Theoretical and experimental investigations on an X-shaped vibration isolator with active controlled variable stiffness

A novel X-shaped variable stiffness vibration isolator(X-VSVI)is proposed.The Runge-Kutta method,harmonic balance method,and wavelet transform spectra are introduced to evaluate the performance of the X-VSVI under various excitations.The layer number,the installation angle of the X-shaped structure,the stiffness,and the active control parameters are systematically analyzed.In addition,a prototype of the X-VSVI is manufactured,and vibration tests are carried out.The results show that the proposed X-VSVI has a superior adaptability to that of a traditional X-shaped mechanism,and shows excellent vibration isolation performance in response to different amplitudes and forms of excitations.Moreover,the vibration isolation efficiency of the device can be improved by appropriate adjustment of parameters.

Seismic Behavior of Specially Shaped Column Joints with X-Shaped Reinforcement

To investigate the seismic behavior of specially shaped column joints with X-shaped reinforcement,two groups of specimens with or without X-shaped reinforcement in joint core region were tested under constant axial compression load and low reversed cyclic loading,which imitated low to moderate earthquake force.The seismic behavior of specially shaped column joints with X-shaped reinforcement in terms of bearing capacity,displacement,ductility,hysteretic curve,stiffness degradation and energy dissipation was studied and compared to that without Xshaped reinforcement in joint core region.With the damage estimation model,the accumulated damage was analyzed.The shearing capacity formula of specially shaped column joints reinforced by X-shaped reinforcement was proposed with a simple form.The test results show that X-shaped reinforcement is an effective measure for improving the seismic behavior of specially shaped column joints including deformation behavior,ductility and hysteretic characteristic.All specimens were damaged with gradual stiffness degeneration.In addition,X-shaped reinforcement in the joint core region is an effective way to lighten the degree of cumulated damage.The good seismic performance obtained from the specially shaped column joint with X-shaped reinforcement can be used in engineering applications.The test value is higher than the calculated value,which indicates that the formula is safe for the design of specially shaped column joints.

TRANSITIONS AND MODRPHOLOGY OF MAIN-CHAIN LIQUID CRYSTALLINE POLYMERS WITH X-SHAPED MESOGENS

The transitions and morphology of a series of main-chain liquid crystalline polymer with X-shaped mesogens were studied by means of DSC,SALS and polarizing microscopy techniques. Aneven-odd effect was observed for samples with different size of the substituents on the mesogenends. The isotropization process was similar to that of main-chain polymers with rod-likemesogens. No crystallization was detected for specimens cooling down from their isotropic meltstate. However two of the samples may crystallize in cooling process directly from the liquidcrystalline state.

SYNTHESIS OF MAIN CHAIN LIQUID CRYSTALLINE COPOLYESTERS WITH X-SHAPED TWO-DIMENSIONAL MESOGENIC UNIT AND CROWN ETHER CYCLE

A novel series of main chain liquid crystalline copolyesters with X-shaped two-dimensional mesogenic unit and crown ether cycle of cis-4,4＇-bis（4-hydroxyphenylazo） dibenzo-18-crown-6 was prepared via solution condensation polymerization from 4,4＇-（a;arhexanedioyloxy） dibenzoyl dichloride （MI）, 2,5-bis（p-octyloxybenzoyloxy） hydro-quinone （M2） and cis-4,4＇-bis（4-hydroxyphenylazo） dibenzo-18-crown-6 （M3）. Monomer MI was synthesized by esterification and substitution of adipoyl chloride with p-hydroxybenzoic acid, monomer M2 was synthesized by esterfication and reduction reaction of 2,5-dihydroxybenzoquinone and p-octanoxybenzoyl chloride and monomer M3 was synthesized by diazotization and coupling reaction of cis-diaminodibenzo-18-crown-6 with phenol. The molecular weights of copolyesters are not high, and the intrinsic viscosity [η] of copolyesters ranges from 0.25-0.35. The monomers＇ structures were identified by using elemental analysis, IR, UV, ^1H-NMR, MS, etc. All the copolyesters are yellowish powders and insoluble in THF and CHC13 at room temperature except cPg. The properties of copolyesters were investigated by using GPC, [η] , DSC, TG, WAXD and POM. It was found that all the copolyesters entered into liquid crystal phase when they were heated to above their melting temperature （Tin）. The typical smectic and nematic phase texture can be observed on POM. Their mesophase transition temperature and thermal stability change regularly with varying the content of cis-4,4＇-bis（4-hydroxyphenylazo） dibenzo-18-crown-6 unit in the copolyesters.

SYNTHESIS AND CHARACTERIZATION OF MAIN CHAIN AROMATIC LIQUID CRYSTAL COPOLYESTERS WITH X-SHAPED AND ROD-SHAPED MESOGENIC UNITS

A series of main chain liquid crystal aromatic copolyesters with X-shaped and rod-shaped mesogenic units were synthesized via solution condensation polymerizations of 4,4'-(alpha,omega-octanedioyloxy)-dibenzoyl dichlorides with 2,5-bis(p-octanoxy benzoyloxy)-hydroquinone and diphenol. All of the copolyesters showed thermotropic liquid crystalline behaviors through observations using DSC, polarized microscopy and X-ray diffraction. The melting point (T-m) and the isotropization temperature (T-i) change regularly with varying the content of diphenol unit in the copolymers.

The review of clinical application of X-shaped balance acupuncture therapy for joint pain and activity disorder

Musculoskeletal diseases such as neck, shoulder, back and leg pain are ext remely common in clinic. Diseases of the joints of the ext remi ti es, especially sputum, wr ist spr ains, and periarthritis of the shoulders, and even lumbar disc herniation, use X-shaped balance acupuncture therapy to relieve pain and improve motor function. The method of obtaining acupoints is simple and easy to operate. Many of clinical comparison shows that this therapy is simple to conventional acupuncture and moxibustion in the treatment of local pain and joint diseases. This review concluded the advantaged about the X-shaped balance acupuncture therapy and it worth to clinical promotion.

Constructal entransy dissipation rate minimization for X-shaped vascular networks

Combining with entransy theory, constructal designs of the X-shaped vascular networks(XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates(EDRs) of the XSVNs are minimized, and the optimal constructs of the XSVNs are derived. Comparison of the optimal constructs of the XSVNs with two optimization objectives(EDR minimization and entropy generation rate(EGR) minimization) is conducted. It is found that when the dimensionless mass flow rate(DMFR) is small, the optimal diameter ratio of the elemental XSVN derived by EDR minimization is different from that derived by EGR minimization. For the multilevel XSVN, when the DMFR is 100, compared the XSVN with the corresponding H-shaped vascular network(HSVN), the dimensionless EDRs of the elemental, second and fourth order XSVNs are reduced by 26.39%, 15.34% and 9.81%, respectively. Compared with the entransy dissipation number(EDN) of the second order XSVN before angle optimization, the EDN after optimization is reduced by 26.15%, which illustrates that it is significant to conduct angle optimization of the XSVN. Entransy theory is applied into the constructal design of the vasculature with heat transfer and fluid flow in this paper, which provides new directions for the vasculature designs.

RELATIONSHIP OF FIRST STEP HEIGHT,STEP SLOPE AND CAVITY IN X-SHAPED FLARING GATE PIERS

The energy dissipation of X-shaped flaring gate piers ahead of a stepped spillway was adopted in the Suofengying Hydroplant. Under the circumstance that the first step is higher than others, at the step surface an aerated cavity occured behind piers. The interaction of the weir head, the elevation difference between crest and chamber outlet, the first step height, the slopes of weir end and step, and the size of cavity, was investigated, the expression was derived to characterize their relationship, and the corresponding curves were plotted. The comparison of the calculated and simulated results with the measured data was performed. When the slopes of step and weir end are equivalent, the relative height difference between the first and second steps becomes the main factor influencing the aerated cavity. These findings may be useful in practical applications.

Characterization of x-shaped nanoaperture antenna arrays operating in mid-infrared regime

The characterization of x-shaped antenna arrays operating in the mid-infrared is proposed. An equivalent circuit model for the resonant characteristic of the x-shaped nanoaperture antenna arrays is also included. In order to understand the resonance behavior of the structure, a detailed study of the field-enhancement capabilities and light transmission characteristics of the structure is proposed. In the experimental stud- ies, the transmission characteristics of the periodic x-apertures are analyzed by varying the geometrical dimensions. Consequently, it is observed that the periodic subwavelength x-apertures show extremely high near-field optical resolution and enhanced transmission compared with the other nm-sized apertures.

Modeling,analysis,and simulation of X-shape quasi-zero-stiffness-roller vibration isolators

Existing quasi-zero stiffness(QZS)isolators are reviewed.In terms of their advantages,a novel X-shape QZS isolator combined with the cam-roller-spring mechanism(CRSM)is proposed.Different from the existing X-shape isolators,oblique springs are used to enhance the negative stiffness of the system.Meanwhile,the CRSM is used to eliminate the gravity of the loading mass,while the X-shape structure leaves its static position.The existing QZS isolators are demonstrated and classified according to their nonlinearity mechanisms and classical shapes.It is shown that the oblique spring can realize negative stiffness based on the simplest mechanism.The X-shape has a strong capacity of loading mass,while the CRSM can achieve a designed restoring force at any position.The proposed isolator combines all these advantages together.Based on the harmonic balance method(HBM)and the simulation,the displacement transmissibilities of the proposed isolator,the X-shape isolators just with oblique springs,and the X-shape isolators in the traditional form are studied.The results show that the proposed isolator has the lowest beginning isolation frequency and the smallest maximum displacement transmissibility.However,it still has some disadvantages similar to the existing QZS isolators.This means that its parameters should be designed carefully so as to avoid becoming a bistable system,in which there are two potential wells in the potential energy curve and thus the isolation performance will be worsened.

Vibration isolation performance analysis of a bilateral supported bio-inspired anti-vibration control system

To achieve better anti-vibration performance in a low frequency region and expand the range of vibration isolation,a bilateral supported bio-inspired anti-vibration(BBAV)structure composed of purely linear elements is proposed,inspired by the motion form of bird legs and the nonlinear extension and compression of muscles and tendons.The kinematic relations and nonlinear dynamic model considering vertical and rotational vibrations are established.The loading capacity and equivalent stiffness are investigated with key parameters.The amplitude-frequency characteristics and force transmissibility are used to evaluate the stability and anti-vibration performance with the effects of the excitation amplitude,rod length,installation angle,and spring stiffness.The results show that the loading requirements and resonant characteristics of the BBAV structure are adjustable,and superior vibration isolation performance can be achieved readily by tuning the parameters.The X-shaped vibration structure is sensitive to the spring stiffness,which exhibits a wider vibration isolation bandwidth with smaller spring stiffness.Besides,depending on the parameters,the nonlinear behavior of the BBAV system can be interconverted between the softening type and the hardening type.The theoretical analysis in this study demonstrates the advantages and effectiveness of the vibration isolation structure.

Hybrid Passive/Active Vibration Control of a Loosely Connected Spacecraft System

In this paper,a hybrid passive/active vibration(HPAV)controller of a loosely connected spacecraft consisting of a servicing satellite,a target and an X-shape structure isolator is first proposed to suppress vibrations of the system when subjected to the impulsive external excitations during the on-orbit missions.The passive dynamic response of the combined system can be adjusted appropriately to achieve the desired vibration isolation performance by tuning the structural parameters of the bio-inspired X-shape structure.Moreover,the adaptive control design through dynamic scaling technique is selected as the active component to maintain high vibration isolation performance in the presence of parameter uncertainties such as mass of the satellite platform,the damping and rotation friction coefficients of the X-shape structure.Compared with the pure passive system and the traditional spring-mass-damper(SMD)isolator,the HPAV strategy witnesses lower transmissibility,smaller vibration amplitude and higher convergence rate when subjected to the post-capture impact.Numerical simulations demonstrate the feasibility and validity of the proposed hybrid control scheme in suppressing vibrations of the free-floating spacecraft.