scholarly journals Likely equilibria of the stochastic Rivlin cube

2019 ◽  
Vol 377 (2144) ◽  
pp. 20180068 ◽  
Author(s):  
L. Angela Mihai ◽  
Thomas E. Woolley ◽  
Alain Goriely
Keyword(s):  
Applied Mathematics ◽  
Experimental Tests ◽  
Constitutive Law ◽  
Elastic Parameters ◽  
Theme Issue ◽  
Stochastic Version ◽  
The Stability ◽  
Material Constitutive Law ◽  
Standard Probability ◽  
Data Variation

The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the elastic parameters are random variables following standard probability laws. Uncertainties in these parameters may arise, for example, from inherent data variation between different batches of homogeneous samples, or from different experimental tests. As for the deterministic elastic problem, we consider the following questions: what are the likely equilibria and how does their stability depend on the material constitutive law? In addition, for the stochastic model, the problem is to derive the probability distribution of deformations, given the variability of the parameters. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

Towards a new design with generic modeling and adaptive control of a transformable quadrotor

2021 ◽  
pp. 1-31
Author(s):  
S.H. Derrouaoui ◽  
Y. Bouzid ◽  
M. Guiatni
Keyword(s):  
Adaptive Control ◽  
Control Strategy ◽  
Experimental Tests ◽  
Generic Model ◽  
System Control ◽  
System A ◽  
Viable Solution ◽  
Generic Modeling ◽  
Adaptive Control Strategy ◽  
The Stability

Abstract Recently, transformable Unmanned Aerial Vehicles (UAVs) have become a subject of great interest in the field of flying systems, due to their maneuverability, agility and morphological capacities. They can be used for specific missions and in more congested spaces. Moreover, this novel class of UAVs is considered as a viable solution for providing flying robots with specific and versatile functionalities. In this paper, we propose (i) a new design of a transformable quadrotor with (ii) generic modeling and (iii) adaptive control strategy. The proposed UAV is able to change its flight configuration by rotating its four arms independently around a central body, thanks to its adaptive geometry. To simplify and lighten the prototype, a simple mechanism with a light mechanical structure is proposed. Since the Center of Gravity (CoG) of the UAV moves according to the desired morphology of the system, a variation of the inertia and the allocation matrix occurs instantly. These dynamics parameters play an important role in the system control and its stability, representing a key difference compared with the classic quadrotor. Thus, a new generic model is developed, taking into account all these variations together with aerodynamic effects. To validate this model and ensure the stability of the designed UAV, an adaptive backstepping control strategy based on the change in the flight configuration is applied. MATLAB simulations are provided to evaluate and illustrate the performance and efficiency of the proposed controller. Finally, some experimental tests are presented.

Numerical and Experimental Approaches to Investigate the Stability of a Motorcycle Vehicle

2006 ◽  
Author(s):  
Federico Cheli ◽  
Marco Bocciolone ◽  
Marco Pezzola ◽  
Elisabetta Leo
Keyword(s):  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Experimental Tests ◽  
Roll Angle ◽  
Longitudinal Motion ◽  
Reference Trajectory ◽  
Steering Angle ◽  
Steady State Condition ◽  
The Stability ◽  
Linearized Model

The study of motorcycle’s stability is an important task for the passenger’s safety. The range of frequencies involved for the handling stability is lower than 10 Hz. A numerical model was developed to access the stability of a motorcycle vehicle in this frequency range. The stability is analysed using a linearized model around the straight steady state condition. In this condition, the vehicle’s vertical and longitudinal motion are decoupled, hence the model has only four degrees of freedom (steering angle, yaw angle, roll angle and lateral translation), while longitudinal motion is imposed. The stability was studied increasing the longitudinal speed. The input of the model can be either a driver input manoeuvre (roll angle) or a transversal component of road input able to excite the vibration modes. The driver is introduced in the model as a steering torque that allows the vehicle to follow a reference trajectory. To validate the model, experimental tests were done. To excite the vehicle modes, the driver input was not taken into account considering both the danger for the driver and the repeatability of the manoeuvre. Two different vehicle configurations were tested: vehicle 1 is a motorcycle [7] and vehicle 2 is a scooter. Through the use of the validated model, a sensitivity analysis was done changing structural (for example normal trail, steering angle, mass) and non structural parameters (for example longitudinal speed).

Influence of Axial Excitations and of Boundary Conditions on the Parametric Instability of a Beam

1995 ◽  
Author(s):  
Régis Dufour ◽  
Alain Berlioz ◽  
Thomas Streule
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

Abstract In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It shows that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

scholarly journals Multibody model of fruit harvesting trucks: comparison with experimental data and rollover analysis

2018 ◽  
Vol 49 (2) ◽  
pp. 92-99 ◽  
Author(s):  
Stefano Melzi ◽  
Edoardo Sabbioni ◽  
Michele Vignati ◽  
Maurizio Cutini ◽  
Massimo Brambilla ◽  
...  
Keyword(s):  
Experimental Tests ◽  
Soil Stiffness ◽  
Safety Issues ◽  
Multibody Model ◽  
Centre Of Gravity ◽  
Rollover Risk ◽  
Speed Up ◽  
The Stability ◽  
Italian National Institute ◽  
Comparison With Experimental Data

Fruit harvesting trucks are used to easy and speed-up the work of agricultural operators. These vehicles are provided with a moving cargo bed, which can be raised up to 3 meters from the ground so that workers are closer to the plants top. Due to factors like height of centre of gravity and operation on soft and irregular soil, these vehicles present several safety issues. This research, carried out inside a project funded by INAIL (Italian National Institute for Insurance against Accidents at Work), analysed the stability of fruit harvesting trucks with particular focus on rollover risk. Experimental tests were carried out to characterise the response of these vehicles. Multibody models of two trucks were then developed and used to determine the rollover angle along a generic direction considering the effect of vehicle configuration and of tire-soil stiffness.

scholarly journals Research on Computer Modeling of Fractional Differential Equation Applied Mathematics

2021 ◽  
Vol 2083 (3) ◽  
pp. 032036
Author(s):  
Linlin Su
Keyword(s):  
Differential Equation ◽  
Time Series ◽  
Hopf Bifurcation ◽  
Equilibrium Solution ◽  
Applied Mathematics ◽  
Bifurcation Diagrams ◽  
Financial Systems ◽  
Fractional Differential ◽  
The Stability ◽  
Evolution Behavior

Abstract This paper qualitatively analyzes the stability of the equilibrium solution of a class of fractional chaotic financial systems and the conditions for the occurrence of Hopf bifurcation, and uses the Adams-Bashford-Melton predictive-correction finite difference method to pass the analysis Bifurcation diagrams, phase diagrams, and time series diagrams are used to simulate the complex evolution behavior of the system.

Design of a Force Feedback Chatter Control System

1972 ◽  
Vol 94 (1) ◽  
pp. 5-10 ◽  
Author(s):  
C. Nachtigal
Keyword(s):  
Machine Tool ◽  
Frequency Domain ◽  
Transient Response ◽  
Force Feedback ◽  
Design Procedure ◽  
Experimental Tests ◽  
Work Piece ◽  
Regenerative Chatter ◽  
Chatter Control ◽  
The Stability

The analysis of machine tool chatter from frequency domain considerations is generally accepted as a valid representation of the regenerative chatter phenomenon. However, active control of regenerative chatter is still in its embryonic stage. It was established in reference [2] that a measurement of the cutting force could be effectively used in conjunction with a controller and a tool position servo system to increase the stability of an engine lathe and to improve its transient response. This paper presents the design basis for such a system, including both analytical and experimental considerations. The design procedure stems from a real part stability criterion based on the work by Merritt [1]. Because of the unknown variability in the dynamics of a machine tool system, the controller parameters were chosen to accomodate some mismatch between structure and tool servo dynamics. Experimental tests to determine the stability zone of the controlled machine tool system qualitatively confirmed the analytical design results. The experimental results were consistent in that the transient response tests confirmed the frequency domain stability tests. It was also demonstrated experimentally that the equivalent static stiffness of a flexible work-piece system could be substantially increased.

scholarly journals From atomistic interfaces to dendritic patterns

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170210 ◽  
Author(s):  
P. K. Galenko ◽  
D. V. Alexandrov
Keyword(s):  
Computational Modelling ◽  
Experimental Tests ◽  
Theoretical Models ◽  
Boundary Integral ◽  
Transport Processes ◽  
Atomic Scale ◽  
Theme Issue ◽  
Two Phase ◽  
Field Methods ◽  
Atomistic Modelling

Transport processes around phase interfaces, together with thermodynamic properties and kinetic phenomena, control the formation of dendritic patterns. Using the thermodynamic and kinetic data of phase interfaces obtained on the atomic scale, one can analyse the formation of a single dendrite and the growth of a dendritic ensemble. This is the result of recent progress in theoretical methods and computational algorithms calculated using powerful computer clusters. Great benefits can be attained from the development of micro-, meso- and macro-levels of analysis when investigating the dynamics of interfaces, interpreting experimental data and designing the macrostructure of samples. The review and research articles in this theme issue cover the spectrum of scales (from nano- to macro-length scales) in order to exhibit recently developing trends in the theoretical analysis and computational modelling of dendrite pattern formation. Atomistic modelling, the flow effect on interface dynamics, the transition from diffusion-limited to thermally controlled growth existing at a considerable driving force, two-phase (mushy) layer formation, the growth of eutectic dendrites, the formation of a secondary dendritic network due to coalescence, computational methods, including boundary integral and phase-field methods, and experimental tests for theoretical models—all these themes are highlighted in the present issue. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

The Stability of a Two-Layer Inviscid Flow Between an Elastic Layer and a Rigid Boundary

1999 ◽  
Vol 66 (1) ◽  
pp. 197-203 ◽  
Author(s):  
P. J. Schall ◽  
J. P. McHugh
Keyword(s):  
Elastic Layer ◽  
Inviscid Flow ◽  
Elastic Parameters ◽  
Rigid Boundary ◽  
Two Fluids ◽  
Coating Flow ◽  
Fluid Layers ◽  
Mode 2 ◽  
Layer Flow ◽  
The Stability

The linear stability of two-layer flow over an infinite elastic substraw is considered. The problem is motivated by coating flow in a printing press. The flow is assumed to be inviscid and irrotational. Surface tension between the fluid layers is included, but gravity is neglected. The results show two unstable modes: one mode associated with the interface between the elastic layer and the fluid (mode 1), and the other concentrated on the interface between the two fluids (mode 2). The behavior of the unstable modes is examined while varying the elastic parameters, and it is found that mode 1 can be made stable, but mode 2 remains unstable at small wavenumber, similar to the classic Kelvin—Helmholtz mode.

CFD Methodology for the Simulation of Mixture Formation of High Performance PFI Engines

2011 ◽  
Author(s):  
Claudio Forte ◽  
Gian Marco Bianchi ◽  
Enrico Corti ◽  
Gaspare Argento ◽  
Stefano Fantoni
Keyword(s):  
High Performance ◽  
Experimental Tests ◽  
Critical Issue ◽  
Spark Ignition Engines ◽  
Mixture Formation ◽  
Injection Process ◽  
Cfd Models ◽  
Cycle Simulation ◽  
Spark Plug ◽  
The Stability

Mixture composition strongly influences the stability of combustion of spark ignition engines. The control of air to fuel ratio at ignition is a critical issue for high performance engines: due to the low stroke-to-bore ratio the maximum power is reached at very high regimes, letting little time to the fuel to evaporate and mix with air. The aim of this work is to present a CFD methodology for the evaluation of mixture formation applied to a Ducati high performance engine. The phenomena involved in the process are highly heterogeneous, and particular care must be taken to the choice of CFD models and their validation. In the present work all the main models involved in the simulations are validated against experimental tests available in the literature, selected based on the similarity of physical conditions with those of the engine configuration under analysis. The multi-cycle simulation methodology here presented reveals to be a useful tool for the evaluation of the mixture quality around the spark plug at ignition, allowing a parametric analysis of the effects of the injection process on engine output.

Dynamic Stability of Unidirectional Fiber-Reinforced Viscoelastic Composite Plates

1989 ◽  
Vol 42 (11S) ◽  
pp. S39-S47 ◽  
Author(s):  
N. K. Chandiramani ◽  
L. Librescu
Keyword(s):  
Shear Deformation ◽  
Dynamic Stability ◽  
Stability Problem ◽  
Micromechanical Model ◽  
Shear Deformation Theory ◽  
Constitutive Law ◽  
Fiber Reinforced ◽  
Viscoelastic Composite ◽  
Unidirectional Fiber ◽  
The Stability

This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a 3-D viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi’s micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.

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