On a Damped Vibration Problem Involving p-Laplacian Operator:Fast Homoclinic Orbits

In this paper,we deal with the nonlinear second-order differential equation with damped vibration term involving p-Laplacian operator.Of particular interest is the resolution of an open problem.An interesting outcome from our result is that we can obtain the fast homoclinic solution with general superlinear growth assumption in suitable Sobolev space.To our knowledge,our theorems appear to be the first such result about damped vibration problem with p-Laplacian operator.

Nonlocal stress gradient formulation for damping vibration analysis of viscoelastic microbeam in thermal environment

An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model,and is utilized to investigate the free damping vibration analysis of the viscoelastic BernoulliEuler microbeams in thermal environment.Hamilton's principle is used to derive the differential governing equations and corresponding boundary conditions.The integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive constraints.The size-dependent axial thermal stress due to the variation of the environmental temperature is derived explicitly.The Laplace transformation is utilized to obtain the explicit expression for the bending deflection and moment.Considering the boundary conditions and constitutive constraints,one can get a nonlinear equation with complex coefficients,from which the complex characteristic frequency can be determined.A two-step numerical method is proposed to solve the elastic vibration frequency and the damping ratio.The effects of length scale parameters,viscous coefficient,thermal stress,vibration order on the vibration frequencies,and critical viscous coefficient are investigated numerically for the viscoelastic Bernoulli-Euler microbeams under different boundary conditions.

Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation

A nonlocal study of the vibration responses of functionally graded(FG)beams supported by a viscoelastic Winkler-Pasternak foundation is presented.The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation,which were not considered in most literature on this subject,and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven(ε-D)and stress-driven(σ-D)two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered,which can address both the stiffness softening and toughing effects due to scale reduction.The generalized differential quadrature method(GDQM)is used to solve the complex eigenvalue problem.After verifying the solution procedure,a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained.Subsequently,the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.

A low-frequency pure metal metamaterial absorber with continuously tunable stiffness

To address the incompatibility between high environmental adaptability and deep subwavelength characteristics in conventional local resonance metamaterials,and overcome the deficiencies in the stability of existing active control techniques for band gaps,this paper proposes a design method of pure metal vibration damping metamaterial with continuously tunable stiffness for wideband elastic wave absorption.We design a dual-helix narrow-slit pure metal metamaterial unit,which possesses the triple advantage of high spatial compactness,low stiffness characteristics,and high structural stability,enabling the opening of elastic flexural band gaps in the low-frequency range.Similar to the principle of a sliding rheostat,the introduction of continuously sliding plug-ins into the helical slits enables the continuous variation of the stiffness of the metamaterial unit,achieving a continuously tunable band gap effect.This successfully extends the effective band gap by more than ten times.The experimental results indicate that this metamaterial unit can be used as an additional vibration absorber to absorb the low-frequency vibration energy effectively.Furthermore,it advances the metamaterial absorbers from a purely passive narrowband design to a wideband tunable one.The pure metal double-helix metamaterials retain the subwavelength properties of metamaterials and are suitable for deployment in harsh environments.Simultaneously,by adjusting its stiffness,it substantially broadens the effective band gap range,presenting promising potential applications in various mechanical equipment operating under adverse conditions.

Vibration Control of a Composite Beam Using Self-sensing Semi-active Approach

Structural vibration control was an active research area for the past twenty years because of their potential applications in aerospace structures,civil structures,naval structures,etc.Semi-active vibration control methods based on piezoelectric actuators and synchronized switch damping on inductance（SSDI） techniques attract the attention of many researchers recently due to their advantages over passive and active methods.In the SSDI method,a switch shunt circuit is connected to the piezoelectric patch to shift the phase and amplify the magnitude of the voltage on the piezoelectric patch.The most important issue in SSDI method is to control the switching actions synchronously with the maximum vibration displacement or maximum strain.Hence,usually a displacement sensor is used to measure the vibration displacement or a collocated piezoelectric sensor is needed to measure the strain of the structure near the piezoelectric actuator.A self-sensing SSDI approach is proposed and applied to the vibration control of a composite beam,which avoids using a separate sensor.In the self-sensing technique,the same piezoelectric element functions as both a sensor and an actuator so that the total number of required piezoelectric elements can be reduced.One problem in the self-sensing actuator,which is the same as that in the traditional collocated piezoelectric sensors,is the noise generated in the sensor signal by the impact of voltage inversion,which may cause extra switching actions and deteriorate control performance.In order to prevent the shunt circuit from over-frequent on-and-off actions,a simple switch control algorithm is proposed.The results of control experiments show that the self-sensing SSDI approach combined with the improved switch control algorithm can effectively suppress over-frequent switching actions and gives good control performance by reducing the vibration amplitude by 45%,about 50% improvement from the traditional SSDI with a separate piezoelectric element and a classical switch.

TENSILE-SHEAR STRENGTH AND BREAKING MORPHOLOGY FOR VIBRATION DAMPING LAMINATED STEEL SHEET

The phenolic resin-chloroprene nthher was used for sandwich in manufueturing the vibra-tion damping laminated steel sheet (also calied laminated sheet), Il is a metal matrix com-posite. The tensie-shear tests have been conducted over a range of temperatures from 20C to 150C and at the strain rates from 1.67× 10 ^(5) to 1.67× 10^(-2)s^(-1). The results show that test temperature will significaiilly affect the tensile shear strength of laminated sheet. and a minimal strength and a minimal activation energy occur near 80C . The tensile-shear breaking morphology of laminated sheet varies with strain rate and test temjteralurc.

Experimental study on integral axial squeeze film damper to suppress longitudinal vibration of propulsion shafting

This paper aims at investigating the effectiveness of squeeze oil film in suppressing the longitudinal vibration of propulsion shaft systems through a novel integral axial squeeze film damper(IASFD).After designing the IASFD,a propulsion shafting test rig for the longitudinal vibration control is built.Longitudinal vibration control experiments of the propulsion shafting are carried out under different magnitude and frequency of the excitation force.The results show that both IASFD elastic support and IASFD elastic damping support have excellent vibration attenuation characteristics,and can effectively suppress the longitudinal vibration of the shaft system in a wide frequency range.However,IASFD elastic damping support has a more significant vibration reduction effect than the other supports,and increasing the damping of the system has obvious effect on reducing the shafting vibration.For an excitation force of 45 N,the maximum reduction of the vibration amplitude is 89.16%.Also,the vibration generated by the resonance phenomenon is also significantly reduced.

Bionic Design and Simulation Analysis of Energy⁃Efficient and Vibration⁃Damping Walking Mechanism

African ostrich can run for 30 min at a speed of 60 km/h in the desert,and its hindlimb has excellent energy saving and vibration damping performance.In order to realize the energy⁃efficient and vibration⁃damping design of the leg mechanism of the legged robot,the principle of engineering bionics was applied.According to the passive rebound characteristic of the intertarsal joint of the ostrich foot and the characteristic of variable output stiffness of the ostrich hindlimb,combined with the proportion and size of the structure of the ostrich hindlimb,the bionic rigid⁃flexible composite legged robot single⁃leg structure was designed.The locomotion of the bionic mechanical leg was simulated by means of ADAMS.Through the motion simulation analysis,the influence of the change of the inner spring stiffness coefficient within a certain range on the vertical acceleration of the body centroid and the motor power consumption was studied,and the optimal stiffness coefficient of the inner spring was obtained to be 200 N/mm,and it was further verified that the inner and outer spring mechanism could effectively reduce the energy consumption of the mechanical leg.Simulation results show that the inner and outer spring mechanism could effectively reduce the motor energy consumption by about 72.49%.

Vibration transmissibility characteristics of smart spring vibration isolation system

The objective of this work was to study the vibration transmissibility characteristics of the undamped and damped smart spring systems. The frequency response characteristics of them were analyzed by using the equivalent linearization technique, and the possible types of the system motion were distinguished by using the starting and ending frequencies. The influences of system parameters on the vibration transmissibility characteristics were discussed. The following conclusions may be drawn from the analysis results. The undamped smart spring system may simultaneously have one starting frequency and one ending frequency or only have one starting frequency, and the damped system may simultaneously have two starting frequencies and one ending frequency. There is an optimal control parameter to make the peak value of the vibration transmissibility curve of the system be minimum. When the mass ratio is far away from the stiffness ratio, the vibration transmissibility is small. The effect of the damping ratio on the system vibration transmissibility is significant while the control parameter is less than its optimal value. But the influence of the relative damping ratio on the vibration transmissibility is small.

Research on Railway Engineering Experiment Teaching Principles Based on Virtual Simulation Experiment Teaching——Taking the Floating Slab Vibration Damping Track Virtual Experiment as an Example

Virtual simulation teaching is an addendum to the experimental teaching mode of railway engineering,and the two teaching methods complement each other and merge with each other.In view of the current research,there is little discussion about the integration path of the two above.Based on the connotation and design of virtual simulation teaching,this research systematically expounds the integration of the real path and path optimization problems,and puts forward the railway engineering experimental teaching principles based on virtual simulation teaching.On the basis of this research,a virtual simulation experiment platform for vibration mechanics and its application in the floating slab vibration damping track was developed to make full use of three-dimensional modeling,virtual reality,human-computer interaction and other technologies,which can realistically simulate the vibration law and vibration damping effect of the rail transit system,and in the hope that the virtual simulation teaching can be widely used in the experimental teaching mode of railway engineering in the future.

Multiplicity of Periodic Bouncing Solutions for Sublinear Damped Variation Systems via Nonsmooth Variational Methods

Two results about the multiplicity of nontrivial periodic bouncing solutions for sublinear damped vibration systems-x=g(t)x+f(t,x) are obtained via the Generalized Nonsmooth Saddle Point Theorem and a technique established by Wu Xian and Wang Shaomin.Both of them imply the condition "f≥0" required in some previous papers can be weakened,furthermore,one of them also implies the condition about ■F(t,x)/■t required in some previous papers,such as "|■F(t,x)/■t|=σ_(0)F(t,x)" and "|■F(t,x)/■t|≤C(1+F(t,x))", is unnecessary,where F(t,x):=∫_(0)~xf(t,x)ds,and σ_(0),C are positive constants.

Static-deformation based fault diagnosis for damping spring of large vibrating screen

Based on the statics theory, a novel and feasible twice-suspended-mass method(TSMM) was proposed to deal with the seldom-studied issue of fault diagnosis for damping springs of large vibrating screen(LVS). With the static balance characteristic of the screen body/surface as well as the deformation compatibility relation of springs considered, static model of the screen surface under a certain load was established to calculate compression deformation of each spring. Accuracy of the model was validated by both an experiment based on the suspended mass method and the properties of the 3D deformation space in a numerical simulation. Furthermore, by adopting the Taylor formula and the control variate method, quantitative relationship between the change of damping spring deformation and the change of spring stiffness, defined as the deformation sensitive coefficient(DSC), was derived mathematically, from which principle of the TSMM for spring fault diagnosis is clarified. In the end, an experiment was carried out and results show that the TSMM is applicable for diagnosing the fault of single spring in a LVS.

The Absorption Behavior of Tetrapod Shaped ZnO Whiskers

The infrared absorption spectrum of zinc oxide whiskers with tetrapod shape was recorded and compared with ZnO powder. The absorptions of microwave and sound were investigated with a result showing that the ZnO whiskers are of excellence as absorbents of microwave and soundproofing. The results of vibration damping tests of polyvinyl chloride indicate that the material containing the tetrapod shaped ZnO whiskers appears superior damping characteristics.

NEW ANALYTICAL METHOD ON SPACE OBLIQUE SPRING

The kinematical characteristic analysis of a space oblique spring is carried out.It first points out that the vibration of a space oblique spring can be regarded as the composition of an oscillatory vibration and a straight linear vibration.The formulas are derived for the calculation of restoring force and damping force of the spring according to the idea above.

Design and Investigation of a High-Sensitivity Tilt Sensor Based on FBG

In this paper,a high-sensitivity fiber Bragg grating(FBG)tilt sensor using a cantilever-based structure is introduced.Two FBGs are fixed on a specially designed elastomer.One end of the elastomer is connected to the mass block,and the other end is connected to the shell.The principle of the tilt sensor is introduced in detail,and the mathematical model is established.The performance of the sensor is studied.The results show that there is a good linear relationship between the central wavelength difference of the two FBGs and the tilt angle in the range of-5°to 5°.The repeatability of the sensor is good,and the tilt sensitivity can reach 231.7 pm/°.The influence of the silicone oil on the damping capacity of the sensor is studied.The results show that the damping capacity of the sensor has been improved by sealing the silicone oil inside the shell of the sensor.The field test is carried out on a pier of an elevated bridge,and the result is good,which verifies the practicability of the sensor.

Potential Application of Entangled Porous Titanium Alloy Metal Rubber in Artificial Lumbar Disc Prostheses

Entangled Porous Titanium Alloy Metal Rubber(EPTA-MR)was used as a nucleus pulposus material in the design of non-fusion intervertebral disc prosthesis for the first time.A novel artificial lumbar intervertebral disc prosthesis was designed by reconstructing the lumbar model with reverse engineering technology,and the biomechanical behavior of the prosthesis was simulated under varied working conditions.The nucleus pulposus size was determined by the actual size of human prosthesis.EPTA-MR samples with different densities were prepared by medical titanium alloy wire experimental studies were conducted on static stiffness,damping energy consumption,and fatigue life.The results indicated that the static stiffness of EPTA-MR could reach approximately 1500 N mm and its loss factor remained higher than 0.2,and the variation range was relatively small,with excellent vibration damping capacity and bearing capacity.Among them,the overall performance of EPTA-MR with a density of 2.5 g em 3 was closer to that of the physiologic intervertebral disc.A macro experiment of five million fatigue vibration tests combined with microstructure observation exhibited a wear rate of only 0.9396 g-MC with no noticeable change in the internal micro-morphology.Therefore,the EPTA-MR has a broad application prospect as the nucleus pulposus material of artificial intervertebral disc prosthesis.

Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads

As a passive means of vibration reduction, particle damping is mainly applied to the horizontal or vertical steady field. However, it is seldom applied to centrifugal fields. Under high speed and heavy loading, the vibration of tooth surfaces of gear transmissions becomes more severe shortening gear service life and augmenting noise. Under centrifugal loading, the particle system exhibits different characteristics, for example, particles are extruded at the end farthest from the center. We investigated gears with drilled via holes filled with damping particles. Using the discrete-element method, we developed an energy dissipation model for the particle system accounting for friction and inelastic collisions. Energy dissipation and damping characteristics of this system were analyzed. Experiments were also conducted with the gear system having different particle filling rates. The results show that this filling rate is an important parameter associated with particle damping in a centrifugal field. An unsuitable filling rate would significantly reduce damping effectiveness. With changes in rotation speed and load, the gear transmission system has different optimal filling rates. The results provide guidelines for the application of particle damping in centrifugal fields of gear transmissions.

A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems

Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems.This paper presents a novel perturbative iteration(PI)algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems.Mathematical formulations of the proposed method are developed and based on these formulations,a computer algorithm is devised.Extensive numerical case examples are given to demonstrate the practicality of the proposed method.When all modes are included,the method is exact and when only a subset of modes are used,very accurate results are obtained.