X-shaped Structures Research Articles

Orbital Support and Evolution of CX/OX Structures in Boxy/Peanut Bars

Barred galaxies exhibit boxy/peanut or X-shapes (BP/X) protruding from their disks in edge-on views. Two types of BP/X morphologies exist depending on whether the X-wings meet at the center (CX) or are off-centered (OX). Orbital studies indicate that various orbital types can generate X-shaped structures. Here we provide a classification approach that identifies the specific orbit families responsible for generating OX- and CX-shaped structures. Applying this approach to three different N-body bar models, we show that both OX and CX structures are associated with the x1 orbit family, but OX-supporting orbits possess higher angular momentum (closer to x1 orbits) than orbits in CX structures. Consequently, as the bar slows down, the contribution of higher angular momentum OX-supporting orbits decreases and that of lower angular momentum orbits increases, resulting in an evolution of the morphology from OX to CX. If the bar does not slow down, the shape of the BP/X structure and the fractions of OX/CX-supporting orbits remain substantially unchanged. Bars that do not undergo buckling but that do slow down initially show the OX structure and are dominated by high angular momentum orbits, transitioning to a CX morphology. Bars that buckle exhibit a combination of both OX- and CX-supporting orbits immediately after the buckling but become more CX dominated as their pattern speed decreases. This study demonstrates that the evolution of BP/X morphology and orbit populations strongly depends on the evolution of the bar angular momentum.

A metasurface based close-proximity two-port circularly polarized MIMO antenna for mid-band sub-6 GHz 5G applications

This work presents a compact dual-band two-port multiple input multiple output (MIMO) antenna with high performance that is specifically used for 5G applications. The proposed design comprises closely spaced, mirror-symmetrical X-shaped structures positioned at an edge spacing of 0.02 λ0 between antenna elements. Subsequently, a metasurface is located at a distance of 0.27 λ0 above the radiator to improve the performance of the MIMO antenna. The proposed antenna resonates at 3.27 GHz within a frequency range of (3.03–3.44) GHz in the primary band, achieving a peak realized gain of 7.57 dBi. In the secondary band, the resonance occurs at 4.78 GHz with a range of (4.01–5.87) GHz below −10 dB reflection coefficient and produces a peak realized gain of 5.60 dBi. After positioning the metasurface on top of the reference antenna, the peak realized gain improves by 116.28 % in the primary band and 69.69 % in the secondary band respectively. Whereas the isolation is increased to −30.01 dB from –22.26 dB in the primary band, similarly for the secondary band the isolation is amended to −21.00 dB from −18.20 dB. Moreover, circular polarization is realized at working frequencies after placing the metasurface on the reference antenna. Simulation and measurement results prove that the S-parameters exceed more than −20 dB in both frequency bands. Additionally, MIMO performance metrics, including envelope correlation coefficient (ECC), channel capacity loss (CCL), total active reflection coefficient (TARC), mean effective gain (MEG), and diversity gain (DG) are simulated and measured. The designed antenna proves suitable for the new radio (NR) 5G of n48 (3.55–3.70 GHz) in the primary band and the n79 (4.4–5.0 GHz) in the secondary band respectively.

Dumbbell Dual-Hairpin Triggered DNA Nanonet Assembly for Cascade-Amplified Sensing of Exosomal MicroRNA.

Exosomal microRNAs (miRNAs) are valuable biomarkers closely associated with cancer progression. Therefore, sensitive and specific exosomal miRNA biosensing has been employed for cancer diagnosis, prognosis, and prediction. In this study, a miRNA-based DNA nanonet assembly strategy is proposed, enabling the biosensing of exosomal miRNAs through dumbbell dual-hairpin under isothermal enzyme-free conditions. This strategy dexterously designs a specific dumbbell dual-hairpin that can selectively recognize exosomal miRNA, inducing conformational changes to cascade-generated X-shaped DNA structures, facilitating the extension of the X-shaped DNA in three-dimensional space, ultimately forming a DNA nanonet assembly. On the basis of the target miRNA, our design enriches the fluorescence signal through the cascade assembly of DNA nanonet and realizes the secondary signal amplification. Using exosomal miR-141 as the target, the resultant fluorescence sensing demonstrates an impressive detection limit of 57.6 pM and could identify miRNA sequences with single-base variants with high specificity. Through the analysis of plasma and urine samples, this method effectively distinguishes between benign prostatic hyperplasia, prostate cancer, and metastatic prostate cancer. Serving as a novel noninvasive and accurate screening and diagnostic tool for prostate cancer, this dumbbell dual-hairpin triggered DNA nanonet assembly strategy is promising for clinical applications.

Direct Numerical Simulation of Supersonic Gas Flow Through a Circular Cylindrical Channel

The results of the theoretical solution of the problem of braking a supersonic flow in a round pipe based on direct numerical simulation by integrating the Navier – Stokes equations without the use of additional models and empirical constants are shown. Shaded maps of density distribution depending on flow parameters are presented. The flow consists of successive rhombus-shaped shock waves distributed along the entire length of the channel. It is determined that the size of x-shaped structures depends on the flow parameters. At a lower Mach number, the rhombuses have a smaller size and, accordingly, their number increases along the length of the channel. The Reynolds number also affects the size of structures, however, it is less pronounced. With a lower Reynolds number, x-shaped structures have a smaller size. It is shown that over time the flow tends to a stationary state.

The X-shaped structure with nonlinear positive stiffness compensation for low-frequency vibration isolation

X-shaped structure with quasi-zero stiffness (QZS) properties are suitable for low-frequency vibration isolation because of its simple structure. The effective working range of classic X-shaped structure (CXS) is narrow for the existence of negative stiffness region, and using positive stiffness compensation to overcome this deficiency is a common way. This paper proposes a novel nonlinear positive stiffness compensation method (NPSC) to improve the load capacity and QZS range of CXS. Different from the previous studies that utilize linear or hardening stiffness compensation, the NPSC exhibits the characteristics of softening stiffness first and then hardening stiffness and is provided by torsion springs simply. The static properties of X-shaped structure with NPSC are investigated. The result indicates the NPSC possesses dual significant advantages. Firstly, the X-shaped structure with NPSC can achieve larger load capacity and wider QZS range than that with linear or hardening stiffness compensation in optimal parameter region. Secondly, the X-shaped structure with NPSC can conveniently overlap the equilibrium position with QZS point to obtain ultra-low frequency vibration isolation effect compared to that with linear stiffness compensation. The motion equation of the proposed system is derived, and the dynamic response is solved through harmonic balance method (HBM). The influence of different parameters on displacement transmissibility is investigated and the result is verified by numerical simulation. The transmissibility comparison between the proposed model and the CXS with linear compensation shows that the proposed model possesses better vibration isolation performance. Besides, the static compression test and dynamic sweep frequency experiment are implemented, and the experiment results verify the validity of proposed model. The proposed NPSC is an important inspiration for the stiffness compensation research of X-shaped structures.

Synthesis, Properties, and Intermolecular Interactions in the Solid States of π-Congested X-Shaped 1,2,4,5-Tetra(9-anthryl)benzenes

Abstract A Negishi coupling based synthesis of 1,2,4,5-tetra(9-anthryl)benzene derivatives, possessing X-shaped molecular structures, is described. The results of X-ray crystallographic analysis show that two-dimensional highly ordered packing structure of the crystalline state of the unsubstituted derivative is a consequence of intermolecular π-π and CH-π interactions between anthracene units. Photoirradiation of the unsubstituted derivative as a precipitated solution promotes intramolecular [4+4] photocycloaddition reactions between both adjacent pairs of anthracene units to produce a crystalline polycyclic product having a unique 1.700 Å long carbon-carbon single bond. Furthermore, charge-transfer complexes, displaying near-infrared absorption and emission, are generated by co-crystallization of the X-shaped unsubstituted member of the group with electron-acceptor molecules.

Improving the solubility, hygroscopicity and permeability of enrofloxacin by forming 1:2 pharmaceutical salt cocrystal with neutral and anionic co-existing p-nitrobenzoic acid

With the purpose of improving the solubility and reducing the hygroscopicity of enrofloxacin (ENR), an unreported pharmaceutical salt cocrystal of enrofloxacin with both neutral and anionic p-nitrobenzoic acid (PNB) (ENR-PNB, C19H23FN3O3·C7H4NO4·C7H5NO4) was designed and synthesized by changing the reaction molar ratio (1:2) of ENR and coformer PNB on the basis of summarizing the past experience of our group, and its crystal structure was characterized. Single-crystal X-ray diffraction (SCXRD) analysis revealed that the salt cocrystal consists of ENR+, PNB− and PNB neutral molecule in a 1:1:1 ratio. The two asymmetric units that become centrosymmetric form an X-shaped structure centered on the ENR dimer R22(20). The adjacent X-shaped structures are interconnected by hydrogen bonds to form 1D chain and form the octamer R88(42) at the same time. As we expected, the formation of the salt cocrystal ENR-PNB results in a simultaneous improvement in the solubility and hygroscopicity of ENR. This may be the fact that ENR and PNB depend on CAHBs to raise the hydrous enthalpy of salt cocrystal. And the presence of PNB neutral molecules lower hygroscopicity of ENR in high humidity environments. Unexpectedly, the permeability of ENR-PNB was also increased compared to that of pure ENR. It is speculated that the number of polar sites in the system is greatly reduced because of hydrogen bonds formation, which increases the permeability of the ENR salt cocrystal. In addition, the in vitro antibacterial activities of ENR-PNB are enhanced at different concentrations compared to ENR. The present study implies that it is possible to improve the solubility, hygroscopic stability, permeability and antibacterial activity of enrofloxacin by changing the chemical reaction molar ratio to form salt cocrystal containing both neutral and anionic coformers, which provides a new strategy and insight to simultaneously improve the solubility and hygroscopicity and even permeability of the active ingredients of solid drugs.

Numerical Investigation on Cooling Performance of Rectangular Channels Filled with X-Shaped Truss Array Structures

In this study, different layout schemes for an X-shaped truss array channel are designed to explore the application of an X-shaped truss array structure in the mid-chord region of turbine blades. The flow and heat transfer performance of X-shaped truss array channels for three layout schemes are numerically investigated. The influence laws of the subchannel height ratio (h/H, 0.2 to 0.4) regarding the cooling performance of the channel with three subchannels are also analyzed. Then, the corresponding heat transfer and friction correlations are obtained. The results show that the layout scheme has significant effects on the flow performance, heat transfer performance and comprehensive thermal performance of X-shaped truss array channels. Among the three layout schemes of X-shaped truss array channels, the single channel has the best flow performance, while the channel with three subchannels has the best heat transfer performance and a comprehensive thermal performance. At different Reynolds numbers, the average Nusselt numbers and comprehensive thermal coefficients of the X-shaped truss array channel with three subchannels range from 38.94% to 63.49% and 27.74% to 46.49% higher than those of a single channel, respectively, and from 5.68% to 18.65% and 11.61% to 21.96% higher than those of the channel with two subchannels, respectively. For the channel with three subchannels, the subchannel height ratio has a great influence on the flow performance, but has a relatively small influence on the heat transfer performance and comprehensive thermal performance of the channel. With the increase in subchannel height ratio, the friction coefficient and average Nusselt number of the channel with three subchannels both show a trend of first increasing and then decreasing, while the comprehensive thermal coefficient shows a slow decreasing trend at higher Reynolds numbers. As a result of comprehensive consideration, the channel with three subchannels at a subchannel height ratio of 0.25 has a better overall cooling performance and is more suitable for cooling the mid-chord region of gas turbine blades. The results may provide a reference for the application of truss array structures in the internal cooling of advanced high-temperature turbine blades in the future.

Stationary scattering solution and logic operations in X-coupled tight-binding chains

The realization of logical operations on X-shaped structures consisting of two discrete input chains, which are linearly connected to two output chains through a central coupling region, is investigated. We provide the exact stationary scattering solution for the harmonic waves propagating in the proposed structure and report the full transmission spectrum. We show that a number of Boolean logic operations can be implemented using a digitization scheme of the output signal based on the amplitude modulation of the transmission coefficients. In particular, we show that the relative phase between input harmonics can be used as a control parameter to select the desired logic operation. A detailed study of the contrast ratio is used to identify optimal regions in the parameter space for the operation of each logical function.

Alkyl chain length regulated diverse 2D polymorphic self-assembly of benzothiadiazole-based π-conjugated fluorophore

Structural diversity induced by the chain-length effect in the field of two-dimensional molecular self-assembly has attracted lots of attention. In this study, the self-assembly behaviors of benzothiadiazole-based fluorophore (FHP-C12) were investigated in different solvents by scanning tunneling microscopy. The STM observations display that the self-assemblies of FHP-C12 have obvious solvent and concentration dependence. At the long-chain n-alkanes (n-tridecane, n-tetradecane)/graphite interface owing to the space matching, the grid-like and X-shaped structures are formed successively from high concentration to low concentration. Whereas the X-shaped structure is not observed at the n-dodecane/graphite interface due to the weak adsorption of solvents. When using octanoic acid and heptanoic acid as the solvents, a new H-shaped pattern is observed, due to the coadsorption of solvents. Moreover, we compare the self-assembly patterns of molecules with carbon chain length of 14 (FHP-C14) at the n-tetradecane/graphite interface. Although these two molecules only differ in the length of alkyl chains, the STM results show great differences, which indicates that the length of alkyl chains can control the self-assembly of benzothiadiazole-based systems. This work not only provides an efficient method for fabricating complex nanostructures, but also helps to promote the study of the chain-length effect in the field of supramolecular chemistry.

Vibration isolation properties of the nonlinear X-combined structure with a high-static and low-dynamic stiffness: Theory and experiment

A nonlinear X-combined structure is proposed and designed using an X-shaped structure (positive/negative stiffness mechanism) and two inclined springs (positive stiffness mechanism) to avoid existing negative stiffness and unstable factors and to improve vibration isolation characteristics. The mechanism possesses high-static and low-dynamic stiffness in a larger displacement range. In order to identify the coupling mechanism of the combination of two nonlinear mechanisms, its static and dynamic properties are investigated. The displacement transmissibility with multi-valued solutions is used to evaluate the vibration isolation of the combined structure. A new mathematical method is used to obtain a multi-valued analytical solution to the nonlinear equation of motion, which is then validated using the ADAMS software and the least square method (LSM). The novelty of this study is (a) the system has a very useful nonlinear stiffness with positive/quasi-zero/zero stiffness over the entire working range, and the quasi-zero stiffness (QZS) range is greater than that of an X-shaped structure; (b) compared to the existing nonlinear vibration isolator, such as three-spring systems and X-shaped structures, the proposed structure has the lower equivalent stiffness in the vibration isolation range, and the vibration isolation performance is better when each system has the same loading capacity; (c) the completed and accurate nonlinear solutions can more scientifically reflect the vibration isolation characteristics of the system; (d) the introduction of oblique springs into the X-shaped structure can make it easier to adjust the stiffness of the structure and use the tensile spring as the oblique spring, and the X-combined structure is easier to be designed and installed. This study shows that the proposed structure can provide excellent vibration isolation by combining two nonlinear mechanisms. These advantages are also confirmed by experiments and comparison with existing QZS isolators. This vibration isolation system will provide a new analytic method and innovative approach to the QZS isolator.

X-shaped mechanism based enhanced tunable QZS property for passive vibration isolation

A novel spring arrangement based on the X-shaped anti-vibration structure with tunable contact mechanism (NXSC) is proposed to explore much better low-frequency vibration isolation performance. An enhanced quasi-zero-stiffness (QZS) with large stroke is obtained by tuning contact position between the horizontal springs and vertical fixed rods. The loading capacity and working range of the NXSC structure can be extended by 2, 3 times compared with classical X-shaped structures. The proposed NXSC structure is adjustable to different loading requirements and resonant frequencies, and excellent vibration isolation performance can be achieved readily by tuning the contact parameter. Three types of the NXSC structure with different contact modes are designed. The effects of structural parameters on the loading capacity and QZS zone are analyzed. By tuning the contact parameter via special tuning mechanisms, the negative stiffness can be compensated completely to ensure the stability of isolation systems. Comparisons with a typical spring-mass-damper (SMD) isolator and an existing QZS isolator exhibit that the stiffness-displacement curve of the NXSC structure is much more adjustable with significantly extended QZS in a wider displacement range, and does not sacrifice loading capacity. Moreover, the NXSC structure is less sensitive to excitation amplitude than the traditional QZS isolator, and it does not produce frequency jump phenomenon and softening and hardening stiffness effects. Experiments are implemented to verify the theoretical result and demonstrate that the proposed NXSC structure possesses superior vibration isolation performance and can effectively attenuate vibration at low-frequency range. This NXSC structure presents a new and efficient way for manipulating beneficial nonlinearity based on the X-shaped structure for better engineering performance.

Critical factors in designing a class of X-shaped structures for vibration isolation

A comparative study is conducted on a class of typical X-shaped structures to explore critical design parameters in passive vibration isolation. Several benchmark X-shaped structures are therefore studied, considering the effects of several critical structural parameters on potential vibration isolation performance in different cases. Theoretical calculations, finite element simulations and experimental results show that this class of X-shaped structures in vibration isolation is critically affected by the ratio between the horizontal displacement in the installed spring and the vertical displacement of the structure, which is further nonlinearly dependent on the values of other structure parameters. This critical design parameter can act as a convenient optimization objective for selecting structural parameters in various practical applications. The results of this study thus present a new understanding of the nonlinear dynamics of the X-shaped structures which can facilitate the design or parametric selection of these structures in practices.

Structure of Our Galactic Bulge from CN Measurements

Abstract The double red clumps (DRCs) are now dominantly believed to be the strong observational line of evidence of the so-called X-shaped Galactic bar structures. Recently, Lee et al. reported a subtle mean δCN(3839) difference between the DRCs and suggested a dichotomic picture that can be seen in globular clusters: the faint red clump is the first generation, while the bright red clump corresponds to the second generation (SG). They argued that the magnitude difference between the DRCs is due to different stellar populations, and is not due to the geometric difference between the DRCs. Our reanalysis shows that their data do not appear to support the idea of multiple population-induced DRCs in our Galactic bulge. We perform fully empirical Monte Carlo simulations and find that the shape of the δCN(3839) distributions is the most stringent evidence to pursue. Our results strongly suggest that the CN distributions toward the Galactic bulge are qualitatively consistent with the X-shaped Galactic bulge with a minor fraction of the SG of about 2%–3%.

Progressive collapse of steel frame-brace structure under a column-removal scenario

Progressive collapse attracted more attention of researchers in recent years, mainly due to the increasing number of terrorist incidents worldwide. Based on the GSA and DOD design guidelines, structural resistance mechanisms to progressive collapse of steel frame, V-shaped and X-shaped braced frame structures are studied by a comparative analysis. The results show that the robustness index (RI) of steel braced frame structure is significantly greater than steel frame structure, and the X-shaped brace is greater than the V-shaped brace. Furthermore, static pushdown and nonlinear dynamic analysis are performed to study dynamic effects attributed to a column removed. The results show that the ultimate failure modes are generally similar by these two analytical method. The presence of the column bracing reduces the dynamic displacement response for a column removed instantly, and the X-shaped brace is better than the V-shaped brace.

LiTFSI/TBP-free hole transport materials with nonlinear π-conjugation for efficient inverted perovskite solar cells

We have synthesized two non-linear molecules with Y-shaped (XSln847) and X-shaped (XSln1453) structures via a facile synthetic route. Comparable to an X-shaped structure, the Y-shaped structural backbone of XSln847 enables a tight molecular stacking arrangement through multiple intermolecular short contacts, which affords a nest-layer in molecules. As a result, the pristine, Y-shaped XSln847 gives higher hole-mobility and more effective photoluminescence quenching than does XSln1453. Additionally, a decreased charge recombination occurs in the XSln847-fabricated inverted perovskite solar cells. As a consequence, the device based on XSln847 affords a higher power conversion efficiency of 15.02% than does that of XSln1453 (12.65%) under standard global AM 1.5 illumination. The efficiency is further improved to 17.16% when using XSln847 doping with 2, 3, 5, 6-tetrafluoro- 7, 7, 8, 8-tetracyanoquinodimethane, which is much higher than that of the widely-used PEDOT:PSS (11.95%) when measured under the same condition. These results demonstrate that the molecular engineering of hole transport materials with non-linear structure is a promising strategy for designing efficient molecules for inverted perovskite solar cells.

Nonlinear analysis of a bio-inspired vertically asymmetric isolation system under different structural constraints

Inspired by the limb configuration of animals in their jumping and landing motions, a systematic investigation on the properties of a class of bio-inspired vertically asymmetric X-shaped (vaX) structures is carried out to explore the advantage of nonlinear characteristics in practical engineering. The nonlinear properties of two different vaX structures are studied under different constraint conditions. Formulations of the nonlinear vibration frequency and absolute displacement transmissibility of the structures are derived by the method of multiple scales. Considering practical conditions, three different constraints (i.e., (a) the same isolations height and assembling angle; (b) the same total rod length and assembling angle; (c) the same total rod length and isolation height) are summarized in this manuscript. Under these conditions, nonlinear properties including nonlinear vibration frequency, isolation performance and static stiffness are systematically discussed. Furthermore, the influences of the assembling pattern (i.e., normal and reverse assembling) on the isolation performance are investigated in detail. The results reveal that there exists rod-length ratio $$s_{1}$$ such that the nonlinear frequency ratio of the vaX-I vibration system is lowest; the natural frequency of the vaX-I structure is independent of the assembling pattern; however, compared with the normally assembled vaX-I structure, a lower resonant peak of the transmissibility can be obtained for the reverse-assembled structure, which suggests that the nonlinear damping of the vaX-I structure is affected by the assembling pattern. Experiments are carried out to verify the influence of the assembling pattern on the natural frequency and isolation performance of the vaX structures.

LBM Simulation of Self-Assembly of Clogging Structures by Evaporation of Colloidal Suspension in 2D Porous Media

Evaporation of colloidal suspension in two-dimensional (2D) porous media leads to the formation of self-assembled clogging structures (SCS). The self-assembly pattern is studied with a hybrid two-phase lattice Boltzmann method incorporating non-isothermal phase change, particle transport and deposition models. During drying, particles accumulate along the liquid–vapor interface while colloidal suspension is evaporating. Upon reaching a certain local concentration threshold, the particles deposit and form a solid structure. The patterns formed by these structures are analyzed in different 2D porous media. In small porous systems of 4 pillars, the self-assembly of C-shaped and X-shaped structures is observed, which compares well with experimental bridge configurations. SCS in porous media of three different initial particle concentrations and of three different porosities are studied in larger porous systems. Simulated self-assembled clogging configurations show good qualitative matches with experimental configuration results. Particle concentration and porosity are both seen to affect the dynamic drying processes as well as the final self-assembled clogging configuration. The liquid configuration and the clogging structure affect each other mutually during drying. With initial concentration increasing from C0 = 0.00 to C0 = 0.16 at a given porosity $$ \phi_{0} = 0.68 $$ , the average evaporation rate and porosity decrease by 21.9% and 1.9%, respectively, due to blockage of pores. With increasing initial porosity from $$ \phi_{0} = 0.53 $$ to $$ \phi_{0} = 0.81 $$ at a given concentration of C0 = 0.16, the average evaporation rate increases by a factor of 2.9 due to larger liquid–vapor interfacial area. Also with the given concentration of C0 = 0.16, the decrease in the porosity (0.94%, 1.9% and 2.7%) is higher for higher initial porosity ( $$ \phi_{0} = 0.53, \, 0.68,{\text{ and }}0.81 $$ ), since more particles (proportional to $$ \phi_{0} \cdot C_{0} $$ ) are initially present. This work opens the door for numerically assisted design of colloid-deposition-based clogging patterns.

What determines the flatness of X-shaped structures in edge-on galaxies?

Recent observational studies of X-shaped structures revealed that values of their opening angles lie in a narrow range: from 20 deg to 43 deg with smaller X-shaped structures appearing to follow a characteristic opening angle ~ 27 deg - 31 deg. We use self-consistent numerical simulations to uncover what parameters of host galaxies govern the opening angle spread. We constructed a series of equilibrium models of galaxies with high spatial resolution, varying the dark halo and bulge contribution in the overall gravitational potential, the initial disc thickness of models and the Toomre parameter Q and followed their evolution for almost 8 Gyrs. Each model demonstrated the formation of clear X-structures with different flatness. We have obtained that opening angles lie in the range from 25 deg to 42 deg throughout the entire evolution. These values are roughly consistent with observational data. The greatest variation in the opening angles is obtained by varying the mass of the dark halo. The initial thickness of the disc and the Toomre parameter are responsible for smaller variations of the angle and shorter X-structures. An increase of both parameters changes the morphology of in-plane bars and X-structures. In some cases we observed even double X-structures. The main effect of the bulge is to prevent buckling at intermediate and late stages of the disc evolution. Comparison of models with different halo masses indicates that the smallest observable values of opening angles can be associated with the presence of a heavy dark halo (more than 3 masses of the disc within the optical radius).

Nonlinear stiffness and dynamical response characteristics of an asymmetric X-shaped structure

Abstract Nonlinearity is more and more shown to be very beneficial to various engineering practice, including vibration control, vibration energy harvesting and structural health monitoring, etc. An X-shaped structure has been investigated recently for its special and beneficial nonlinear stiffness and damping characteristics in passive vibration isolation and suppression. In this study, a novel n-layer vertically-asymmetric X-shaped structure is systematically studied for its generic modelling, nonlinear stiffness/damping features and dynamic response in vibration isolation. It is shown that, (a) micro-gravity environment can reduce the linear natural frequency and it can improve the vibration isolation performance in the vertical direction (good for micro-gravity environment vibration control), and an optimal assembly angle α1 and rod-length ratio s1 can be designed to achieve the minimum natural frequency when the gravity acceleration is not equal to zero for the best vibration isolation performance; (b) the asymmetric structure can produce lower natural frequency than that of symmetric counterparts (i.e. s1 = 1/s2 = 1) by properly adjusting rod-length ratio s1 (or s2), and the developed generic model can be used freely to study the structure response under different asymmetric settings; (c) the transmissibility of the asymmetric X-shaped structure can be tuned to have much lower transmissibility than that of the symmetric counterpart, which is very beneficial for vibration isolation; (d) the structure in the horizontal direction demonstrates very special dynamic response characteristics which can well explain a linear damper in the horizontal direction much better for vibration energy absorption for a much wider frequency range compared with the vertical direction. It should be noticed that instead of direct modeling of the vibration system in vertically direction, the dynamical equation is established with an intermediate variable, due to vertical asymmetry of the structure. The results provide new understanding on the X-shaped structures including its modelling, gravity effect, asymmetric ratio and nonlinear response in both vertical and horizontal directions, which can help practical applications of this class of structures.