Optimization of Axial Vibration Attenuation of Periodic Structure With Nonlinear Stiffness Without Addition of Mass

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Diego P. Vasconcellos ◽  
Marcos Silveira
Keyword(s):  
Periodic Structure ◽  
Total Mass ◽  
Periodic Structures ◽  
Original Structure ◽  
Dynamical Response ◽  
Nonlinear Stiffness ◽  
Optimal Position ◽  
Simplified Approach ◽  
Vibration Attenuation ◽  
Linear And Nonlinear

Abstract We explore the vibration attenuation of a periodic structure when one absorber with nonlinear cubic stiffness is included without increasing the total mass. Metastructures, and specifically periodic structures, present interesting characteristics for vibration attenuation that are not found in classical structures. These characteristics have been explored for automotive and aerospace applications, among others, as structures with low mass are paramount for these industries, and keeping low vibration levels in wide frequency range is also desirable. It has been shown that the addition of vibration absorbers in a periodic arrangement can provide vibration attenuation for shock input without increasing the total mass of a structure. In this work, the dynamical response of a metastructure with one nonlinear vibration absorber, with same mass as original structure, optimized for vibration attenuation under harmonic input is compared with a base metastructure without absorbers and a metastructure with linear absorbers via the evaluation of the H2 norm of the frequency response. A simplified approach is used to compare linear and nonlinear stiffness based on deformation energy, by considering linear and nonlinear restoring forces to be equal at mean deformation. The dynamical response of the optimal system is obtained numerically, and an optimization procedure based on sequential quadratic programming (SQP) is proposed to find the optimal position and stiffness coefficients of only one nonlinear absorber, showing that it results in lower level of vibrations than original structure and than structure with linear absorbers, while almost the same level as a structure with all nonlinear absorbers.

Excitation of Rotationally Periodic Structures

1979 ◽  
Vol 46 (4) ◽  
pp. 878-882 ◽  
Author(s):  
S. J. Wildheim
Keyword(s):  
Periodic Structure ◽  
Periodic Structures ◽  
Resonance Condition ◽  
Forced Response ◽  
Closed Ring ◽  
Additional Resonance ◽  
Rotationally Symmetric ◽  
Deformation Patterns ◽  
Frequency Diagram ◽  
Rotationally Periodic Structure

A rotationally periodic structure consists of a finite number of identical substructures forming a closed ring. The vibrational behavior of such structures is considered, especially the forced response due to a rotating force. It is known that for a rotationally symmetric structure, excited by a rotating force, resonance for the n nodal diameters mode is obtained when the corresponding natural frequency is ωn = nΩ, where Ω is the angular velocity of the force. This resonance condition also holds for a rotationally periodic structure. But then additional resonance possibilities exist, given by ωn = (kN ± n)Ω, where N is the number of substructures and k = 0, 1, 2,… These resonance conditions give a zigzag line in the nodal diameters versus frequency diagram, which here is introduced as the ZZENF diagram. The deformation patterns at the resonances are both forward and backward traveling waves.

Wave Propagation in Two-Dimensional Nonlinear Periodic Lattices

2009 ◽  
Author(s):  
Raj K. Narisetti ◽  
Massimo Ruzzene ◽  
Michael J. Leamy
Keyword(s):  
Wave Propagation ◽  
Linear Models ◽  
Periodic Structures ◽  
Harmonic Wave ◽  
Excitation Amplitude ◽  
Pass Band ◽  
Perturbation Approach ◽  
Nonlinear Stiffness ◽  
Two Dimensional ◽  
Low Amplitude

This paper investigates wave propagation in two-dimensional nonlinear periodic structures subject to point harmonic forcing. The infinite lattice is modeled as a springmass system consisting of linear and cubic-nonlinear stiffness. The effects of nonlinearity on harmonic wave propagation are analytically predicted using a novel perturbation approach. Response is characterized by group velocity contours (derived from phase-constant contours) functionally dependent on excitation amplitude and the nonlinear stiffness coefficients. Within the pass band there is a frequency band termed the “caustic band” where the response is characterized by the appearance of low amplitude regions or “dead zones.” For a two-dimensional lattice having asymmetric nonlinearity, it is shown that these caustic bands are dependent on the excitation amplitude, unlike in corresponding linear models. The analytical predictions obtained are verified via comparisons to responses generated using a time-domain simulation of a finite two-dimensional nonlinear lattice. Lastly, the study demonstrates amplitude-dependent wave beaming in two-dimensional nonlinear periodic structures.

Parametric Study on Rectangular Sonic Crystal

2012 ◽  
Vol 152-154 ◽  
pp. 281-286 ◽  
Author(s):  
Arpan Gupta ◽  
Kian Meng Lim ◽  
Chye Heng Chew
Keyword(s):  
Band Gap ◽  
Periodic Structure ◽  
Parametric Study ◽  
Sound Propagation ◽  
Periodic Structures ◽  
Sound Attenuation ◽  
Experimental Results ◽  
Center Frequency ◽  
Sonic Crystal ◽  
Sonic Crystals

Sonic crystals are periodic structures made of sound hard scatterers which attenuate sound in a range of frequencies. For an infinite periodic structure, this range of frequencies is known as band gap, and is determined by the geometric arrangement of the scatterers. In this paper, a parametric study on rectangular sonic crystal is presented. It is found that geometric spacing between the scatterers in the direction of sound propagation affects the center frequency of the band gap. Reducing the geometric spacing between the scatterers in the direction perpendicular to the sound propagation helps in better sound attenuation. Such rectangular arrangement of scatterers gives better sound attenuation than the regular square arrangement of scatterers. The model for parametric study is also supported by some experimental results.

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.

Linear and nonlinear stiffness and friction in biological rhythmic movements

1995 ◽  
Vol 73 (6) ◽  
pp. 499-507 ◽  
Author(s):  
P. J. Beek ◽  
R. C. Schmidt ◽  
A. W. Morris ◽  
M.-Y. Sim ◽  
M. T. Turvey
Keyword(s):  
Nonlinear Stiffness ◽  
Rhythmic Movements ◽  
Linear And Nonlinear

Peptide-mediated deposition of nanostructured TiO2 into the periodic structure of diatom biosilica

2008 ◽  
Vol 23 (12) ◽  
pp. 3255-3262 ◽  
Author(s):  
Clayton Jeffryes ◽  
Timothy Gutu ◽  
Jun Jiao ◽  
Gregory L. Rorrer
Keyword(s):  
Titanium Dioxide ◽  
Electron Diffraction ◽  
Thermal Annealing ◽  
Periodic Structure ◽  
Outer Surface ◽  
Periodic Structures ◽  
Diatom Frustule ◽  
X Ray Diffraction ◽  
X Ray ◽  
Reported Study

Diatoms are single-celled algae that make silica shells called frustules that possess periodic structures ordered at the micro- and nanoscale. Nanostructured titanium dioxide (TiO2) was deposited onto the frustule biosilica of the diatom Pinnularia sp. Poly-l-lysine (PLL) conformally adsorbed onto surface of the frustule biosilica. The condensation of soluble Ti-BALDH to TiO2 by PLL-adsorbed diatom biosilica deposited 1.32 ± 0.17 g TiO2/g SiO2 onto the frustule. The periodic pore array of the diatom frustule served as a template for the deposition of the TiO2 nanoparticles, which completely filled the 200-nm frustule pores and also coated the frustule outer surface. Thermal annealing at 680 °C converted the as-deposited TiO2 to its anatase form with an average nanocrystal size of 19 nm, as verified by x-ray diffraction, electron diffraction, and SEM/TEM. This is the first reported study of directing the peptide-mediated deposition of TiO2 into a hierarchical nanostructure using a biologically fabricated template.

scholarly journals Number of Wavevectors for Each Frequency in a Periodic Structure

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Farhad Farzbod
Keyword(s):  
Periodic Structure ◽  
Degrees Of Freedom ◽  
Phonon Dispersion ◽  
Periodic Structures ◽  
Dispersion Curves ◽  
Neighbor Interaction ◽  
Phonon Dispersion Curves ◽  
Hexagonal Form ◽  
Vibration Properties ◽  
Unit Cells

Periodic structures have interesting acoustic and vibration properties making them suitable for a wide variety of applications. In a periodic structure, the number of frequencies for each wavevector depends on the degrees-of-freedom of the unit cell. In this paper, we study the number of wavevectors available at each frequency in a band diagram. This analysis defines the upper bound for the maximum number of wavevectors for each frequency in a general periodic structure which might include damping. Investigation presented in this paper can also provide an insight for designing materials in which the interaction between unit cells is not limited to the closest neighbor. As an example application of this work, we investigate phonon dispersion curves in hexagonal form of boron nitride to show that first neighbor interaction is not sufficient to model dispersion curves with force-constant model.

scholarly journals Optimal position of piezoelectric actuators for active vibration reduction of beams

2020 ◽  
Vol 5 (1) ◽  
pp. 385-392
Author(s):  
Bendine Kouider ◽  
Alper Polat
Keyword(s):  
Optimization Technique ◽  
Shear Deformation Theory ◽  
Piezoelectric Actuators ◽  
Optimization Criterion ◽  
Optimal Placement ◽  
Feedback Gain ◽  
Optimal Position ◽  
First Order ◽  
Vibration Attenuation ◽  
Active Vibration

AbstractThis paper investigates the optimal placement of piezoelectric actuators for the active vibration attenuation of beams. The governing equation of the beam is achieved by coupled first order shear deformation theory with two node element. The velocity feedback controller is designed and used to calculate the feedback gain and then apply to the beam. In order to search for the optimal placement of the piezoelectric actuators, a new optimization criterion is considered based on the use of genetic algorithm to reduce the displacement output of the beam. The proposed optimization technique has been tested for two boundary conditions configurations; clamped -free and clamped-clamped beam. Numerical examples have been provided to analyze the effectiveness of the proposed technic.

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