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Applying a two degree of freedom model for drive-by identification
Bayer, Jan
A new concept of drive-by identification is examined applying the analogy with a Two Degree Of Freedom (DOF) system where the bridge is considered the ground-supported spring-mass and the moving spring-mass the second DOF. The response of the moving spring-mass is simulated on a bridge model using different road profiles and compared to parameters of the corresponding two DOF system. The focus is the spectral shift that can be observed on the moving spring-mass during its passage along the bridge and could possibly be applied for drive-by identification. The accuracy mainly depends on the relation of the moving spring-mass to the bridge mass and the relation between the natural frequency of the spring-mass and those of the bridge. The simulations showed that road profile can significantly reduce the accuracy of identified results, which imposes limits on practical applications.
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Identification of quasiperiodic processes in the vicinity of the resonance
Fischer, Cyril ; Náprstek, Jiří
In nonlinear dynamical systems, strong quasiperiodic beating effects appear due to combination of self-excited and forced vibration. The presence of symmetric or asymmetric beatings indicates an exchange of energy between individual degrees of freedom of the model or by multiple close dominant frequencies. This effect is illustrated by the case of the van der Pol equation in the vicinity of resonance. The approximate analysis of these nonlinear effects uses the harmonic balance method and the multiple scale method.
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Consistency of mathematical and experimental model of the autoparametric system
Fischer, Cyril ; Náprstek, Jiří
This paper presents a long-overdue comparison of data obtained from experimental investigation of a spherical vibration absorber with the results of two mathematical models of the motion of a heavy sphere in a spherical surface. It shows that the danger posed by the potentially unstable self-parametric nature of the mathematical system is not too great in the case of realistic configurations, and that the values of the parameters describing the realistic structures remain within intervals corresponding to the stable behaviour of the absorber.
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Analysis suggestion for vehicle scanning method
Bayer, Jan
An analytical approach is suggested that can be conveniently applied in the framework of the Vehicle scanning method (VSM). It assumes that the modal parameters of a bridge will be imported from a finite element (FE) program into MATLAB, where the structural response caused by a moving mass and a moving spring mass is solved using coupling equations and numerical integration. A mathematical formulation of the solution is presented together with a short numerical case study that compares the results to a traditional closed form solution. It is shown that when comparing both forms of analysis the suggested approach is more accurate in the case of slow velocities of the passing sprung mass. Other advantages are that the method allows for the mass of the vehicle or (tractor) towing vehicle and a damping \nto be included in the calculation. The user-friendly preprocessing in commercial FE programs can also be considered an advantage.
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Analyzing stochastic stability of a gyroscope through the stochastic Lyapunov function
Náprstek, Jiří ; Fischer, Cyril
The text delves into the application of first integrals in the construction of Lyapunov functions for analyzing the stability of dynamic systems in stochastic domains. It emphasizes the distinct characteristics of first integrals that warrant the introduction of additional constraints to ensure the essential properties required for a Lyapunov function. These constraints possess physical interpretations associated with system stability. The general approach to testing stochastic stability is illustrated using the example of a 3-degrees-of-freedom system representing a gyroscope.
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Adaptation of methods for cyclo-stationary processes for noisy structural health data
Fischer, Cyril ; Bayer, Jan ; Náprstek, Jiří ; Urushadze, Shota
In structural health analysis, various techniques, including indirect measurement via monitoring vehicles, often yield data with significant randomness and insufficient frequency separation. Conversely, the desired attributes under scrutiny are periodic in nature. Thus, methodologies designed to identify cyclo-stationary properties within noisy data can be adapted for such scenarios, assuming an adequate length of the recorded data.
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Construction of the Lyapunov function reflecting the physical properties of the model
Náprstek, Jiří ; Fischer, Cyril
Practical experience shows that the random excitation component can affect the system response and its dynamic stability not only negatively but also positively. Such mechanisms are usually developed heuristically and are often not sufficiently justified theoretically. The paper presents a possibility of using the properties of first integrals for the construction of a Lyapunov function for the analysis of a dynamic system stability in the stochastic domain. In such case, the Lyapunov function itself contains information on the examined system and, consequently, it is able to provide a more detailed insight into the system stability properties. The procedure is illustrated by a nonlinear SDOF example.
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Analysis of van der Pol equation on slow time scale for combined random and harmonic excitation
Náprstek, Jiří ; Fischer, Cyril
Vortex shedding represents one of the most important processes that constantly attract the attention of experimental and theoretical research. A number of non-linear effects arise from the fluid-structure interaction. The non-stationary response in the vicinity of the lock-in region has a quasi-periodic character, beating frequency of which varies considerably with the distance from the lock-in frequency. This property is significantly affected by the assumption of combined random and harmonic excitation. This paper describes several details that contribute to the probabilistic characteristics of the system on a time-slow scale using partial response amplitudes.
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Application of first integrals in the construction of the Lyapunov function for the random response stability testing
Náprstek, Jiří ; Fischer, Cyril
The paper deals with a possibility of using the properties of first integrals for the construction of Lyapunov function for the analysis of a dynamic system stability in the stochastic domain. It points out certain characteristics of first integrals resulting in the necessity to introduce additional constraints to assure the principal properties of the Lyapunov function. A number of these constraints has their physical interpretation with reference to system stability. The advantage of this method constructing the Lyapunov function consists in the fact that the Lyapunov function itself contains information on the examined system and, consequently, it is not merely a positive definite function without any relation to the actual case concerned. The presented theory finds application in many dynamical systems. The procedure is illustrated by a nonlinear SDOF example.
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