with respect to arbitrarily small external disturbances. To deal with this problem, hybrid proportional-derivative controllers with hysteresis are proposed to render the attitude system ISS. The controller is far from new, but it is investigated in a new aspect. To illustrate the applications of the results about ISS, 2 new robust hybrid controllers are designed. In the case of large bounded time-varying disturbances, the hybrid proportional-derivative controller is designed to incorporate a saturated high-gain feedback term, and arbitrarily small ultimate bounds of the state can be obtained; in the case of constant disturbances, a hybrid adaptive controller is proposed, which is robust against small estimate error of inertia matrix. Finally, simulations are conducted to illustrate the effectiveness of the proposed control strategies.

Purpose The purpose of this paper is to identify the flexible aircraft model accurately from the frequency responses. Design/methodology/approach The frequency domain output error method is used to estimate the aerodynamic (rigid body and elastic body) derivatives, and mode shape parameters in the process of identification of flexible aircraft model. The accurate identification of lightly damped low frequency rigid-body response modes requires a careful selection of the frequency sweep length and the fast Fourier transform (FFT) window size, as the FFT window length cannot be longer than any individual sweep records. To address this issue, an effort is made to derive the FFT window length for the application of frequency domain estimation approach. Findings The investigations are initially made to select a suitable FFT window size for the accurate identification of the lightly damped low frequency rigid-body response modes of the flexible aircraft. Subsequently, frequency domain estimation approach is applied to simulated data of flexible aircraft. Besides the stability and control derivatives, the structural modes of the flexible aircraft are also estimated as part of state space model identification, and it is shown that all the model parameter estimates are accurate. Identification of such flexible aircraft aerodynamic (rigid body and elastic body) derivatives and structural mode shape parameters will lead to mathematical models of flexible aircraft that are accurate over a wide frequency range. The identified models are validated using the time response of frequency sweep data. Research limitations/implications Aircraft system identification is an integral part of aerospace system design and life cycle process. This becomes a complex process when the aircraft has significant effects of flexibility on the flight dynamics, especially as the frequencies of the elastic modes become lower and approach those of the rigid body modes. Thus, an integrated mathematical model of flexible aircraft is required to develop, and it should be valid for a wide frequency range and relevant for the design of flight control system. Originality/value This paper focuses on the application of frequency domain approach to identify the valid model of flexible aircraft by estimating the aerodynamic (rigid body and elastic body) derivatives and structural mode shape parameters of flexible aircraft. The unknown frequencies of structural modes are also able to identify accurately in frequency domain. This gives more value addition to analyze the flight data of flexible aircraft, as it is challenging problem in parameter estimation of flexible aircraft.

A mathematical modelling of a shaft-hub press-fit subjected to bending couples applied to the shaft extremities is developed, and the value of the bending couple inducing an undesired shaft-hub incipient detachment is analytically determined. The shaft-hub contact is modelled in terms of two elastic Timoshenko beams connected by a distributed elastic spring, whose stiffness is analytically evaluated. Two models of the distributed spring are considered. The first model expresses the combined deformability of both the shaft and the hub cross sections. The second model accounts for the stiffening effect exerted by the shaft portion protruding from the hub on the adjacent shaft part that is in contact with the hub, and, consequently, it assumes only a rigid body motion of the shaft cross section, thus neglecting its deformability. Based upon this beam-like model, the bending couple producing the incipient detachment between the shaft and the hub is theoretically determined in term of the shaft-hub geometry, of the initial shaft-hub interference, and of the elastic constants. Comparisons with selected Finite Element (FE) forecasts indicate that the first modelling produces an incipient detachment couple that appreciably overrates the FE forecasts, whereas the second modelling lowers the error down to technically acceptable predictions.

Three dimensional Digital Image Correlation (3D-DIC) is used in the present study in combination with traditional clip gauges to assess the efficiency of osteosynthesis techniques widely applied to fixate acetabular fractures. Thirty-five cadaveric semi-pelvises were artificially fractured and fixated with the aid of various combinations of either simple or locking fixation plates and screws. The fractures simulate a variation of the acetabular fractures known as “T-type”. The fixated constructs were properly supported to simulate single-leg stance. Quasi-static loading under displacement-control mode was monotonically imposed until one out of two predefined failure criteria (related either to the load attained or the displacement induced) was satisfied. It was proved that 3D-DIC, besides its advantages related to the full-field description of the displacement field, is an extremely valuable recording tool for the needs of the present protocol since it permits post-mortem evaluation of the relative displacement and relative sliding of the fixated parts, relieved from the influence of rigid body displacement and rotation. Proper elaboration of the data provided by the 3D-DIC system, implemented on the basis of an alternative assessing criterion, permitted a “fair” comparison between the fixation techniques, in terms of the response of all three independent fractures forming the specific variation of the T-type fracture. It was concluded that suitable combination of simple and locking reconstruction plates offers increased stability of the fixated semi-pelvises, compared to the other fixation techniques studied.

Leaf flexure hinges are key-components in compliant mechanisms. With their simple shape and intrinsic flexibility, they connect bulky parts and allow relative motion. In order to address the synthesis and the analysis of mechanisms embodying such components, leaf hinges are often modelled with a pseudo-rigid assembly including a revolute joint and a torsion spring. However, this approximation is only valid within a limited range of motion thus it is not completely suitable for precision mechanisms or for mechanisms undergoing large displacements. In this paper, the authors propose a novel and accurate pseudo-rigid model to approximate the relative motion of the bodies connected by a leaf hinge within a large range of relative rotation. The proposed equivalent mechanism is composed of two circular shaped bodies with pure rolling contact. The body shapes represent the polodes of relative displacement between the connected bodies and the real mechanism kinematics is approximated through an epicyclic arrangement. Hence, the concept of polodes, usually limited to rigid body motion, is herein extended to compliant mechanisms. For the definition of the relative motion between bodies coupled by means of compliant hinges, new analytical expressions of kinematic invariants are deduced. In particular, polodes’ radii of curvature and diameter of inflection circle are deduced. The reliability and accuracy of the proposed leaf hinge modelling is confirmed by the agreement, within a large range of rotation and for the case of a pure bending, by a comparison of FEM analysis results with those obtained using the herein proposed model.

In this study, a fully coupled fluid–structure interaction model was used to compute the mean drift force on a flexible barge under various wave conditions. The fluid domain was solved using a time domain B-spline 3-D Rankine panel method. The structural domain was modeled using a shell-element-based 3-D finite element model. The fluid model was coupled with the 3-D FE model via eigenvectors. Seakeeping analysis of the flexible body was performed by the fully coupled model. In the computation of drift force, two approaches were employed: a near-field method and a far-field method. The near-field method included an extension of the rigid body formula in the flexible body formula. The far-field method used the same formula for the rigid body and the flexible body. To the knowledge of the authors, it was not easy to find validation data for the mean drift force on a flexible barge. Therefore, an indirect validation was conducted by comparison of numerical results using a different approach. As a test model, a virtual barge model was used. The motion and mean drift force on the rigid barge were compared with the results of a commercial software, WADAM. The mean drift force on the flexible barge was compared to the results of the near-field and far-field methods.

Both marine surface vehicles and underwater vehicles are often equipped with cranes, robotic manipulators, or similar equipment. Much attention is given to modeling of both the dynamics of marine vehicles and the dynamics of manipulators, cranes, and other equipment. However, less attention is given to the interconnected behavior of the vehicle and equipment, even though such equipment may have a considerable impact on the vehicle dynamic behavior, and therefore risk, or conversely, the vehicle may have a considerable impact on the equipment dynamic behavior. With main focus on ships equipped with cranes, this paper presents a framework for modeling the interconnected dynamics of rigid body systems, based on Lagrangian dynamics. The resulting equations of motion are implemented as a bond graph template to which any subsystem of interest, such as actuators, hydrodynamics, and controllers, may be interfaced. An example on how this framework can be used to develop a high-fidelity simulator of an offshore installation vessel with a heavy duty crane is presented. This work represents the first bond graph implementation of crane and vessel dynamics where the interconnections are modeled according to true physical rigid body principles without nonphysical limitations such as diagonal mass-inertia matrix. © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.”

Summary A new model is presented for multiblock columns subjected to earthquakes, which contains an impact and an opening model. Both in the impact and in the opening model, all the possible opening configurations are investigated because it was found that in many practical cases, unexpected patterns may occur. The model is purely mechanical: assuming rigid blocks and classical (inelastic) impact. The effect of energy dissipation during impact was investigated. Using our model in accordance with the literature, it was found that monolithic blocks are more vulnerable to overturning than multiblock systems.

This paper presents path following control for fully actuated rigid body systems in 3-D space. Transverse feedback linearization and a parallel transport frame are used to design a path following controller that is suitable for paths that are parametrized as regular threefold continuously differentiable curves. The application of this frame enables the handling of paths with zero curvature and reduces the complexity of the control law. The path following controller is combined with a compliance control concept. The strategy is verified by a series of measurement results on a DELTA robot with linear drives.

This paper presents a dynamic modeling approach for flexible spacecraft with multiple solar panels and flexible joints. Firstly, the characteristic equation for the flexible spacecraft is derived in terms of the partial differential equations of motion for the solar panels, the ordinary differential equations of motion for the central rigid body, the matching conditions at the joints, and the boundary conditions. The natural frequencies and global mode shapes of the flexible spacecraft are determined, and orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to truncate the dynamical equation of the flexible spacecraft to a set of ordinary differential equations with multiple-DOF. The validity of the derived model is verified by comparing the natural frequencies obtained from the characteristic equation with those obtained from FEM. For each global mode shape, a translation index and a set of rotation indexes are introduced to describe the interaction between the elastic deformation of the solar arrays and the displacements of the central rigid body. Based on the truncated dynamic model obtained in this paper, dynamical responses of the flexible spacecraft with flexible joints are worked out numerically for the cases of orbit control and attitude control, respectively. The corresponding results of the flexible spacecraft with rigid joints are given to illustrate the effects of flexible joints on the responses of the system. The results show that the joint flexibility has a significant effect on the dynamical responses of the flexible spacecraft, especially, in the case of very small stiffness of the joints.

Time efficient attitude maneuver for a flexible satellite containing a main rigid body with some flexible appendages is studied in this paper. For the rigid body, an ideal braking curve is designed based on a constrained torque distribution algorithm and the satellite is forced to track this curve. To reduce the influence of the flexible appendages, a corresponding state feedback control scheme is adopted to stabilize the vibration modal. Considering that the variation mode are always unmeasurable, an observer is constructed to estimate the flexible state. Moreover, a shape input or time delay controller is designed with the utilization of piezoelectric actuator. The stability of the closed-loop system is analyzed using Lyapunov method and the effectiveness has been verified through practical numerical examples. Simulation results show that the controller provides smooth control torque, time efficiency, high control precision and the vibration can be suppressed by the designed input shaper.

Safety during interaction with unstructured and dynamic environments is now a well established requirement for complex robotic systems. A wide variety of approaches focus on the introduction of safety evaluation methods in order to shape a consequent safety-oriented control strategy, able to reactively prevent collisions between the robot and potential obstacles, including a human being. This paper presents a new safety assessment, named kinetostatic safety field, that captures the risk in the vicinity of an arbitrary rigid body source of danger (e.g. an obstacle, a human body part or a robot link) moving in R3. The safety field depends on the position and velocity of the body but it is also influenced by its real shape and size, exploiting its triangular mesh. The introduction of a body-fixed reference frame in the definition of the field provides closed form computability and an effective computation time reduction, that allows for real-time applications. In particular, intensive computations, connected to the specific body geometry, can be performed only once and off-line, ensuring a fast and constant on-line computation time, independently of the number of mesh elements. Furthermore, we combine the safety field concept with a safety-oriented reactive control strategy for redundant manipulators. Our approach allows to enhance safety in several real-time collision avoidance scenarios, including collision avoidance with potential obstacles, self-collision avoidance and safe humanrobot coexistence. The proposed control strategy is validated through experiments performed on an ABB FRIDA dual arm robot. HighlightsA new safety assessment, named kinetostatic safety field, for robots in interaction with humans and the environment is proposed.The safety field is easily and efficiently computable for a moving rigid body, represented by a triangular mesh with arbitrary number of mesh elements, thus allowing for real-time applications.The safety field concept is combined with a safety oriented control strategy for redundant robots, experimentally validated on an ABB FRIDA dual arm robot.

Trajectory tracking of micro UAVs requires accurate thrust and velocity estimates. High-quality motion control of quadrotors typically employs accurate high-speed optical sensing indoors. However, these measurements are not available outdoors, and GPS is unreliable and inadequate for performance motion control. We have developed small embedded force sensors that mount between a micro UAV's airframe and motors—forces generated by the rotors are measured as they are transmitted to the rigid body of the aircraft. The direct force measurements can be directly integrated with a model of the mapping between aircraft motion and induced rotor forces. From this, the translational velocities of the rotors relative to the local wind can be measured, and thus the overall velocity of the aircraft can be inferred. We have assembled a proof-of-concept quadrotor platform with all four rotors fitted with force sensors, and demonstrate accurate measurement of a quadrotor's lateral velocity during prescribed motions using the onboard force sensors. The vertical velocity measurement was found to be insensitive.

High throughput requirements on high-precision manufacturing systems lead to a situation where the flexible dynamics hamper the performance at the positions of interest. Since these points are typically not measured directly, high performance local control of measured positions may lead to deteriorated performance due to internal deformations. A possible solution is to employ a control strategy which ensures that the desired rigid body motion is achieved, without exciting the parasitic flexible dynamics. In this paper, a feedforward controller design procedure is developed that achieves this type of global performance, which in turn leads to increased performance at the unmeasured positions of interest. The proposed method is applied to an experimental wafer stage showing that the proposed approach indeed leads to superior results with respect to the traditional local control approach.

The paper presents the experimental and numerical investigations of a novel design of a pneumatic life raft in calm water conditions. Two main issues were considered: the life raft performance under tow and its resistance in calm water conditions. The experiment and CFD simulations were performed by using the full scale prototype to eliminate the scale effect. The towing tank tests confirmed the results of numerical computations. The compatibility of the results of numerical and experimental tests was high mainly because the new life raft does not deform under the hydrodynamic and aerodynamic loads. The characteristics similar to rigid body behaviour result mainly from a new construction and materials used for manufacturing the life raft.

Take-up judder is the first rigid body torsional mode of the clutch system, which occurs during clutch engagement. This phenomenon is induced by stick-slip oscillations at the friction lining interfaces between the clutch disc and flywheel, and the pressure plate. The phenomenon is influenced by the clutch lining friction characteristics, the topography of the mating-sliding surfaces, and the operational conditions during the engagement process. Therefore, the interfacial characteristics are affected by contact pressure, interfacial slip speed, and surface temperature. Take-up judder causes driver and vehicle occupant discomfort, as well as gradual wear of contacting surfaces. The response frequency of the system is reported to be in the range 5–20 Hz, depending on the clutch system and vehicle inertia. In this paper, the measured interfacial friction characteristics together with clamp load variation (contact pressure) under different surface temperatures are included in a multi-degree of freedom dynamic analysis to obtain torsional vibrations of the system, pertaining to take-up judder conditions. Such an in-depth investigation has not hitherto been reported in literature. The paper shows that take-up judder is omnipresent under all clutch engagement conditions, but its poignancy is most evident at cold surface temperatures. It is also shown that the transient judder response has a broader spectral content that is generally acknowledged.

Cutting force monitoring is an important technology for tool condition monitoring. However, a high precision and wideband cutting force estimation, including cross-feed components, with a sensorless approach of the ball-screw-driven stage, is still challenging because of its multiple structural modes and non-linear friction. This study proposes a process monitoring technique that independently estimates the cutting force components in rigid body and in vibration mode coordinate systems, based on multi-encoder signals. In the rigid body mode, the cutting force components were estimated by extracting the static rigid-body motion. In the vibration mode, the cutting force was estimated by using the relative displacement, velocity, and acceleration between the motor and the table. The estimation accuracy of the cutting force in feed and cross-feed directions was evaluated through several end milling tests. In the rigid body mode, a temporal variation of the feed force components was observed. However, high-frequency variations irrelevant to the cutting force were included because of variations in motor current, which had position/rotation-dependent characteristics. On the other hand, in the vibration mode, it was possible to estimate both feed and cross-feed components with less than maximum static friction force, including high harmonics.

Purpose The purpose of this paper is to present a mathematical model of one very flexible transport category airplane whose structural dynamics was modeled with the strain-based formulation. This model can be used for the analysis of couplings between the flight dynamics and structural dynamics. Design/methodology/approach The model was developed with the use of Hamiltonian mechanics and strain-based formulation. Nonlinear flight dynamics, nonlinear structural dynamics and inertial couplings are considered. Findings The mathematical model allows the analysis of effects of high structural deformations on airplane flight dynamics. Research limitations/implications The mathematical model has more than 60 degrees of freedom. The computational burden is too high, if compared to the traditional rigid body flight dynamics simulations. Practical implications The mathematical model presented in this work allows a detailed analysis of the couplings between flight dynamics and structural dynamics in very flexible airplanes. The better comprehension of these couplings will contribute to the development of flexible airplanes. Originality/value This work presents the application of nonlinear flight dynamics-nonlinear structural dynamics-strain-based formulation (NFNS_s) methodology to model the flight dynamics of one very flexible transport category airplane. This paper addresses also the way as the analysis of results obtained in nonlinear simulations can be made. Comparisons of the NFNS_s and nonlinear flight dynamics-linear structural dynamics methodologies are presented in this work.

In this study, a new analytical model is proposed for estimating natural frequencies of retaining walls, and accordingly three closed-form formulas are presented for calculating the first three natural frequencies. In the first step, rigid body motion of retaining walls is taken into account and two closed-form formulas for calculating natural frequencies of the rigid mode of deformation are presented via exact solution. Next, applying the energy method, a new closed-form formula is developed for calculating the natural frequency of the flexural deformation mode. Another innovation of this paper is the modeling of the foundation soil with both torsional and translational springs that make it possible to consider rocking and sliding modes for retaining wall motion. Additionally, the effect of backfill soil interaction is taken into consideration by massless translational springs along the wall. The results thus obtained from the proposed formulas are then compared with numerical analysis using ANSYS software, and a good agreement was observed.

This paper presents a novel development of lower limb exoskeleton, which is named as CASWELL, and its repetitive learning control design for movement assistance. CASWELL has five degrees of freedom per leg, two of which are driven by linear single-rod electrohydraulic actuators. First, the mechanical structure and embedded electronic system are constructed, respectively. Second, by incorporating the systems of rigid body and electrohydraulic actuators, the complete dynamics of CASWELL are analyzed and modeled. Third, under the framework of backstepping design, a repetitive learning control scheme is presented to address the periodic tracking control of lower limbs of exoskeleton, where the learning convergence of the closed-loop system is proved rigorously in a Lyapunov way. Finally, the proposed controller is implemented in the embedded electronic system via a 32-bit microcontroller, and tested on the developed CASWELL. The experimental results are given to demonstrate the performance of the whole exoskeleton system.

The paper presents a new modeling of the behavior of an underwater vehicle (UV) operating in the littoral sea, including the umbilical cable (UC) effect, where we derive a new simulation method of the full equations of the combined rigid body motion of a UV and flexible motion of the UC. In the modeling of flexible UC dynamics, we establish the governing equations of the UC dynamics based on the catenary equation method, and apply the shooting method to solve the two-point boundary value problem of the catenary equation. Using this, we propose a new formulation and solution of the governing equations to estimate the space position and forces of the UC end point under the action of concentrated and distributed forces due to underwater currents. We propose a new mathematical model on the hydrodynamics of a UV affected by the UC dynamics. For this, we map the applied forces of the UC to the dynamics of the UV through rotation matrices, and perform computer simulations to analyze the derived modeling of the UV affected by the UC dynamics. We perform simulations on the UV motion, including surge, heave, sway, and turning motions, for the cases with the UC and without the UC effect, and discuss their results.

This paper is focused on the relationship between rigid body translation and rigid body precession in a squeeze film damper–rigid-rotor system with unsymmetrical stiffness supports. Two cases are considered: the precession motion non-resonance and internal resonance when translation motion occur primary resonant. In the first case, the amplitudes of translation and precession can be connected with an integration parameter about rotor parameters such as geometric size, stiffness, and mass. Some combination of system parameters will make the amplitudes of precession motion reach the same magnitude of the amplitudes of translation motion, so this integration parameter become an index to reflect the precessional motion degree, it is can be used to judge the feasibility of neglecting processional motion and simplifying asymmetry rotor as reasonable symmetry model. In the second case, the translation motion and precessional motion are strongly coupled, the vibration energy transfer between two kind of motion and the system occur internal resonant, which is possible appear in the rotor with cantilever disk. Each of case may appear nonlinear phenomenon, which is closely related with system parameters. The bifurcation analysis by using singularity methods is carried out to delimit the range of applicative operation parameters to avoid harmful phenomenon in unsymmetrical rotor system. The results of this paper provide a theoretical foundation for the convenient model simplification judgment and parameters optimization of the squeeze film damper-unsymmetrical rotor systems.

An integrated guidance and feedback control scheme for steering an underactuated vehicle through desired waypoints in three-dimensional space, is developed here. The underactuated vehicle is modeled as a rigid body with four control inputs. These control inputs actuate the three degrees of freedom of rotational motion and one degree of freedom of translational motion in a vehicle body-fixed coordinate frame. This actuation model is appropriate for a wide range of underactuated vehicles including spacecraft with internal attitude actuators, vertical take-off and landing (VTOL) aircraft, fixed-wing multirotor unmanned aerial vehicles (UAVs), maneuverable robotic vehicles, etc. The guidance problem is developed on the special Euclidean group of rigid body motions, SE(3), in the framework ofgeometric mechanics, which represents the vehicle dynamics globally on this configuration manifold. The integrated guidance and control algorithm selects the desired trajectory for the translational motion that passes through the given waypoints, and the desired trajectory for the attitude based on the desired thrust direction to achieve the translational motion trajectory. A feedback control law is then obtained to steer the underactuated vehicle towards the desired trajectories in translation and rotation. This integrated guidance and control scheme takes into account known bounds on control inputs and generates a trajectory that is continuous and at least twice differentiable, which can be implemented with continuous and bounded control inputs. The integrated guidance and feedback control scheme is applied to an underactuated quadcopter UAV to autonomously generate a trajectory through a series of given waypoints in SE(3) and track the desired trajectory in finite time. The overall stability analysis of the feedback system is addressed. Discrete time models for the dynamics and control schemes of the UAV are obtained in the form of Lie group variational integrators using the discrete Lagrange-d’Alembert principle. Almost global asymptotic stability of the feedback system over its state space is shown analytically and verified through numerical simulations.

Some groups of fish have evolved to generate propulsion using undulatory elongated fins while maintaining a relatively rigid body. The fins run along the body axis and can be dorsal, ventral, dorso...