Analyses of multi-bandgap property of a locally resonant plate composed of periodic resonant subsystems

2018 ◽  
Vol 32 (24) ◽  
pp. 1850269 ◽  
Author(s):  
Qi Qin ◽  
Mei-Ping Sheng
Keyword(s):  
Unit Element ◽  
Vibration Modes ◽  
Plane Wave Expansion ◽  
Flexural Waves ◽  
Bandgap Width ◽  
Finite Plate ◽  
Vibration Attenuation ◽  
Different Types ◽  
Periodic Element ◽  
Plate System

A locally resonant (LR) plate made up of a thin plate attached with different types of resonators is analyzed in this paper. Each periodic element may consist of one or more spring-mass resonators attached onto one and the same surface of the plate lattice. The correctness of theoretical plane wave expansion (PWE) method adopted in this paper is validated through the comparisons with the classical theory and finite element method (FEM). When composing the LR plate system with two types of periodic resonant subsystems, there will appear two complete bandgaps, while other additional resonators may cause mainly directional gaps, calculated theoretically and numerically. From the comparisons of band-structure curves between a two-resonator-per-unit-element (TR-UE) system and both corresponding one-resonator-per-unit-element (OR-UE) systems, the bandgap width of the TR-UE system are not stacking effects of two OR-UE systems due to resonance interaction of different types of resonators. Moreover, via the deformation contours by FEM, the correspondence between the vibration modes of subsystems and the bandgap frequencies is demonstrated. The finite plate with limited resonators of two periodic types of parameters is modeled to show visually how flexural waves propagate within/without the bandgaps. Further, by adjusting the damping characteristic of both types of resonators, vibration attenuation band can be broadened widely.

Dynamic Analysis of Tapered Plates Based on Higher Order Beam Theory

2014 ◽  
Vol 919-921 ◽  
pp. 79-82
Author(s):  
S.M. Ibrahim ◽  
Y.A. Al-Salloum ◽  
H. Abbas
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Beam Theory ◽  
Longitudinal Axis ◽  
Vibration Modes ◽  
Bending Vibration ◽  
3D Finite Element ◽  
Different Types ◽  
Tapered Plates ◽  
Good Agreement

Modal solutions of plates with uniformly varying cross section using unified beam theory are presented. The results are given in the form of Euler-Bernoulli, Timoshenko and quasi 3D solutions. Numerical results for cantilever and CFCF supported rectangular planform plates are presented. Different types of modes, i.e. axial, bending and torsional modes are observed. The frequency values are in good agreement with 3D finite element results as well as published literature. Due to uniform taper in plate cross section, bending vibration modes become asymmetric along the longitudinal axis of the structure. Further, it can also be noticed that the vibration behavior of thick tapered plates is characterized by the appearance of significant number of axial and torsional modes at lower frequency values.

Spectral Element Approach for Flexural Waves Control in Smart Material Beam With Single and Multiple Resonant Impedance Shunt Circuit

2020 ◽  
Vol 15 (12) ◽  
Author(s):  
Marcela R. Machado ◽  
Adriano T. Fabro ◽  
Braion B. de Moura
Keyword(s):  
Control Strategies ◽  
Spectral Element ◽  
Smart Material ◽  
Smart Structure ◽  
Flexural Waves ◽  
Structural Dynamic ◽  
Vibration Attenuation ◽  
Resonant Behavior ◽  
Element Approach ◽  
Shunt Circuit

Abstract The accurate prediction of the dynamic characteristics of a structure is key to successful vibration control strategies. A typical vibration and wave propagation control is performed through periodic and shunted piezoelectric patches, also known as a smart material. Therefore, the smart metamaterial considers periodic arrangement of shunted piezoelectric patches providing a beam with attenuation properties which depend on the resonant behavior of the shunts. The vibration attenuation occurs due to an elastic-electrical system characterized by an internal resonance of the shunt circuit. The spectral element approach provides very accurate solutions for the structural dynamic response. In this paper, a beam-piezoelectric structure is introduced to focus on the control of flexural waves in beams with piezolayers connected to single and multiresonant shunt approaches. The smart structure is modeled using the spectral element method. It is shown that the effective wavenumber presents the locally resonant behavior at the same frequencies of the vibration attenuation for both single and multishunt approached, indicating that each shunt circuit is independently associated with a attenuation frequency. The spectral element approach presented in this paper shows to be an accurate and simple approach for the design smart metamaterial beams.

scholarly journals Dynamic interfacial trapping of flexural waves in structured plates

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150658 ◽  
Author(s):  
S. G. Haslinger ◽  
R. V. Craster ◽  
A. B. Movchan ◽  
N. V. Movchan ◽  
I. S. Jones
Keyword(s):  
Standing Waves ◽  
Periodic Array ◽  
Two Dimensional ◽  
Flexural Waves ◽  
Homogeneous Part ◽  
Interface Boundary ◽  
Dimensional Array ◽  
Different Types ◽  
Doubly Periodic Array ◽  
Localized Waves

The paper presents new results on the localization and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, localized waves are identified and studied at the interface boundary between the homogeneous part of the flexural plate and the part occupied by rigid pins. A formal connection has been made with the dispersion properties of flexural Bloch waves in an infinite doubly periodic array of rigid pins. Special attention is given to regimes corresponding to standing waves of different types as well as Dirac-like points that may occur on the dispersion surfaces. A single half-grating problem, hitherto unreported in the literature, is also shown to bring interesting solutions.

scholarly journals On the Effect of Nonlinear Energy Sink Damping in Seismic Vibration Attenuation

2021 ◽  
Author(s):  
Eliot Motato ◽  
Fabio G. Guerrero
Keyword(s):  
Nonlinear Energy Sink ◽  
Tuned Mass Dampers ◽  
Building Model ◽  
Wide Range ◽  
Vibration Attenuation ◽  
Different Types ◽  
Energy Sink ◽  
Shear Building ◽  
Model Subject ◽  
Nonlinear Energy

Abstract Nonlinear Energy Sinks (NESs) have been proposed for passively reducing the amplitude of vibrations in different types of structures. The main advantage of NES over traditional Tuned Mass Dampers (TMDs) lies in its capability to redistribute the vibrating energy inside a primary structure, what effectively reduces the amplitude of the structure oscillations over a wide range of frequencies. However, the performance of an NES can be substantially affected even by small variations on input energy as in the case of buildings under seismic ground excitation. In this work it is shown that the NES energy sensibility can be significantly reduced by properly selecting the NES damping coefficient. A three stories shear building model subject to seismic ground excitation is used to numerically study the effect that NES damping has on its vibration reduction performance.

scholarly journals Broadband Vibration Attenuation Achieved by 2D Elasto-Acoustic Metamaterial Plates with Rainbow Stepped Resonators

Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 4759
Author(s):  
Wenming Wei ◽  
Dimitrios Chronopoulos ◽  
Han Meng
Keyword(s):  
Expansion Method ◽  
Two Dimensional ◽  
Plane Wave Expansion ◽  
Plane Wave Expansion Method ◽  
Plate Structures ◽  
One Dimensional ◽  
Acoustic Metamaterial ◽  
Modelling Method ◽  
Vibration Attenuation ◽  
Spatially Varying

This paper investigates the influences of nonperiodic rainbow resonators on the vibration attenuation of two-dimensional metamaterial plates. Rainbow metamaterial plates composed of thin host plates and nonperiodic stepped resonators are considered and compared with periodic metamaterial plates. The metamaterial plates are modelled with the finite element modelling method and verified by the plane wave expansion method. It was found that the rainbow metamaterial plates with spatially varying resonators possess broader vibration attenuation bands than the periodic metamaterial plate with the same host plates and total mass. The extension of attenuation bands was found not to be attributed to the extended bandgaps for the two-dimensional metamaterial plates, as is generally believed for a one-dimensional metamaterial beam. The complete local resonance bandgap of the metamaterial plates is separated to discrete bandgaps by the modes of nonperiodic resonators. Although the additional modes stop the formation of integrated bandgaps, the vibration of the plate is much smaller than that of resonators at these modal frequencies, the rainbow metamaterial plates could have a distinct vibration attenuation at these modal frequencies and achieve broader integrated attenuation bands as a result. The present paper could offer a new idea for the development of plate structures with broadband vibration attenuation by introducing non-periodicity.

PROPAGATION OF ULTRASOUND IN SOLID CYLINDERS (TRANSVERSE WAVES)

1932 ◽  
Vol 7 (1) ◽  
pp. 86-94 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Phase Velocity ◽  
Wave Length ◽  
Flexural Waves ◽  
Natural Period ◽  
Transverse Waves ◽  
Mechanical Coupling ◽  
Resonance Effects ◽  
Different Types ◽  
Pass Through ◽  
Good Agreement

The expression giving the phase velocity c with which flexural waves pass through long solid rods is deduced for frequencies varying between zero and over 1,000,000 cycles per sec. and rods of any diameter. As the frequency increases, the velocity c increases gradually from very low values toward c2 = mE/2s(m+1), reached when the wave-length is much smaller than the diameter of the rod. Published experimental results for transverse waves are in good agreement with the theory given. In general at least four effects enter into the propagation of ultrasound through solid cylinders: first, longitudinal waves, for which the phase velocity decreases toward c as the frequency increases; second, transverse waves, for which the phase velocity increases toward c as the frequency increases; third, pure radial waves at certain frequencies; fourth, resonance effects between the different types of waves, which, on account of the mechanical coupling existing between them, change the natural period of vibration of the rod without affecting the velocity.

Adaptive Trajectory Control and Dynamic Friction Compensation for a Flexible-Link Robot

2010 ◽  
Vol 26 (2) ◽  
pp. 205-217 ◽  
Author(s):  
Vahid Erfanian ◽  
Mansour Kabganian
Keyword(s):  
Internal State ◽  
Friction Model ◽  
Distributed Parameter ◽  
Friction Compensation ◽  
Flexible Link ◽  
Lugre Friction Model ◽  
Control Schemes ◽  
Vibration Attenuation ◽  
Different Types ◽  
Lugre Friction

AbstractFriction compensation techniques are studied for control of a flexible-link robot based on the LuGre friction model. To overcome the problem of uncertain parameters in the friction model, adaptive control schemes are used for two different types of parametric uncertainties. A novel dual-observer technique is proposed to estimate the internal state inside the friction model. A distributed-parameter dynamic model is used for the flexible arm to design the controllers. The Lyapunov stability theorem is used to guarantee the global asymptotic stability of the controllers. The performance of position tracking and link vibration attenuation is verified through experimental results. The results also confirm the effectiveness of the proposed friction compensation schemes.

Elastic Wave Band Structures and Defect States in a Periodically Corrugated Piezoelectric Plate

2014 ◽  
Vol 81 (8) ◽  
Author(s):  
Y. Huang ◽  
C. L. Zhang ◽  
W. Q. Chen
Keyword(s):  
Symmetry Breaking ◽  
Piezoelectric Plate ◽  
Band Gaps ◽  
Wave Band ◽  
Plane Wave Expansion ◽  
Defect States ◽  
Band Structures ◽  
Sh Waves ◽  
Different Types ◽  
Shear Horizontal

The band structures of shear horizontal (SH) waves in a periodically corrugated piezoelectric plate (PCPP) are studied by using the supercell plane wave expansion (SC-PWE) method. The effect of plate symmetry on the defect state caused by a defect in the plate is investigated in detail. The PCPPs with different types of symmetry give rise to different kinds of band gaps and the associated defect states. The increase of defect size lowers the frequency of defect bands, and it can be used to tune the narrow-passband frequencies in acoustic band gaps. Symmetry breaking is also introduced by reducing the lower corrugation depth of the PCPP. Results show that symmetry breaking leads to both the appearance and disappearance of new kinds of gaps and the corresponding defect bands in these gaps.

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