Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases, The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Influence of mortar gap on natural vibration frequencies of high-speed railway track-bridge system

Based on Hamilton’s principle, the differential equations of free vibration of track-bridge systems with mortar gap are derived. Hence, a method for calculating the natural frequencies of track-bridge systems is proposed. The influence of the flexural stiffness of the track-bridge system, the vertical and longitudinal stiffness of the mortar layer,gap position and gap length on the natural frequencies of a track-bridge system is discussed. The results show that the natural frequencies of the track-bridge system are more sensitive to the change of the flexural stiffness of the bridge layer. The change of the longitudinal stiffness of the mortar layer and gap position has no obvious effect on the trackbridge system’s natural frequencies, while the interlayer vertical stiffness has a larger impact. The gap length has a more significant effect on the 4th-5th order natural frequencies of the track-bridge system. The range of the natural frequencies that are affected by the gap widens as the gap length increases.

VIBRATION PROBLEMS OF FLEXIBLE CIRCULAR PLATES WITH INITIAL DEFLECTION

In this paper, the differential equations of flexible circular plates with initial deflection are derived. The stability of motion is investigated in phase plane. The periodical solutions of nonlinear vibration for circular plates with initial deflection are obtained by use of Galerkin method and Lindstedt-Poincare perturbation method. The effect of initial deflection on the dynamic behavior of the flexible plates are also discussed.

Ultra-wide band gap and wave attenuation mechanism of a novel star-shaped chiral metamaterial

A novel hollow star-shaped chiral metamaterial(SCM)is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial,exhibiting a wide band gap over 1500 Hz.To broaden the band gap,solid single-phase and two-phase SCMs are designed and simulated,which produce two ultra-wide band gaps(approximately 5116 Hz and 6027 Hz,respectively).The main reason for the formation of the ultra-wide band gap is that the rotational vibration of the concave star of two novel SCMs drains the energy of an elastic wave.The impacts of the concave angle of a single-phase SCM and the resonator radius of a two-phase SCM on the band gaps are studied.Decreasing the concave angle leads to an increase in the width of the widest band gap,and the width of the widest band gap increases as the resonator radius of the two-phase SCM increases.Additionally,the study on elastic wave propagation characteristics involves analyzing frequency dispersion surfaces,wave propagation directions,group velocities,and phase velocities.Ultimately,the analysis focuses on the transmission properties of finite periodic structures.The solid single-phase SCM achieves a maximum vibration attenuation over 800,while the width of the band gap is smaller than that of the two-phase SCM.Both metamaterials exhibit high vibration attenuation capabilities,which can be used in wideband vibration reduction to satisfy the requirement of ultra-wide frequencies.

Optimal design for rubber concrete layered periodic foundations based on the analytical approximations of band gaps and mapping relations

The seismic performance of rubber concrete-layered periodic foundations are significantly influenced by their design,in which the band gaps play a paramount role.Aiming at providing better designs for these foundations,this study first proposes and validates the analytical formulas to approximate the bounds of the first few band gaps.In addition,the mapping relations linking the frequencies of different band gaps are presented.Furthermore,an optimal design method for these foundations is developed,which is validated through an engineering example.It is demonstrated that ensuring the superstructure’s resonance zones are completely covered by the corresponding periodic foundation’s band gaps can achieve satisfactory vibration attenuation effects,which is a good strategy for the design of rubber concrete layered periodic foundations.

纳米GaP粉体对结晶紫的光催化降解及其振动光谱分析

对纳米 Ga P粉体 -结晶紫水溶液光催化降解进行了研究。纳米 Ga P粉体在紫外光照射条件下对结晶紫具有光催化降解作用 ;随平均颗粒度的降低 ,纳米 Ga P粉体的光催化活性增加。红外光谱测试结果表明 :进行光催化过程以后 ,纳米 Ga P表面存在的几种主要振动模式变化较小或不变 ;拉曼光谱测试结果表明 :纳米 Ga P粉体的横向光学声子模与纵向光学声子模 。

DU20模拟振法对MCAO模型大鼠缺血区GAP-43表达的影响

目的观察"百会"(DU20)模拟振法对局灶性脑缺血大鼠(MCAO)模型中生长相关蛋白-43(GAP-43)表达的变化,探讨其对脑缺血早期结构可塑性的影响。方法采用大鼠大脑中动脉栓塞法制成MCAO模型,研究缺血后1、7、14 d缺血区GAP-43的表达及振法对其影响。结果各组大鼠在不同时间段GAP-43表达的比较:1)在造模后第1天,空白对照组和假手术组与其他3组有统计学意义(P<0.01),空白对照组、假手术组和模型组与电针组、振法组无统计学意义(P>0.05);2)第7天,模型组与空白对照组和假手术组有统计学意义(P<0.01),模型组与电针组、振法组有统计学意义(P<0.05),空白对照组和假手术组与电针组、振法组有统计学意义(P<0.05);3)第14天,模型组与其他3组有统计学意义(P<0.05),空白对照组和假手术组与电针组、振法组无统计学意义(P>0.05);4)在各个时段,电针组与振法组比较无统计学意义(P>0.05),空白组与假手术组无统计学意义(P>0.05)。结论 "百会"模拟振法可以提高MCAO模型大鼠GAP-43在缺血区的表达,对加快脑缺血早期结构可塑性具有一定的影响。

A brief review of metamaterials for opening low-frequency band gaps

Metamaterials are an emerging type of man-made material capable of obtaining some extraordinary properties that cannot be realized by naturally occurring materials.Due to tremendous application foregrounds in wave manipulations,metamaterials have gained more and more attraction.Especially,developing research interest of low-frequency vibration attenuation using metamaterials has emerged in the past decades.To better understand the fundamental principle of opening low-frequency(below 100 Hz)band gaps,a general view on the existing literature related to low-frequency band gaps is presented.In this review,some methods for fulfilling low-frequency band gaps are firstly categorized and detailed,and then several strategies for tuning the low-frequency band gaps are summarized.Finally,the potential applications of this type of metamaterial are briefly listed.This review is expected to provide some inspirations for realizing and tuning the low-frequency band gaps by means of summarizing the related literature.

Local resonance phononic band gaps in modifiedtwo-dimensional lattice materials

In this paper, modified two-dimensional peri- odic lattice materials with local resonance phononic band gaps are designed and investigated. The design concept is to introduce some auxiliary structures into conventional pe- riodic lattice materials. Elastic wave propagation in this kind of modified two-dimensional lattice materials is studied us- ing a combination of Bloch＇s theorem with finite element method. The calculated frequency band structures of illus- trative modified square lattice materials reveal the existence of frequency band gaps in the low frequency region due to the introduction of the auxiliary structures. The mechanism underlying the occurrence of these frequency band gaps is thoroughly discussed and natural resonances of the auxiliary structures are validated to be the origin. The effect of geo- metric parameters of the auxiliary structures on the width of the local resonance phononic band gaps is explored. Finally, a conceptual broadband vibration-insulating structure based on the modified lattice materials is designed and its capabil- ity is demonstrated. The present work is anticipated to be useful in designing structures which can insulate mechanical vibrations within desired frequency ranges.

Study on the vibration band gap and vibration attenuation property of phononic crystals

Phononic crystals (PCs) are functional materials with periodic structures and elas- tic wave (vibration) band gaps, where propagation of vibrations with frequencies within band gaps is forbidden. PCs with finite periods can restrain the propagation of vibrations with frequencies in band gaps and thus has vibration attenuation property. Worldwide, many institutions and researchers are engaged in the re- search of PCs, however, studies on the vibration attenuation property of PCs are still limited. In this paper, we report our study of band gaps and vibration attenua- tion properties of 1) a simplified PC—periodic mass-spring structures, 2) longitu- dinal vibration of one-dimensional (1D-), 2D-, 3D-PCs, and 3) the flexural vibration of 1D- and 2D-PCs. These studies provide a foundation for the applications of PCs in vibration attenuation.

Thickness-shear vibration of a circular cylindrical ceramic cylinder with unattached electrodes and air gaps

We analyze thickness-shear vibration of an axially poled circular cylindrical tube with unattached electrodes and air gaps. Both free and electrically forced vibrations are studied. Exact solutions are obtained from the equations of linear piezoelectricity. Resonant frequencies and the impedance of the transducer are calculated from the solution. Results show that the resonant frequencies are sensitive to the dimensions of the air gaps when the gaps are thin. The impedance depends strongly on the air gaps.

Application and optimization design of non-obstructive particle damping-phononic crystal vibration isolator in viaduct structure-borne noise reduction

The problems associated with vibrations of viaducts and low-frequency structural noise radiation caused by train excitation continue to increase in importance.A new floating-slab track vibration isolator-non-obstructive particle damping-phononic crystal vibration isolator is proposed herein,which uses the particle damping vibration absorption technology and bandgap vibration control theory.The vibration reduction performance of the NOPD-PCVI was analyzed from the perspective of vibration control.The paper explores the structure-borne noise reduction performance of the NOPD-PCVIs installed on different bridge structures under varying service conditions encountered in practical engineering applications.The load transferred to the bridge is obtained from a coupled train-FST-bridge analytical model considering the different structural parameters of bridges.The vibration responses are obtained using the finite element method,while the structural noise radiation is simulated using the frequency-domain boundary element method.Using the particle swarm optimization algorithm,the parameters of the NOPD-PCVI are optimized so that its frequency bandgap matches the dominant bridge structural noise frequency range.The noise reduction performance of the NOPD-PCVIs is compared to the steel-spring isolation under different service conditions.

Large Amplitude Flexural Vibration of the Orthotropic Composite Plate Embedded with Shape Memory Alloy Fibers

The free and forced vibration of large deformation composite plate embedded with shape memory alloy （SMA） fibers is investigated. A thermo-mechanical constitutive equation of SMA proposed by Brinson et al. is employed and the constitutive equations for evaluation of the properties of a hybrid SMA composite laminate are obtained. Based on the nonlinear theory of symmetrically laminated anisotropic plates, the governing equations of flexural vibration in terms of displacement and stress functions are derived. The Galerkin method has been used to convert the original partial differential equation into a nonlinear ordinary differential equation, which is then solved with harmonic balance method. The numerical results show that the relationship between nonlinear natural frequency ratio and temperature for the nonlinear plate has similar characteristics compared with that of the linear one, and the effects of temperature on forced response behavior during phase transformation from Martensite to Austenite are significant. The effects of the volume fraction of the SMA fiber, aspect ratio and free vibration amplitude on the dynamical behavior of the plate are also discussed.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

Multi-resonator coupled metamaterials for broadband vibration suppression

In this study,multi-resonator coupled metamaterials(MRCMs)with local resonators are proposed to obtain the multiple and wide band gaps.Kinetic models of the MRCMs are established,and the boundary conditions of the unit cell are obtained with Bloch's theorem.The effects of structural parameters,including the mass of the resonator and the spring stiffness,on the distributions of the band gaps are studied.Furthermore,the frequency domain responses and the time domain responses are calculated for analyzing the structural vibration characteristics and the effects of damping on structural vibration.The results show that the frequency domain response can accurately express the distributions of the band gaps of the MRCMs,and we can increase the number and the width of the band gaps by using the MRCMs for the superior vibration suppression capability.

Analysis on vibration characteristics of large-size rectangular piezoelectric composite plate based on quasi-periodic phononic crystal structure

Based on the theory of composite materials and phononic crystals(PCs),a large-size rectangular piezoelectric composite plate with the quasi-periodic PC structure composed of PZT-4 and epoxy is proposed in this paper.This PC structure can suppress the transverse vibration of the piezoelectric composite plate so that the thickness mode is purer and the thickness vibration amplitude is more uniform.Firstly,the vibration of the model is analyzed theoretically,the electromechanical equivalent circuit diagram of three-dimensional coupled vibration is established,and the resonance frequency equation is derived.The effects of the length,width,and thickness of the piezoelectric composite plate at the resonant frequency are obtained by the analytical method and the finite element method,the effective electromechanical coupling coefficient is also analyzed.The results show that the resonant frequency can be changed regularly and the electromechanical conversion can be improved by adjusting the size of the rectangular piezoelectric plate.The effect of the volume fraction of the scatterer on the resonant frequency in the thickness direction is studied by the finite element method.The band gap in X and Y directions of large-size rectangular piezoelectric plate with quasi-periodic PC structures are calculated.The results show that the theoretical results are in good agreement with the simulation results.When the resonance frequency is in the band gap,the decoupling phenomenon occurs,and then the vibration mode in the thickness direction is purer.

A Design Method of Bending Deflection on Hyper-Static Leaf Spring

A group of leaf springs which provides the flexible support of stator is designed to satisfy the requirement of low vibration motor at megawatt （MW） level. Spring steel 65Mn is chosen as the material of the leaf spring. The size of the leaf spring is obtained by calculation and load analysis according to a deflection formula. The deflection and stiffness of the single leaf spring is calculated with both theoretical method and finite element analysis （FEA）. A deflection test platform is established based on actual force and boundary condition to verify the deflection and stiffness of the leaf spring. The results show that the maximal deflection of the three pieces of 1.2 mm leaf spring group is 0.71 mm and the stiffness of the leaf spring group is 364 N/mm, which satisfies the requirements of the motor. The design method is also applicable for other MW power level motors.

Further Investigation for Nonlinear Free Vibration of Elastic Circular Plate with Large Amplitude

The nonlinear free vibrations of the elastic circular thin plate with large amplitude taking radial force of inertia into account are investigated by using method similar to modified iterative method.The algorithm and formulas finding its approximate analytical solution are provided,and the solution behaviors are also discussed through the calculating example.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅲ)--CANTILEVER RECTANGULAR PLATES

In this paper,applying the method of the reciprocal theorem,we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates,the figures and tables of number value of bending moment and the deflection amplitudes as well.

Analysis of Plate Vibration under Exponentially Varying Thermal Condition

A mathematical model is developed to assist the design engineers by analyzing the vibration response of non-homogeneous orthotropic rectangular plate under exponentially varying thermal condition. Plate thickness varies parabolically in both directions. Using Rayleigh Ritz approach, frequency parameter and two term deflection function is calculated for diverse values of taper constants. For the best comprehension of the vibration analysis, results are depicted graphically.