Vibration-based methods for structural and machinery fault diagnosis based on nonlinear dynamics tools

This study explains and demonstrates the utilisation of different nonlinear-dynamics-based procedures for the purposes of structural health monitoring as well as for monitoring of robot joints

Vibration-based damage detection in plates by using time series analysis

This paper deals with the problem for vibration health monitoring (VHM) in structures with nonlinear dynamic behaviour. It aims to introduce two viable VHM methods that use large amplitude vibrations and are based on nonlinear time series analysis. The methods suggested explore some changes in the state space geometry/distribution of structural dynamic response with damage and their use for damage detection purposes. One of the methods uses the statistical distribution of state space points on the attractor of a vibrating structure, while the other one is based on the Poincaré map of the state space projected dynamic response. In this paper both methods are developed and demonstrated for a thin vibrating plate. The investigation is based on finite element modelling of the plate vibration response. The results obtained demonstrate the influence of damage on the local dynamic attractor of the plate state space and the applicability of the proposed strategies for damage assessment. The approach taken in this study and the suggested VHM methods are rather generic and permit development and applications for other more complex nonlinear structures

Large amplitude vibrations and damage detection of rectangular plates

In this work, geometrically nonlinear vibrations of fully clamped rectangular plates are used to study the sensitivity of some nonlinear vibration response parameters to the presence of damage. The geometrically nonlinear version of the Mindlin plate theory is used to model the plate behaviour. Damage is represented as a stiffness reduction in a small area of the plate. The plate is subjected to harmonic loading with a frequency of excitation close to the first natural frequency leading to large amplitude vibrations. The plate vibration response is obtained by a pseudo-load mode superposition method. The main results are focussed on establishing the influence of damage on the vibration response of the plate and the change in the time-history diagrams and the Poincaré maps caused by the damage. Finally, a criterion and a damage index for detecting the presence and the location of the damage is proposed. The criterion is based on analyzing the points in the Poincaré sections of the damaged and healthy plate. Numerical results for large amplitude vibrations of damaged and healthy rectangular and square plates are presented and the proposed damage index for the considered cases is calculated. The criterion demonstrates quite good abilities to detect and localise damage

Analytical modeling and vibration analysis of partially cracked rectangular plates with different boundary conditions and loading

This study proposes an analytical model for vibrations in a cracked rectangular plate as one of the results from a program of research on vibration based damage detection in aircraft panel structures. This particular work considers an isotropic plate, typically made of aluminum, and containing a crack in the form of a continuous line with its center located at the center of the plate and parallel to one edge of the plate. The plate is subjected to a point load on its surface for three different possible boundary conditions, and one examined in detail. Galerkin's method is applied to reformulate the governing equation of the cracked plate into time dependent modal coordinates. Nonlinearity is introduced by appropriate formulations introduced by applying Berger's method. An approximate solution technique—the method of multiple scales—is applied to solve the nonlinear equation of the cracked plate. The results are presented in terms of natural frequency versus crack length and plate thickness, and the nonlinear amplitude response of the plate is calculated for one set of boundary conditions and three different load locations, over a practical range of external excitation frequencies

Dynamics of a Circular Mindlin Plate under Mechanical Loading and Elevated Temperature

Dynamics of a nonlinear circular Midlin plate is studied in the paper. The mathematical model represented by partial differential equations includes nonlinear geometrical terms resulted from large displacements. The plate is subjected to mechanical and thermal loadings. The dynamics of a coupled thermo-mechanical problem is reduced from partial to ordinary differential equations. Considering the first mode reduction and uniformly distributed temperature just a single nonlinear differential equation is obtained. The bifurcation analysis shows that elevated temperature shifts the rezonanse curve and new solutions arise. Depending on initial conditions this may lead to buckling phenomenon and then relatively small oscillations around this state, symmetric periodic oscillations of large amplitude, or irregular oscillations

Vibration Based Damage Detection of Rotating Beams

The early detection and localization of damages is essential for operation, maintenance and cost of the structures. Because the frequency of vibration cannot be controlled in real-life structures, the methods for damage detection should work for wide range of frequencies. In the current work, the equation of motion of rotating beam is derived and presented and the damage is modelled by reduced thickness. Vibration based methods which use Poincaré maps are implemented for damage localization. It is shown that for clamped-free boundary conditions these methods are not always reliable and their success depends on the excitation frequency. The shapes of vibration of damaged and undamaged beams are shown and it is concluded that appropriate selection criteria should be defined for successful detection and localization of damages

Dynamics of a Circular Mindlin Plate under Mechanical Loading and Elevated Temperature

Dynamics of a nonlinear circular Midlin plate is studied in the paper. The mathematical model represented by partial differential equations includes nonlinear geometrical terms resulted from large displacements. The plate is subjected to mechanical and thermal loadings. The dynamics of a coupled thermo-mechanical problem is reduced from partial to ordinary differential equations. Considering the first mode reduction and uniformly distributed temperature just a single nonlinear differential equation is obtained. The bifurcation analysis shows that elevated temperature shifts the rezonanse curve and new solutions arise. Depending on initial conditions this may lead to buckling phenomenon and then relatively small oscillations around this state, symmetric periodic oscillations of large amplitude, or irregular oscillations

Vortex-Induced Vibrations of an Elastic Micro-Beam with Gas Modeled by DSMC

The fluid–structure interaction is one of the most important coupled problems in mechanics. The topic is crucial for many high-technology areas. This work considers the interaction between an elastic obstacle and rarefied gas flow, seeking specific problems that arise during this interaction. The Direct Simulation Monte Carlo method was used to model the rarefied gas flow and the linear Euler–Bernoulli beam theory was used to describe the motion of the elastic obstacle. It turned out that the vibrations caused by the gas flow could provoke a resonance-like phenomenon when the frequency of vortex shedding of the flow was close to the natural frequency of the beam. This phenomenon could be useful in certain high-technology applications

A Reduced Model of a Thermo-Elastic Nonlinear Circular Plate

Nonlinear vibrations of a circular plate subjected to mechanical and thermal loadings are presented in the paper. A model of the plate is based on the extended Mindlin theory, taking into account nonlinear geometrical terms and acting heat uniformly distributed along the plate span. The dynamics of a coupled thermo-mechanical problem is reduced from a set of partial differential equations to ordinary differential equations. Considering oscillations around the first natural frequency just one mode reduction is proposed. The analysis shows that elevated temperature shifts the resonance curve and new post-buckling oscillations arise. Depending on initial conditions for the post-buckling state various scenarios of bifurcations take place and transient irregular oscillations may occur. The proposed one degree of freedom model shows a good agreement with response of the model based on three or five-modes reduction

Vortex-Induced Vibrations of an Elastic Micro-Beam with Gas Modeled by DSMC

The fluid–structure interaction is one of the most important coupled problems in mechanics. The topic is crucial for many high-technology areas. This work considers the interaction between an elastic obstacle and rarefied gas flow, seeking specific problems that arise during this interaction. The Direct Simulation Monte Carlo method was used to model the rarefied gas flow and the linear Euler–Bernoulli beam theory was used to describe the motion of the elastic obstacle. It turned out that the vibrations caused by the gas flow could provoke a resonance-like phenomenon when the frequency of vortex shedding of the flow was close to the natural frequency of the beam. This phenomenon could be useful in certain high-technology applications