Time–frequency varying response functions of non-classically damped linear structures under fully non-stationary stochastic excitations

Alderucci, Tiziana; Muscolino, G.

doi:10.1016/j.probengmech.2017.08.004

Cited by 11 publications

(14 citation statements)

References 39 publications

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“…35 At the same time, modal complexity cannot be always neglected (for instance, when external dissipators are inserted into structures); in these cases, a complex formulation must be suitably adopted to get the relevant outcomes. 36,37 In this work we base on a peculiar meaning of damage. Undamaged structures meet the assumption of proportional damping: as a result, their mode shapes are real.…”

Section: Modal Complexity For Damage Detectionmentioning

confidence: 99%

“…This objective difficulty in detecting the sources of complexification makes applications on large structures usually require specific modal complexity checks before the final clustering of structural modes 35 . At the same time, modal complexity cannot be always neglected (for instance, when external dissipators are inserted into structures); in these cases, a complex formulation must be suitably adopted to get the relevant outcomes 36,37 …”

Section: Governing Equationsmentioning

confidence: 99%

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Dynamic damage identification using complex mode shapes

Lofrano

Paolone

Ruta

2020

Struct Control Health Monit

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Damage, be it a material or a geometric degradation, modifies some features of the response foreseen by the original structural design. These variations, once the dependence on the damage causing them is established, can be used for identification purposes. In the literature, vibration-based approaches usually compare some responses of linear elastic structures with dissipative properties that are assumed proportional to the mass and stiffness measures. However, such an assumption is reasonable for new, undamaged structures, but can be unreliable in existing, potentially damaged structures, particularly for damages localised in narrow areas. The eigenmodes of a proportionally damped system can be reduced to the real ones of the relevant ideal undamped system. On the other hand, non-proportional damping exhibits complex eigenmodes that cannot be reduced to those of the ideal, or of the proportionally damped, structure. Thus, we may assume the complexity of the eigenmodes as a measure of nonproportional damping, hence of damage. On this basis, some contributions in the literature verified the relationship among presence of damage and amount of complexity. Here, we propose a perturbation approach and an objective function able to identify presence, location and amplitude of localised damages, intended as sources of non-proportionality in viscously damped linear systems. A prototype naturally discrete structure with four degrees-of-freedom is chosen to test and show capability and accuracy of the proposed method.

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Section: Modal Complexity For Damage Detectionmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

Dynamic damage identification using complex mode shapes

Lofrano

Paolone

Ruta

2020

Struct Control Health Monit

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“…By substituting the transition matrix (6) into Eq. (19), the nodal PEC matrix can be written also as [20,21]:…”

Section: ( )mentioning

confidence: 99%

“…, can be determined in explicit form, the TFR vector function, according to the dynamics of non-classically damped systems, can be written as [21]:…”

Section: ( )mentioning

confidence: 99%

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Response Sensitivity of Structural Systems Subjected to Fully Non-Stationary Random Processes

Alderucci¹,

Genovese²,

Muscolino³

2019

Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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A method for the evaluation of the statistics of response sensitivity of both classically and non-classically damped discrete linear structural systems under fully non-stationary stochastic seismic processes is presented. To do this the evolutionary frequency response function, also referred in literature as the time-frequency varying response function, plays a central role in the evaluation of the spectral characteristics of non-stationary response. The proposed approach requires the following items: a) to write governing motion equations in state-variables, which are very suitable to evaluate the statistics of the response of both classically and non-classically damped discrete linear structural systems by an unified approach; b) to evaluate in explicit closed form solutions the derivatives of time-frequency response vector functions with respect to the parameters that define the modified structural model; c) to obtain the sensitivity of the structural response statistics by frequency domain integrals. A numerical application shows that the proposed approach is suitable to cope with practical problems of engineering interest.

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Semi‐analytical solutions for stochastic response of non‐classically damped linear structures to arbitrary time‐frequency modulated seismic excitations

Wang

et al. 2020

Earthq Engng Struct Dyn

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This paper presents a semi‐analytical method for stochastic response analysis of non‐classically damped linear structures subjected to non‐stationary seismic excitations modeled by arbitrary time‐frequency modulating functions. In this method, the inherent randomness of seismic excitation process is characterized by a set of orthogonal random variables obtained using the spectral representation method. Then, by adopting piecewise polynomials to interpolate the time‐frequency modulating function of seismic excitation, an explicit expression for the structural stochastic response in term of the orthogonal random variables is derived using the complex modal analysis. This expression can be used not only to efficiently predict the seismic response of structures subjected to an arbitrary excitation sample, but also to directly evaluate the structural response statistics in the time domain. Finally, a robust algorithm is proposed to determine the optimal locations of segmentation points for the piecewise polynomials, the computational efficiency can be further improved. In the numerical application, a typical non‐classically damped structural system subjected to two models of non‐stationary seismic excitations are studied. The classical evolutionary spectral method and the Monte Carlo simulation are used to verify the accuracy and efficiency of the proposed method. The effects of several parameters such as the order of polynomials on the performance of the proposed method are investigated.

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Time–frequency varying response functions of non-classically damped linear structures under fully non-stationary stochastic excitations

Cited by 11 publications

References 39 publications

Dynamic damage identification using complex mode shapes

Dynamic damage identification using complex mode shapes

Response Sensitivity of Structural Systems Subjected to Fully Non-Stationary Random Processes

Semi‐analytical solutions for stochastic response of non‐classically damped linear structures to arbitrary time‐frequency modulated seismic excitations

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