Flexural waves in elastically coupled telescopic metabeams

2021 ◽  
pp. 1-28
Author(s):  
Rajan Prasad ◽  
Arnab Banerjee
Keyword(s):  
Wave Propagation ◽  
Band Gap ◽  
Wave Attenuation ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Length Ratio ◽  
Beam Equation ◽  
Flexural Wave ◽  
Constitutive Components

Abstract This paper investigates the flexural wave propagation through elastically coupled metabeams. It is assumed that the metabeam is formed by connecting successive beams with each other using distributed elastic springs. The equations of motion of a representative unit of the above mentioned novel structural form is established by dividing it into three constitutive components that are two side beams, modeled employing Euler-Bernoulli beam equation and an elastically coupled articulated distributed spring connection (ECADSC) at middle. ECADSC is modeled as parallel double beams connected by distributed springs. The underlying mechanics of this system in context of elastic wave propagation is unique when compared with the existing state of art in which local resonators, inertial amplifiers etc. are attached to the beam to widen the attenuation bandwidth. The dynamic stiffness matrix is employed in conjunction with Bloch-Floquet theorem to derive the band-structure of the system. It is identified that the coupling coefficient of the distributed spring layer and length ratio between the side beams and the elastic coupling plays the key role in the wave attenuation. It has been perceived that a considerable widening of the attenuation band gap in the low-frequency can be achieved while the elastically distributed springs are weak and distributed in a small stretch. Specifically, 140% normalized band gap can be obtained only by tuning the stiffness and the length ratio without adding any added masses or resonators to the structure.

scholarly journals Low-frequency broadband vibration attenuation of sandwich plate-type metastructures with periodic thin-wall tube cores

2021 ◽  
pp. 146134842110355
Author(s):  
Huan Zi ◽  
Yinggang Li
Keyword(s):  
Wave Propagation ◽  
Band Gap ◽  
Sandwich Plate ◽  
Low Frequency ◽  
Flexural Wave ◽  
Wave Band ◽  
Thin Wall ◽  
Vibration Attenuation ◽  
Flexural Wave Propagation ◽  
Plate Type

Sandwich structures are widely applied in modern industry such as aerospace, automobile as well as marine structures. However, the vibroacoustic properties of sandwich structures are adversely influenced by low effective mass. In this study, the flexural wave propagation characteristics and vibration mitigation performances of the periodic sandwich plate-type metastructures are investigated. The proposed sandwich plate-type metastructures are constituted of a sandwich plate with periodic thin-wall circular tube cores and periodically attached local stepped resonators. A finite element method combining Solid-Shell coupling numerical method and Bloch theory is presented to calculate the dispersion relations and the displacement fields of the eigenmodes of the infinite periodic sandwich plate-type metastructures. In addition, the acceleration frequency responses and vibration attenuation performances of finite periodic sandwich plate-type metastructures are numerically investigated and compared with the experimental measurements. Furthermore, the influences of geometric parameters on flexural wave band gaps are conducted. Results show that the sandwich plate-type metastructures can yield a low-frequency broad flexural wave band gap, in which the flexural wave propagation is conspicuously suppressed, resulting in significant flexural vibration attenuation. The flexural wave band gap and vibration attenuation performances can be effectively manipulated by designing geometric parameters of the sandwich plate-type metastructures.

Tunable Nonlinear Band Gaps in a Sandwich-Like Meta-Plate

2021 ◽  
Author(s):  
Yu Xue ◽  
Jinqiang Li ◽  
Yu Wang ◽  
Fengming Li
Keyword(s):  
Band Gap ◽  
Vibration Suppression ◽  
Wave Attenuation ◽  
Structural Parameters ◽  
Low Frequency ◽  
Dispersion Analysis ◽  
Response Analysis ◽  
Working Mechanism ◽  
Frequency Wave ◽  
The Galerkin Method

Abstract This paper aims to explore the actual working mechanism of sandwich-like meta-plates by periodically attaching nonlinear mass-beam-spring (MBS) resonators for low-frequency wave absorption. The nonlinear MBS resonator consists of a mass, a cantilever beam and a spring that can provide negative stiffness in the transverse vibration of the resonator, and its stiffness is tunable by changing the parameters of the spring. Considering the nonlinear stiffness of the resonator, the energy method is applied to obtain the dispersion relation of the sandwich-like meta-plate and the band-gap bounds related to the amplitude of resonator is derived by dispersion analysis. For the finite sized sandwich-like meta-plate with the fully free boundary condition subjected to external excitations, its dynamic equation is also established by the Galerkin method. The frequency response analysis of the meta-plate is carried out by the numerical simulation, whose band-gap range demonstrates good agreement with the theoretical one. Results show that the band-gap range of the present meta-plate is tunable by the design of the structural parameters of the MBS resonator. Furthermore, by analyzing the vibration suppression of the finite sized meta-plate, it can be observed that the nonlinearity of resonators can widen the wave attenuation range of meta-plate.

scholarly journals Longitudinal wave propagation in a one-dimensional quasi-periodic waveguide

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190392
Author(s):  
Vladislav S. Sorokin
Keyword(s):  
Wave Propagation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Periodic Waveguide ◽  
One Dimensional ◽  
Vibration Attenuation ◽  
Direct Separation ◽  
Longitudinal Wave Propagation ◽  
Spatial Modulations

The paper deals with the analysis of wave propagation in a general one-dimensional (1D) non-uniform waveguide featuring multiple modulations of parameters with different, arbitrarily related, spatial periods. The considered quasi-periodic waveguide, in particular, can be viewed as a model of pure periodic structures with imperfections. Effects of such imperfections on the waveguide frequency bandgaps are revealed and described by means of the method of varying amplitudes and the method of direct separation of motions. It is shown that imperfections cannot considerably degrade wave attenuation properties of 1D periodic structures, e.g. reduce widths of their frequency bandgaps. Attenuation levels and frequency bandgaps featured by the quasi-periodic waveguide are studied without imposing any restrictions on the periods of the modulations, e.g. for their ratio to be rational. For the waveguide featuring relatively small modulations with periods that are not close to each other, each of the frequency bandgaps, to the leading order of smallness, is controlled only by one of the modulations. It is shown that introducing additional spatial modulations to a pure periodic structure can enhance its wave attenuation properties, e.g. a relatively low-frequency bandgap can be induced providing vibration attenuation in frequency ranges where damping is less effective.

Bandgap of flexural wave in periodic bi-layer beam

2016 ◽  
Vol 24 (14) ◽  
pp. 2970-2985 ◽  
Author(s):  
Zhiwei Guo ◽  
Meiping Sheng
Keyword(s):  
Wave Propagation ◽  
Floquet Theory ◽  
Wave Attenuation ◽  
Vibration Reduction ◽  
Single Layer ◽  
Beam Theory ◽  
Flexural Wave ◽  
Transmission Characteristic ◽  
Beam Structure ◽  
Software Simulation

A periodic bi-layer beam structure is proposed and the bandgap characteristic of flexural wave is studied in this paper. The single cell is made up of two bi-layer beams with four components. For the infinite structure, the flexural wave bandgap frequency algorithm is theoretically derived through Timoshenko beam theory, Hamilton principle, Bloch-Floquet theory and transfer matrix method. An analytical example is presented to illustrate the bandgap characteristic and FEA software simulation is conducted to demonstrate the validation of the algorithm. For the finite structure, the vibration transmission characteristic is studied with FEA software to show the flexural wave attenuation behavior of the periodic bi-layer beam. The results reveal that, the flexural wave is attenuated gradually in the stopband along the direction of wave propagation, while in the passband, it will propagate without attenuation. Comparisons with periodic single layer beam are studied to verify the convenience and flexibility of bi-layer beam. Finally, parametric influences on bandgaps are discussed, which will help the designers to make a better design for vibration reduction.

Determination of formation shear attenuation from dipole sonic log data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D73-D79 ◽  
Author(s):  
Qiaomu Qi ◽  
Arthur C. H. Cheng ◽  
Yunyue Elita Li
Keyword(s):  
Reservoir Characterization ◽  
Wave Attenuation ◽  
Synthetic Data ◽  
Low Frequency ◽  
P Wave ◽  
Flexural Wave ◽  
S Wave ◽  
Additional Energy ◽  
Log Data ◽  
Sonic Log

ABSTRACT Formation S-wave attenuation, when combined with compressional attenuation, serves as a potential hydrocarbon indicator for seismic reservoir characterization. Sonic flexural wave measurements provide a direct means for obtaining the in situ S-wave attenuation at log scale. The key characteristic of the flexural wave is that it propagates at the formation shear slowness and experiences shear attenuation at low frequency. However, in a fast formation, the dipole log consists of refracted P- and S-waves in addition to the flexural wave. The refracted P-wave arrives early and can be removed from the dipole waveforms through time windowing. However, the refracted S-wave, which is often embedded in the flexural wave packet, is difficult to separate from the dipole waveforms. The additional energy loss associated with the refracted S-wave results in the estimated dipole attenuation being higher than the shear attenuation at low frequency. To address this issue, we have developed a new method for accurately determining the formation shear attenuation from the dipole sonic log data. The method uses a multifrequency inversion of the frequency-dependent flexural wave attenuation based on energy partitioning. We first developed our method using synthetic data. Application to field data results in a shear attenuation log that is consistent with lithologic interpretation of other available logs.

Detection of damage through coupled axial–flexural wave interactions in a sagged rod using the spectral finite element method

2016 ◽  
Vol 23 (20) ◽  
pp. 3345-3364 ◽  
Author(s):  
T Jothi Saravanan ◽  
N Gopalakrishnan ◽  
N Prasad Rao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Dynamic Stiffness ◽  
Single Frequency ◽  
Flexural Wave ◽  
Rod Theory ◽  
Spectral Finite Element Method ◽  
Spectral Finite Element ◽  
Element Method

This paper presents the results of a computational and experimental validation exercise performed towards damage identification of a sagged rod with known damage by using the coupled axial–flexural wave interaction mechanics. Towards simulating the damage scenario in a sagged conductor made of steel wire rope, a prismatic steel rod is taken up for study. An initial axial wave, tangential to the curve of the arc, manifests as both axial and flexural waves as it propagates alongside the length of the rod. This interaction effect between axial and flexure wave propagation is studied in this paper. Impedance mismatch is made in the rod by changing its cross-sectional area along its length. Numerical simulations are implemented using the spectral finite element method with a combined axial and flexure effect. The concept of obtaining the exact spectral element dynamic stiffness matrix for a wave propagation analysis sagged rod is discussed. Computation is implemented in the Fourier domain using Fast Fourier Transform (FFT). In the time domain, post processing of the response is done, which is applicable in structural diagnostics in addition to the wave propagation problem. The predominant single-frequency-based amplitude-modulated, narrow-banded, burst wave propagation is found to be better matched if the elemental rod theory is replaced with a modified rod theory called the Love theory. The differences in the propagating waves allow identification of the damage location in a very clear-cut way. The methodology of the moving correlation coefficient is also successfully employed to detect the damage precisely. This fact is very encouraging for future work on structural health monitoring.

Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
Liao Liu ◽  
Mahmoud I. Hussein
Keyword(s):  
Wave Propagation ◽  
Band Structure ◽  
Band Gap ◽  
Frequency Band ◽  
Band Gaps ◽  
Flexural Wave ◽  
Propagation Mechanism ◽  
Bragg Scattering ◽  
Frequency Spectra ◽  
Local Resonance

Band gaps appear in the frequency spectra of periodic materials and structures. In this work we examine flexural wave propagation in beams and investigate the effects of the various types and properties of periodicity on the frequency band structure, especially the location and width of band gaps. We consider periodicities involving the repeated spatial variation of material, geometry, boundary and/or suspended mass along the span of a beam. In our formulation, we implement Bloch’s theorem for elastic wave propagation and utilize Timoshenko beam theory for the kinematical description of the underlying flexural motion. For the calculation of the frequency band structure we use the transfer matrix method, derived here in generalized form to enable separate or combined consideration of the different types of periodicity. Our results provide band-gap maps as a function of the type and properties of periodicity, and as a prime focus we identify and mathematically characterize the condition for the transition between Bragg scattering and local resonance, each being a unique wave propagation mechanism, and show the effects of this transition on the lowest band gap. The analysis presented can be extended to multi-dimensional phononic crystals and acoustic metamaterials.

Low-frequency flexural wave attenuation in metamaterial sandwich beam with hourglass lattice truss core

Wave Motion ◽  
2021 ◽  
pp. 102750
Author(s):  
Zhenkun Guo ◽  
Guobiao Hu ◽  
Vladislav Sorokin ◽  
Lihua Tang ◽  
Xiaodong Yang ◽  
...  
Keyword(s):  
Wave Attenuation ◽  
Sandwich Beam ◽  
Low Frequency ◽  
Flexural Wave ◽  
Truss Core
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