Damping control in viscoelastic beam dynamics

Pierro, Elena

doi:10.1177/1077546320903195

Cited by 13 publications

(15 citation statements)

References 42 publications

(81 reference statements)

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“…Then, we have calculated the Fast Fourier Transform (FFT) of the ten averaged time histories, for both the accelerations A (x, ω) and the impacting forces that the transition region of the material, where damping effects are more significant, should be found at lower frequencies. For both the material and the beam geometry considered in the present study, a slight mitigation of the resonances can be observed, and not a complete peak suppression [17,18]. This fact helps in interpreting the nature of the peaks in the frequency range considered, and thus enables us to perform a correct viscoelastic modulus fitting.…”

Section: Theoretical Model Of the Viscoelastic Beam Dynamicsmentioning

confidence: 75%

“…( 10) are the same of the perfectly elastic case, and can be substituted in Eq. ( 7) to calculate the complex conjugate eigenvalues s n corresponding to the n modes of the beam, and the real poles s k related to the material viscoelasticity [17,18]. Furthermore, by means of the solutions β n L = c n of Eq.…”

Section: Theoretical Model Of the Viscoelastic Beam Dynamicsmentioning

confidence: 99%

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A new technique for the characterization of viscoelastic materials: theory, experiments and comparison with DMA

Pierro,

Carbone

2021

Preprint

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In this paper we present a theoretical and experimental study aimed at characterizing the hysteretic properties of viscoelastic materials. In the last decades viscoelastic materials have become a reference for new technological applications, which require lightweight, deformable but ultra-tough structures. The need to have a complete and precise knowledge of their mechanical properties, hence, is of utmost importance. The presented study is focused on the dynamics of a viscoelastic beam, which is both experimentally investigated and theoretically characterized by means of an accurate analytical model. In this way it is possible to fit the experimental curves to determine the complex modulus. Our proposed approach enables the optimal fitting of the viscoelastic modulus of the material by using the appropriate number of relaxation times, on the basis of the frequency range considered. Moreover, by varying the length of the beams, the frequency range of interest can be changed/enlarged. Our results are tested against those obtained with a well established and reliable technique as compared with experimental results from the Dynamic Mechanical Analysis (DMA), thus definitively establishing the feasibility, accuracy and reliability of the presented technique.

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Section: Theoretical Model Of the Viscoelastic Beam Dynamicsmentioning

confidence: 75%

Section: Theoretical Model Of the Viscoelastic Beam Dynamicsmentioning

confidence: 99%

A new technique for the characterization of viscoelastic materials: theory, experiments and comparison with DMA

Pierro,

Carbone

2021

Preprint

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“…from which it is possible to calculate the complex conjugate eigenvalues s n corresponding to the n th mode and the real poles s k related to the material viscoelasticity (Pierro, 2020). Furthermore, the values γ 1n allow to determine the eigenfunctions f n ðxÞ…”

Section: Flexural Vibrations Of the Tensioned Beammentioning

confidence: 99%

Effect of an axial pre-load on the flexural vibrations of viscoelastic beams

Pierro

2022

Journal of Vibration and Control

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Polymers are ultra-versatile materials that adapt to a myriad of applications, as they can be designed appropriately for specific needs. The realization of new compounds, however, requires the appropriate experimental characterizations, also from the mechanical point of view, which is typically carried out by analyzing the vibrations of beams, but which still have some unclear aspects, with respect to the well-known dynamics of elastic beams. To address this shortcoming, the paper deals with the theoretical modeling of a viscoelastic beam dynamics and pursues the elucidation of underlying how the flexural vibrations may be affected when an axial pre-load, compressive or tensile, is applied. The analytical model presented is able to shed light on a peculiar behavior, which is strongly related to the frequency-dependent damping induced by viscoelasticity. By considering as an example a real polymer, that is, a synthetic rubber, it is disclosed that an axial pre-load, in certain conditions, may enhance or suppress the oscillatory counterpart of a resonance peak of the beam, depending on both the frequency distribution of the complex modulus and the length of the beam. The analytical model is assessed by a finite element model, and it turns out to be an essential tool for understanding the dynamics of viscoelastic beams, typically exploited to experimentally characterize polymeric materials, and which could vary enormously simply through the application of constraints and ensued pre-loads.

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“…Müller [14] studied the nature of eigenvalues for single-dof systems based on a Zener three-parameter damping model. The critical oscillatory motion of nonviscous beams has been studied by Pierro [15], solving the eigenvalues for one and two exponential kernels and discussing their nature (real or complex). Wang [16] obtained fractional orders compatible with critical damping in fractional derivative-based, viscoelastic, classically damped structures.…”

Section: Introductionmentioning

confidence: 99%

Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers

Lázaro

Garcı́a-Raffi

2022

Applied Sciences

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In this paper, a new methodology for the determination of the boundaries between oscillatory and non-oscillatory motion for nonviscously damped nonproportional systems is proposed. It is assumed that the damping forces are expressed as convolution integrals of the velocities via hereditary exponential kernels. Oscillatory motion is directly related to the complex nature of eigensolutions in a frequency domain and, in turn, on the value of the damping parameters. New theoretical results are derived on critical eigenmodes for viscoelastic systems with multiple degrees of freedom, with no restrictions on the number of hereditary kernels. Furthermore, these outcomes enable the construction of a numerical approach to draw the critical curves as solutions of certain parameter-dependent eigenvalue problems. The method is illustrated and validated through two numerical examples, covering discrete and continuous systems.

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Damping control in viscoelastic beam dynamics

Cited by 13 publications

References 42 publications

A new technique for the characterization of viscoelastic materials: theory, experiments and comparison with DMA

A new technique for the characterization of viscoelastic materials: theory, experiments and comparison with DMA

Effect of an axial pre-load on the flexural vibrations of viscoelastic beams

Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers

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