Damping Effects Induced by a Mass Moving along a Pendulum

The experimental study of damping in a time-varying inertia pendulum is presented. The system consists of a disk travelling along an oscillating pendulum: large swinging angles are reached, so that its equation of motion is not only time-varying but also nonlinear. Signals are acquired from a rotary sensor, but some remarks are also proposed as regards signals measured by piezoelectric or capacitive accelerometers. Time-varying inertia due to the relative motion of the mass is associated with the Coriolis-type effects appearing in the system, which can reduce and also amplify the oscillations. The analytical model of the pendulum is introduced and an equivalent damping ratio is estimated by applying energy considerations. An accurate model is obtained by updating the viscous damping coefficient in accordance with the experimental data. The system is analysed through the application of a subspace-based technique devoted to the identification of linear time-varying systems: the so-called short-time stochastic subspace identification (ST-SSI). This is a very simple method recently adopted for estimating the instantaneous frequencies of a system. In this paper, the ST-SSI method is demonstrated to be capable of accurately estimating damping ratios, even in the challenging cases when damping may turn to negative due to the Coriolis-type effects, thus causing amplifications of the system response.

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Biorthogonal Wavelet Based Identification of Fast Linear Time-Varying Systems—Part II: Algorithms and Performance Analysis12

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1409550 ◽

2000 ◽

Vol 123 (4) ◽

pp. 593-600 ◽

Cited By ~ 8

Author(s):

Haipeng Zhao ◽

Joseph Bentsman

Keyword(s):

System Dynamics ◽

High Speed ◽

Linear Time ◽

A Priori ◽

Time Varying ◽

Function Decomposition ◽

Time Varying Systems ◽

Random Disturbances ◽

And Performance ◽

Short Time

The present work proposes a new class of algorithms for identification of fast linear time-varying systems on short time intervals, based on the biorthogonal function decomposition. When certain features of the system dynamics are known a priori, the algorithms admit their embedding into the identification procedure through the choice of the matching bases, yielding the rapidly convergent identification laws. The speed-up is attained via utilizing both time and frequency localized bases, permitting identification of fewer coefficients without noticeable loss of accuracy. Simulation shows that the resulting high speed identification algorithms can reject small persistent random disturbances as well as capture the fast changes in system dynamics. The algorithm development is based on the results of Part I where it is shown that the sets of all bounded-input-bounded-output (BIBO) stable or l2-stable linear discrete-time-varying (LTV) systems are Banach spaces, and modeling and identification of these systems are reducible to linear approximation problems in a Banach space setting.

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Instantaneous Modal Parameter Identification of Linear Time-Varying Systems Based on Chirplet Adaptive Decomposition

Shock and Vibration ◽

10.1155/2019/1475981 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Jie Zhang ◽

Zhiyu Shi

Keyword(s):

Parameter Identification ◽

Energy Analysis ◽

Linear Time ◽

Damping Ratio ◽

Energy Concentration ◽

Time Varying ◽

Modal Parameter ◽

Modal Parameter Identification ◽

Time Frequency ◽

Time Varying Systems

Instantaneous modal parameter identification of time-varying dynamic systems is a useful but challenging task, especially in the identification of damping ratio. This paper presents a method for modal parameter identification of linear time-varying systems by combining adaptive time-frequency decomposition and signal energy analysis. In this framework, the adaptive linear chirplet transform is applied in time-frequency analysis of acceleration response for its higher energy concentration, and the response of each mode can be adaptively decomposed via an adaptive Kalman filter. Then, the damping ratio of the time-varying systems is identified based on energy analysis of component response signal. The proposed method can not only improve the accuracy of instantaneous frequency extraction but also ensure the antinoise ability in identifying the damping ratio. The efficiency of the method is first verified through a numerical simulation of a three-degree-of-freedom time-varying structure. Then, the method is demonstrated by comparing with the traditional wavelet and time-domain peak method. The identified results illustrate that the proposed method can obtain more accurate modal parameters in low signal-to-noise ratio (SNR) scenarios.

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Time-Varying Output-Only Identification of a Cracked Beam

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.413-414.643 ◽

2009 ◽

Vol 413-414 ◽

pp. 643-650 ◽

Cited By ~ 6

Author(s):

A. Bellino ◽

Luigi Garibaldi ◽

Stefano Marchesiello

Keyword(s):

Subspace Identification ◽

Open Crack ◽

Moving Mass ◽

Time Varying ◽

Cracked Beam ◽

Stochastic Subspace Identification ◽

Identification Method ◽

Time Varying Systems ◽

Output Only ◽

Short Time

In this paper a time-varying identification method is presented, in order to detect the presence of an open crack in a beam with a moving mass travelling on it. The ratio between the considered moving mass and the total mass of the beam is high, thus the identified modal frequencies of the whole structure are time-varying. This situation often occurs when considering the dynamic interaction beetween a train and a bridge and specific identification tools must be used. It is shown that the identification method, referred to here as Short-Time Stochastic Subspace Identification, can give information about the presence of damage in case of time-varying systems.

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Controllability of Linear Time Varying Systems: New Algebraic Criteria

1993 American Control Conference ◽

10.23919/acc.1993.4793155 ◽

1993 ◽

Author(s):

Hngo Leiva ◽

Brad Lehman

Keyword(s):

Linear Time ◽

Time Varying ◽

Time Varying Systems

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The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽

10.3390/eng2010008 ◽

2021 ◽

Vol 2 (1) ◽

pp. 99-125

Author(s):

Edward W. Kamen

Keyword(s):

Discrete Time ◽

Initial Conditions ◽

Linear Time ◽

Order Term ◽

Initial Time ◽

Time Varying ◽

Varying Coefficients ◽

Time Signals ◽

Time Varying Systems ◽

Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

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