On the use of Lagrange Multiplier State-Space Substructuring in dynamic substructuring analysis

Dias, R. S. O.; Martarelli, Milena; Chiariotti, Paolo

doi:10.1016/j.ymssp.2022.109419

Cited by 5 publications

(9 citation statements)

References 24 publications

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“…Hence, any kind of signal that excites frequencies included in the frequency band for which the dynamics of the system is relevant (i.e. approximately, from 20 Hz to 500 Hz (see [14], [15])) could have been used.…”

Section: Experimental Validation 31 Testing Campaignmentioning

confidence: 99%

“…Then, to obtain the modal parameters representative of the dynamics of the assembly for the other rubber mount temperatures of interest, we have exploited the ML-MM method to update the modal parameters estimated from the measured FRFs for T rb =14℃. Afterwards, by following the procedures described in [20], [26], state-space models representative of the dynamics of the system for rubber mount temperatures of 14℃, 20℃, 25℃, 30℃ and 35.2℃ were constructed by using the estimated modal parameters. Note that, the modal parameters were estimated by assuming a proportionally damped model.…”

Section: Computation Of the Linear Parameter Varying Modelmentioning

confidence: 99%

“…By performing this assumption, we have the guarantee that the residue matrices of the computed modal models will be purely imaginary. In this way, we make sure that the state-space models will obey Newton's second law (see [26]). If the modal parameters used to construct the state-space models have not been computed by assuming a proportionally damped modal model, we would be required to force them to verify Newton's second law by following the approach proposed in [27].…”

Section: Computation Of the Linear Parameter Varying Modelmentioning

confidence: 99%

“…The RCMs responsible for including the contribution of the lower out-of-band modes were set-up by selecting a value for their natural frequencies and damping ratios of 0.1 Hz and 0.1, respectively. Whereas, the RCMs responsible for including the contribution of the upper out-of-band modes were set-up by selecting a value for their natural frequencies and damping ratios of 1.5 × 10 3 Hz and 0.1, respectively (see, [20], [26]).…”

Section: Computation Of the Linear Parameter Varying Modelmentioning

confidence: 99%

“…The use of LPV models is indeed advantageous as it enables the characterization of assembled systems presenting time-varying dynamic behaviour subjected to any kind of excitation. In alternative, one may also think on exploiting these LPV models to characterize the dynamic behaviour of simple components presenting time-varying dynamic behaviour, which can then be included in the complete assembly through State-Space Substructuring (see, for instance, [12], [13], [14], [15]).…”

Section: Introductionmentioning

confidence: 99%

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On the prediction of the time-varying behaviour of dynamic systems by interpolating state-space models

Dias,

Martarelli,

Chiariotti

2024

J. Phys.: Conf. Ser.

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In this article, a local Linear Parameter Varying (LPV) model identification approach is exploited to analyze the dynamic behaviour of a structure whose dynamics varies over time. This structure is composed by two aluminum crosses connected by a rubber mount. To observe time-dependent variations on the dynamics of this assembly, it is placed in a climate chamber and submitted to a six minute temperature run-up. During this run-up the structure is continuously excited by a shaker. The load provided by this device is measured by a load cell, while six accelerometers are measuring the responses of the system. The temperatures of the air inside the climate chamber and at the surface of the mount are also continuously measured. It is found that during the performed temperature run-up, the rubber mount temperature increased from, roughly, 14℃ to, approximately, 35.2℃. By using the measured load provided by the shaker and the measured accelerations, Frequency Response Functions (FRFs) at five different rubber mount temperatures are computed. From each of these sets of FRFs, state-space models are estimated. Afterwards, these models are used to define an interpolating LPV model, which enables the computation of interpolated state-space models representative of the dynamics of the system at each time sample. It is found that by feeding the interpolated state-space models with the measured load, an accurate simulation of the measured accelerations is obtained. Moreover, by exploiting a joint input-state estimation algorithm with the interpolated state-space models and with the measured accelerations, a very good prediction of the applied load can be obtained. It is also shown that if the time dependency of the dynamics of the system is ignored, the results are less accurate.

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Section: Experimental Validation 31 Testing Campaignmentioning

confidence: 99%

Section: Computation Of the Linear Parameter Varying Modelmentioning

confidence: 99%

Section: Computation Of the Linear Parameter Varying Modelmentioning

confidence: 99%

Section: Computation Of the Linear Parameter Varying Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the prediction of the time-varying behaviour of dynamic systems by interpolating state-space models

Dias,

Martarelli,

Chiariotti

2024

J. Phys.: Conf. Ser.

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In-Situ Component-Based TPA for Time-Variant Dynamic Systems: A State-Space Formulation

Dias,

Martarelli,

Chiariotti

2023

Conference Proceedings of the Society for Experimental Mechanics Series

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In this article, a methodology to calculate equivalent forces by taking into account possible time-varying dynamic behaviour of the components under analysis is presented. This methodology is based on the use of the state-space realization of the in-situ component-based TPA method. To take into account possible time-varying dynamic behaviour of the systems under study, a local Linear Parameter Varying (LPV) model identification approach is used. This approach enables the computation of statespace models representative of the components at each time instant by interpolating a given set of Linear Time-Invariant (LTI) state-space models representative of the dynamics of the components under study for fixed operating conditions. By exploiting a numerical example, it is found that when dealing with structures presenting time-varying behaviour, accurate equivalent forces can be computed in time-domain by using the approaches presented in this paper. Furthermore, it is clearly demonstrated that ignoring the time dependency of the dynamic behaviour of mechanical systems can lead to an important deterioration of the results.

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Including connecting elements into the Lagrange multiplier state-space substructuring formulation

Dias

Martarelli

Chiariotti

2023

Journal of Sound and Vibration

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On the use of Lagrange Multiplier State-Space Substructuring in dynamic substructuring analysis

Cited by 5 publications

References 24 publications

On the prediction of the time-varying behaviour of dynamic systems by interpolating state-space models

On the prediction of the time-varying behaviour of dynamic systems by interpolating state-space models

In-Situ Component-Based TPA for Time-Variant Dynamic Systems: A State-Space Formulation

Including connecting elements into the Lagrange multiplier state-space substructuring formulation

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