Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations

2022 ◽  
pp. 239779142110694
Author(s):  
Soroush Sepehri ◽  
Mahmoud Mosavi Mashhadi ◽  
Mir Masoud Seyyed Fakhrabadi
Keyword(s):  
Wave Propagation ◽  
Shear Deformation ◽  
Wave Attenuation ◽  
Softening Effect ◽  
Aspect Ratios ◽  
Lattice Materials ◽  
Out Of Plane ◽  
Plane Direction ◽  
Bloch’S Theorem ◽  
Euler Bernoulli Beam

The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.

Mechanism of the Transition From In-Plane Buckling to Helical Buckling for a Stiff Nanowire on an Elastomeric Substrate

2016 ◽  
Vol 83 (4) ◽  
Author(s):  
Youlong Chen ◽  
Yong Zhu ◽  
Xi Chen ◽  
Yilun Liu
Keyword(s):  
High Performance ◽  
Three Dimensional ◽  
Stretchable Electronics ◽  
Buckling Mode ◽  
Design And Optimization ◽  
Out Of Plane ◽  
Plane Direction ◽  
Plane Displacement ◽  
Helical Buckling ◽  
Selection Of

In this work, the compressive buckling of a nanowire partially bonded to an elastomeric substrate is studied via finite-element method (FEM) simulations and experiments. The buckling profile of the nanowire can be divided into three regimes, i.e., the in-plane buckling, the disordered buckling in the out-of-plane direction, and the helical buckling, depending on the constraint density between the nanowire and the substrate. The selection of the buckling mode depends on the ratio d/h, where d is the distance between adjacent constraint points and h is the helical buckling spacing of a perfectly bonded nanowire. For d/h > 0.5, buckling is in-plane with wavelength λ = 2d. For 0.27 < d/h < 0.5, buckling is disordered with irregular out-of-plane displacement. While, for d/h < 0.27, buckling is helical and the buckling spacing gradually approaches to the theoretical value of a perfectly bonded nanowire. Generally, the in-plane buckling induces smaller strain in the nanowire, but consumes the largest space. Whereas the helical mode induces moderate strain in the nanowire, but takes the smallest space. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and three-dimensional complex nanostructures.

A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate

2006 ◽  
Vol 128 (4) ◽  
pp. 477-488 ◽  
Author(s):  
A. Chakraborty ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Shear Deformation ◽  
Mechanical Response ◽  
Laminated Composite ◽  
Wave Number ◽  
Single Element ◽  
Element Formulation ◽  
Frequency Wave ◽  
Spectral Finite Element

A new spectral plate element (SPE) is developed to analyze wave propagation in anisotropic laminated composite media. The element is based on the first-order laminated plate theory, which takes shear deformation into consideration. The element is formulated using the recently developed methodology of spectral finite element formulation based on the solution of a polynomial eigenvalue problem. By virtue of its frequency-wave number domain formulation, single element is sufficient to model large structures, where conventional finite element method will incur heavy cost of computation. The variation of the wave numbers with frequency is shown, which illustrates the inhomogeneous nature of the wave. The element is used to demonstrate the nature of the wave propagating in laminated composite due to mechanical impact and the effect of shear deformation on the mechanical response is demonstrated. The element is also upgraded to an active spectral plate clement for modeling open and closed loop vibration control of plate structures. Further, delamination is introduced in the SPE and scattered wave is captured for both broadband and modulated pulse loading.

scholarly journals Experimental and Computational Study of a Liquid Crystalline Dimesogen Exhibiting Nematic, Twist-Bend Nematic, Intercalated Smectic, and Soft Crystalline Mesophases

Molecules ◽  
2021 ◽  
Vol 26 (3) ◽  
pp. 532
Author(s):  
Emily E. Pocock ◽  
Richard J. Mandle ◽  
John W. Goodby
Keyword(s):  
Liquid Crystalline ◽  
Computational Study ◽  
Structure Property ◽  
Correlation Lengths ◽  
Aspect Ratios ◽  
Smectic Phases ◽  
Out Of Plane ◽  
Lower Temperature ◽  
Soft Crystal ◽  
Optical Textures

Liquid crystalline dimers and dimesogens have attracted significant attention due to their tendency to exhibit twist-bend modulated nematic (NTB) phases. While the features that give rise to NTB phase formation are now somewhat understood, a comparable structure–property relationship governing the formation of layered (smectic) phases from the NTB phase is absent. In this present work, we find that by selecting mesogenic units with differing polarities and aspect ratios and selecting an appropriately bent central spacer we obtain a material that exhibits both NTB and intercalated smectic phases. The higher temperature smectic phase is assigned as SmCA based on its optical textures and X-ray scattering patterns. A detailed study of the lower temperature smectic ‘’X’’ phase by optical microscopy and SAXS/WAXS demonstrates this phase to be smectic, with an in-plane orthorhombic or monoclinic packing and long (>100 nm) out of plane correlation lengths. This phase, which has been observed in a handful of materials to date, is a soft-crystal phase with an anticlinic layer organisation. We suggest that mismatching the polarities, conjugation and aspect ratios of mesogenic units is a useful method for generating smectic forming dimesogens.

Estimation of Seismic Energy Dissipation for Steel Slit Shear Walls Considering Out-of-Plane Buckling

2021 ◽  
Author(s):  
Yiming Ma ◽  
Liusheng He ◽  
Ming Li
Keyword(s):  
Energy Dissipation ◽  
Shear Walls ◽  
Seismic Energy ◽  
Thickness Ratio ◽  
Design Parameters ◽  
Test Results ◽  
Loading Test ◽  
Aspect Ratios ◽  
Out Of Plane ◽  
Energy Dissipation Capacity

Steel slit shear walls (SSSWs), made by cutting slits in steel plates, are increasingly adopted in seismic design of buildings for energy dissipation. This paper estimates the seismic energy dissipation capacity of SSSWs considering out-of-plane buckling. In the experimental study, three SSSW specimens were designed with different width-thickness ratios and aspect ratios and tested under quasi-static cyclic loading. Test results showed that the width-thickness ratio of the links dominated the occurrence of out-of-plane buckling, which produced pinching in the hysteresis and thus reduced the energy dissipation capacity. Out-of-plane buckling occurred earlier for the links with a larger width-thickness ratio, and vice versa. Refined finite element model was built for the SSSW specimens, and validated by the test results. The concept of average pinching parameter was proposed to quantify the degree of pinching in the hysteresis. Through the parametric analysis, an equation was derived to estimate the average pinching parameter of the SSSWs with different design parameters. A new method for estimating the energy dissipation of the SSSWs considering out-of-plane buckling was proposed, by which the predicted energy dissipation agreed well with the test results.

scholarly journals Comparison of Induced Deflection and Forces in Piles Adjacent to Tunnelling and Deep Excavation in 2D and 3D Problems

2018 ◽  
Vol 203 ◽  
pp. 04011
Author(s):  
Ong Yin Hoe ◽  
Hisham Mohamad
Keyword(s):  
Bending Moment ◽  
Pile Group ◽  
3D Models ◽  
Deep Excavation ◽  
Pile Groups ◽  
Out Of Plane ◽  
National University ◽  
Plane Direction ◽  
2D And 3D ◽  
2D Model

There is a trend in Malaysia and Singapore, engineers tend to model the effect of TBM tunneling or deep excavation to the adjacent piles in 2D model. In the 2D model, the pile is modelled using embedded row pile element which is a 1-D element. The user is allowed to input the pile spacing in out-of-plane direction. This gives an impression to engineers the embedded pile row element is able to model the pile which virtually is a 3D problem. It is reported by Sluis (2014) that the application of embedded pile row element is limited to 8D of pile length. It is also reported that the 2D model overestimates the axial load in pile and the shear force and bending moment at pile top and it is not realistic in comparison to 3D model. In this paper, the centrifuge results of single pile and 6-pile group - tunneling problem carried out in NUS (National University of Singapore) are back-analysed with Midas GTS 3D and a 2D program. In a separate case study, pile groups adjacent to a deep excavation is modelled by 3D and 2D program. This paper compares the deflection and forces in piles in 2D and 3D models.

SOFTENING BRANCHES OF A TWO-DEGREE-OF-FREEDOM SYSTEM INDUCED BY SPATIAL BUCKLING

2006 ◽  
Vol 06 (04) ◽  
pp. 493-512 ◽  
Author(s):  
NOËL CHALLAMEL
Keyword(s):  
Structural Model ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Lateral Loading ◽  
Load Parameter ◽  
Imperfection Sensitivity ◽  
Softening Effect ◽  
Out Of Plane ◽  
Secondary Bifurcation ◽  
Two Degree Of Freedom

The aim of this paper is to show how geometrical non-linearity may induce equivalent softening in a simple two-degree-of-freedom spatial elastic system. The generic structural model studied is a generalization of Augusti's spatial model, incorporating lateral loading. This model could be used as a teaching model to understand the softening effect induced by out-of-plane buckling. The lateral loading in the plane of maximal stiffness is considered as the varying load parameter, whereas the vertical load is perceived as a constant parameter. It is shown that a bifurcation occurs at the critical horizontal load. The fundamental path becomes unstable, beyond this critical value. However, two symmetrical bifurcate solutions appear, whose stability depend on the structural parameters value. No secondary bifurcation is observed for this system. The presented system possesses imperfection sensitivity, and imperfection insensitivity, depending on the values of the structural parameters. In any case, for sufficiently large rotations, collapse occurs with unstable softening branches induced by spatial buckling.

Magnetic quantum oscillations in doped antiferromagnets

2017 ◽  
Vol 31 (25) ◽  
pp. 1745015
Author(s):  
V. V. Kabanov
Keyword(s):  
Magnetic Field ◽  
Polar Angle ◽  
Two Dimensional ◽  
Plane Angle ◽  
Arbitrary Direction ◽  
Magnetization Direction ◽  
Quantum Oscillations ◽  
Out Of Plane ◽  
Plane Direction ◽  
Magnetic Quantum Oscillations

Energy spectrum of electrons (holes) doped into two-dimensional (2D) antiferromagnetic (AF) semiconductors is quantized in an external magnetic field of arbitrary direction. A peculiar dependence of de Haas–van Alphen (dHvA) magneto-oscillation amplitudes on the azimuthal in-plane angle from the magnetization direction and on the polar angle from the out-of-plane direction is found. The angular dependence of the amplitude is different if the measurements are performed in the field above and below of the spin-flop field.

scholarly journals Prediction of Crushing Response for Metal Hexagonal Honeycomb under Quasi-Static Loading

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xinyu Geng ◽  
Yufei Liu ◽  
Wei Zheng ◽  
Yongbin Wang ◽  
Meng Li
Keyword(s):  
Mathematical Models ◽  
Static Loading ◽  
Theoretical Basis ◽  
Theoretical Models ◽  
Excellent Correlation ◽  
Static Compression ◽  
Out Of Plane ◽  
Plane Direction ◽  
Element Theory ◽  
Quasi Static Compression

To provide a theoretical basis for metal honeycombs used for buffering and crashworthy structures, this study investigated the out-of-plane crushing of metal hexagonal honeycombs with various cell specifications. The mathematical models of mean crushing stress and peak crushing stress for metal hexagonal honeycombs were predicted on the basis of simplified super element theory. The experimental study was carried out to check the accuracy of mathematical models and verify the effectiveness of the proposed approach. The presented theoretical models were compared with the results obtained from experiments on nine types of honeycombs under quasi-static compression loading in the out-of-plane direction. Excellent correlation has been observed between the theoretical and experimental results.

scholarly journals Development of a New Piezoelectric Actuator with Slits

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yasutomo Uetsuji ◽  
Hiroyuki Kuramae ◽  
Kazuyoshi Tsuchiya ◽  
Hidetoshi Sakamoto
Keyword(s):  
Piezoelectric Actuator ◽  
Large Deflection ◽  
Superior Performance ◽  
Uniform Electric Field ◽  
Optimum Geometry ◽  
Out Of Plane ◽  
Fixed Condition ◽  
Plane Direction ◽  
Health Monitoring Systems ◽  
Bimorph Actuators

A piezoelectric actuator was developed for fluid pumps in health monitoring systems. We devised a piezoelectric actuator with some slits, which allows the stretching and contracting deformation in in-plane direction and creates large deflection in out-of-plane direction. The static behaviors under uniform electric field have been analyzed by finite element method. And then, the optimum geometry of slits was searched by response surface methodology for unimorph and bimorph actuators to output the largest deflection under various fixed conditions. The computational results indicated that a bimorph actuator with cross-shaped slit under outside-fixed condition has superior performance for fluid pumps. The proposed slit-inserted actuators have been manufactured as an experiment. As a result, it was verified that the developed actuator can amplify the deflection compared with conventional nonslit actuators.

Energy harvesting from aeroelastic vibrations induced by discrete gust loads

2016 ◽  
Vol 28 (1) ◽  
pp. 47-62 ◽  
Author(s):  
Claudia Bruni ◽  
James Gibert ◽  
Giacomo Frulla ◽  
Enrico Cestino ◽  
Pier Marzocca
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Flow Region ◽  
Rotational Displacement ◽  
Reduced Order ◽  
Piezoelectric Elements ◽  
Out Of Plane ◽  
Gust Loads ◽  
Three Degree Of Freedom ◽  
Euler Bernoulli Beam

This article evaluates the amount of energy that can be extracted from a gust using an aeroelastic energy harvester composed of a flexible wing with attached piezoelectric elements. The harvester operates in a subcritical flow region. It is modeled as a linear Euler–Bernoulli beam sandwiched between two piezoceramics. The extended Hamilton’s principle is used to derive the harvester’s equations of motion and an eigenfunction expansion is used to form a three-degree-of-freedom reduced-order model. The degrees of freedom retained in the model are two flexural degrees for the in-plane and out-of-plane displacements, and a torsional degree for the rotational displacement. Wagner and Küssner functions are used to represent the unsteady aerodynamic and gust loading, respectively. The amount of energy extracted from the system is then compared for two different deterministic gust profiles, 1-COSINE and two sharp-edged gusts forming a square gust, for various magnitudes and durations. The results show that the harvester is able to extract more energy from the square gust profile, although for both profiles the harvester extracts more power after the gust has subsided.

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