scholarly journals Non-Linear Oscillations and Beats in the Beta Canis Majoris Stars

1993 ◽  
Vol 134 ◽  
pp. 73-76
Author(s):  
A. S. Baranov
Keyword(s):  
Incompressible Fluid ◽  
Equatorial Plane ◽  
Equations Of Motion ◽  
Critical Evaluation ◽  
Oscillation Theory ◽  
Ideal Incompressible Fluid ◽  
Equilibrium Figure ◽  
Theory Analysis ◽  
Oscillation Modes ◽  
Non Linear

Notwithstanding a great number of hypotheses, suggested for explaining superpositions of the light- and of the velocity variations of the ß Canis Majoris stars, no one of these does it satisfactorily. Possibly it is due to an inadequate elaboration of the non-linearly oscillation theory. Analysis and critical evaluation of the existing hypotheses are given by Mel’nikov and Popov (1970). Our explanation consists in existence of close frequencies corresponding to various oscillation modes which are non-linearly interacting.Equations of motion of an ideal incompressible fluid under condition of preserving the equilibrium figure symmetry with respect to the equatorial plane (lateral oscillations) have the form (Baranov 1988):

Modeling the Climber Fall Arrest Dynamics

2005 ◽  
Author(s):  
Lionel Manin ◽  
Jarir Mahfoudh ◽  
Matthieu Richard ◽  
David Jauffres
Keyword(s):  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Close Approximation ◽  
Non Linear ◽  
The Future ◽  
Safety Recommendations ◽  
Improved Design ◽  
Fall Arrest

Sports and mountaineering activities are becoming more and more popular. Equipment constructors seek to develop products and devices that are easy to use and that take into account all safety recommendations. PETZL and INSA have collaborated to develop a model for the simulation of displacements and efforts involved during the fall of a climber in the “safety chain”. The model is based on the classical equations of motion, in which climber and belayer are considered as rigid masses, while the rope is considered as a series of non-linear stiffness passing through several devices as brakes and runners. The main goal is to predict the forces in the rope and on the return anchor at the first rebound of the fall. Experiments were first performed in order to observe and determine the dynamic characteristics of the rope, and then to validate results stemming from simulations. Several fall configurations are simulated, and the model performs satisfactorily. It also provides a close approximation of the phenomena observed experimentally. The model enables the assessment of the existing equipments and the improved design of the future one.

GPR-based novel approach for non-linear aerodynamic modelling from flight data

2018 ◽  
Vol 123 (1259) ◽  
pp. 79-92
Author(s):  
A. Kumar ◽  
A. K. Ghosh
Keyword(s):  
Aerodynamic Force ◽  
Equations Of Motion ◽  
Gaussian Process Regression ◽  
Likelihood Estimation ◽  
Flight Data ◽  
Novel Approach ◽  
Non Linear ◽  
Research Aircraft ◽  
Novel Method ◽  
Aerodynamic Modelling

ABSTRACTIn this paper, a Gaussian process regression (GPR)-based novel method is proposed for non-linear aerodynamic modelling of the aircraft using flight data. This data-driven regression approach uses the kernel-based probabilistic model to predict the non-linearity. The efficacy of this method is examined and validated by estimating force and moment coefficients using research aircraft flight data. Estimated coefficients of aerodynamic force and moment using GPR method are compared with the estimated coefficients using maximum-likelihood estimation (MLE) method. Estimated coefficients from the GPR method are statistically analysed and found to be at par with estimated coefficients from MLE, which is popularly used as a conventional method. GPR approach does not require to solve the complex equations of motion. GPR further can be directed for the generalised applications in the area of aeroelasticity, load estimation, and optimisation.

Non-Linear Vibrations of Plates Under Thermal and Mechanical Loads

2005 ◽  
Author(s):  
P. Ribeiro
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Implicit Time ◽  
Linear Elastic ◽  
Time Integration Method ◽  
Thermal Fields ◽  
Non Linear ◽  
Linear Vibrations ◽  
The Time Domain ◽  
Constitutive Material

The geometrically non-linear vibrations of plates under the combined effect of thermal fields and mechanical excitations are analyzed. With this purpose, an accurate model based on a p-version, hierarchical, first-order shear deformation finite element is employed. The constitutive material of the plates is linear elastic and isotropic. The equations of motion are solved in the time domain by an implicit time integration method. The temperature and the amplitude of the mechanical excitation are varied, and transitions from periodic to non-periodic motions are found.

Non-Linear Dynamic Analysis of a Cable-Stayed Beam

2005 ◽  
Author(s):  
Carlos E. N. Mazzilli ◽  
Franz Rena´n Villarroel Rojas
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Multiple Scale ◽  
Local Mode ◽  
Numerical Application ◽  
Global Mode ◽  
Lower Mode ◽  
Reduced Equations ◽  
External Resonance ◽  
Non Linear

The dynamic behaviour of a simple clamped beam suspended at the other end by an inclined cable stay is surveyed in this paper. The sag due to the cable weight, as well as the non-linear coupling between the cable and the beam motions are taken into account. The formulation for in-plane vibration follows closely that of Gattulli et al. [1] and confirms their findings for the overall features of the equations of motion and the system modal properties. A reduced non-linear mathematical model, with two degrees of freedom, is also developed, following again the steps of Gattulli and co-authors [2,3]. Hamilton’s Principle is evoked to allow for the projection of the displacement field of both the beam and the cable onto the space defined by the first two modes, namely a “global” mode (beam and cable) and a “local” mode (cable). The method of multiple scales is then applied to the analysis of the reduced equations of motion, when the system is subjected to the action of a harmonic loading. The steady-state solutions are characterised in the case of internal resonance between the local and the global modes, plus external resonance with respect to either one of the modes considered. A numerical application is presented, for which multiple-scale results are compared with those of numerical integration. A reasonable qualitative and quantitative agreement is seen to happen particularly in the case of external resonance with the higher mode. Discrepancies should obviously be expected due to strong non-linearities present in the reduced equations of motion. That is specially the case for external resonance with the lower mode.

The Role of Modal Coupling on the Non-Linear Response of Cylindrical Shells Subjected to Dynamic Axial Loads

2000 ◽  
Author(s):  
Paulo B. Gonçalves ◽  
Zenón J. G. N. Del Prado
Keyword(s):  
Dynamic Instability ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Parametric Instability ◽  
Compressive Load ◽  
Basins Of Attraction ◽  
Dynamic Component ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Low Dimensional

Abstract This paper discusses the dynamic instability of circular cylindrical shells subjected to time-dependent axial edge loads of the form P(t) = P0+P1(t), where the dynamic component p1(t) is periodic in time and P0 is a uniform compressive load. In the present paper a low dimensional model, which retains the essential non-linear terms, is used to study the non-linear oscillations and instabilities of the shell. For this, Donnell’s shallow shell equations are used together with the Galerkin method to derive a set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. To study the non-linear behavior of the shell, several numerical strategies were used to obtain Poincaré maps, stable and unstable fixed points, bifurcation diagrams and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions: parametric instability and escape from the pre-buckling potential well. The numerical results obtained from this investigation clarify the conditions, which control whether or not instability may occur. This may help in establishing proper design criteria for these shells under dynamic loads, a topic practically unexplored in literature.

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