FURTHER STUDY ON LARGE AMPLITUDE VIBRATION OF CIRCULAR SANDWICH PLATES

In this paper, a solution of axisymmetric large amplitude vibration is presented for a circular sandwich plate with the flexure rigidity of the face layers taken into account . In solving the problem , the modified iteration method is proposed. Then our results are compared with those from paper [1].

SHEAR EFFECTS ON LARGE AMPLITUDE FORCED VIBRATIONOF SYMMETRICALLY LAMINATED RECTILINEARLYORTHOTROPIC CIRCULAR PLATES

In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.

Evaluation of Vibration Amplitude Stepping and Welding Performance of 20 kHz and 40 kHz Ultrasonic Power of Metal Welding

Today ultrasonic power technique is consider a mandatory technique which is always entered in many processes such as in metal and plastic welding to overcomes many issues,with aided of applying force(pressure)and supplied high frequency vibration,a solid-state weld can be generated by ultrasonic metal welding technique.That gives a technique the ability to join not only a small component,whereas also to join thicker specimens,which depends on a proper control of matching welding conditions.Therefore a welding performance can be studied and compared after designed welding horn to resonance at frequencies of 20 kHz and 40 kHz.The analyses of the designed horn are completed through use a vibration mathematical expressions,modal and harmonic analyses to ensure the weldability due to applying ultrasonic power to the working area and also to compare the performance of joint at using two resonance frequencies of 20 kHz and 40 kHz.The dimensions of the horns were determined to match the selected resonance frequencies,which the lengths were calculated as 132 mm and 66 mm respectively.The analysis of the exciting model indicates that the axial vibration modes of 19,584 Hz and 39,794 Hz are obtained in 10th mode,while the two frequency values are recorded 19,600 Hz and 39,800 Hz from the frequency response of the two horns.The weld strength between Al and Cu specimens with a thickness 0.5 mm was evaluated using a tensile test,which the analyses were obtained under using different welding pressure and varied amplitudes.The results were recorded within exciting a horn with two different resonance frequencies,show the enhancement of weld strength and quality through control of stepping amplitude,the enhancement means obtain good strength of the weld,reduce sticking horn to specimen,and lower specimen marking.

Various performance-enhancing effects from the same intensity of whole-body vibration training

Purpose:The purpose of this study was to compare the effects of an 8-week whole-body vibration training program in various frequency and amplitude settings under the same acceleration on the strength and power of the knee extensors.Methods:Sixty-four young participants were randomly assigned to 1 of 4 groups with the same acceleration(4 g):high frequency and low amplitude(n = 16,32 Hz,1 mm) group,medium frequency and medium amplitude(n = 16,18 Hz,3 mm) group,low frequency and high amplitude(n = 16,3 Hz,114 mm) group,and control(n = 16,no vibration) group.All participants underwent 8 weeks of training with body mass dynamic squats,3 sessions a week.Results:The results showed that the high frequency and low amplitude group increased significantly in isometric contraction strength and 120°/s isokinetic concentric contraction strength;the medium frequency and medium amplitude group increased significantly in 60°/s and 120°/s isokinetic strength of both concentric and eccentric contraction;and the low frequency and high amplitude group increased significantly in 60°/s and 120°/s isokinetic eccentric contraction strength.Conclusion:All frequency and amplitude settings in the 8-week whole-body vibration training increased muscle strength,but different settings resulted in various neuromuscular adaptations despite the same intensity.

Effects of sonication amplitude on the microstructure and mechanical properties of AZ91E magnesium alloy

Light metals are gaining increased attention due to ecological sustainability concerns and strict emission regulations. Magnesium(Mg)is one such metal that has the potential to replace high density components, which can reduce emissions through lightweighting. However,the mechanical properties of Mg alloys must be improved for them to become viable candidates for structural applications. To this end, the current study examines the effect of sonication vibrational amplitude on the microstructure and mechanical properties of AZ91E Mg alloy.The molten alloys were subjected to ultrasonic treatment at a frequency of 20 kHz, 180 s of processing time and vibrational amplitudes ranging from 1.25 to 15 μm. The resultant castings were characterized using optical microscopy, scanning electron microscopy and tensile testing. It was found that sonication with amplitudes up to 7.5 μm was able to effectively refine the secondary phases of the alloy. Similar trends were observed for grain size and yield strength. The refinement in microstructure was likely caused by the finer grain size and cavitation induced undercooling of the liquid metal. In addition, it was also noted that even the lowest level of amplitude(1.25 μm) was able to increase the density, improve the ultimate tensile strength and ductility of the castings. The tensile strength and ductility were thought to have been enhanced by ultrasonic degassing and refinement in microstructure, while the yield strength was improved through the Hall-Petch effect. The results from this study provided a basis for optimizing the sonication process and promoting its use in industry. As a result, Mg alloys improved through ultrasonic processing have the potential to replace higher density components, with consequent energy efficiency and environmental and ecological benefits.

Non-Linear Vibration of Rectangular Reticulated Shallow Shell Structures

This paper deals with non-linear vibration of rectangular reticulated shallow shells by applying non-linear elastic theory of such structures established by the author .Us-ing the assumed (generalized)Fourier series solutions for transverse deflection (latticejoint transverse displacement )and force function,weighted means of the trial functions lead to the relations among the coefficients related to the solutions and vibration equ-ation which determines the unknown time function,and then the amplitude -frequeney relations for free vibration and forced vibration due to harmonic force are derived withthe aid of the regular perturbation method and Galerkin procedure,respectively.Nu-merical examples are given as well.

The Progress of the Study on the Effect of Vibration Training on Muscle Strength Exercise

Vibration training is more and more extensively applied to the field of strength training. It, as a beneficial supplement to the traditional strength, is able to improve specific strength or the strength of weak positions, for the purpose of achieving the muscle strength development in an all-round way. In this paper, the anatomy, physiology, and biomechanics foundations for vibration training to increase muscle strength are mainly analyzed, and then the principle of vibration training to increase muscle strength is further expounded, and also the increase of muscle strength is discussed from the aspects such as vibration frequency, vibration amplitude, vibration posture, vibration intermittent time, and vibration mode, so as to clarify the domestic and foreign progress of the study on vibration training.

Analytical solutions to nonlinear conservative oscillator with fifth-order nonlinearity

This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method （HPM） and an ancient Chinese method called the max-rain approach are presented to obtain an approximate solution. The major concern is to assess the accuracy of these approximate methods in predicting the system response within a certain range of system parameters by examining their ability to establish an actual （numerical） solution. Therefore, the analytical results are compared with the numerical results to illustrate the effectiveness and convenience of the proposed methods.

Simultaneous measurement of vibration amplitude and rotation angle based on a single-channel laser self-mixing interferometer

Based on a single-channel laser self-mixing interferometcr, we present a new silnultaneous measurement of the vibration amplitude and tile rotation angle of objects that both affect the power spectrum containing two peaks of the interferometer signals. The fitted results indicate that the curve of the peak frequency versus the vibration amplitude follows a linear distribution, and the curve of the difference of the two-peak power values versus the angle follows a Gaussian distribution. A vibration amplitude with an error less than 3.0% and a rotation angle with an error less than 11.7% are calculated from the fitted results.

A Correlation Coefficient Approach for Evaluation of Stiffness Degradation of Beams Under Moving Load

This paper presents a new approach using correlation and cross-correlation coefficients to evaluate the stiffness degradation of beams under moving load.The theoretical study of identifying defects by vibration methods showed that the traditional methods derived from the vibration measurement data have not met the needs of the actual issues.We show that the correlation coefficients allow us to evaluate the degree and the effectiveness of the defects on beams.At the same time,the cross-correlation model is the basis for determining the relative position of defects.The results of this study are experimentally conducted to confirm the relationship between the correlation coefficients and the existence of the defects.In particular,the manuscript shows that the sensitivity of the correlation coefficients and cross-correlation is much higher than the parameters such as changes in stiffness(EJ)and natural frequency values(Δf).This study suggests using the above parameters to evaluate the stiffness degradation of beams by vibration measurement data in practice.

Numerical Study of an Oscillating Smaller Cylinder in the Wake of an Upstream Larger Cylinder

A numerical study of flow around two tandem cylinders with unequal diameters was carried out. The upstream larger cylinder was fixed and the downstream smaller cylinder was allowed to oscillate in the transverse direction only. Comparisons of the experimental and numerical results were made to investigate the effects of the gap ratio on the maximum vibration amplitude and vortex shedding frequency. The results showed that the vibration response of the smaller cylinder was significantly affected by the presence of the upstream larger cylinder, and resulted in greatly reduced vibration amplitudes. With an increasing gap ratio, the vibration amplitude increased. However, the magnitude was lower than that corresponding to a single cylinder (with the same diameter as that of the downstream smaller cylinder) under the same flow conditions.

Technical note：Large amplitude free vibration of a flexible panel coupled with a leaking cavity

This paper addresses the effect of leakage on the natural frequencies of a large amplitude vibrating panel backed by a cavity, which has not been considered in many other related studies. The structural-acoustic governing equations are employed to study this nonlinear problem. An elliptical integral method, which was recently developed for the nonlinear panel cavity problem, is introduced here to solve for the structural-acoustics responses. The present results agree reasonably well with those obtained from the classical harmonic balance method. Modal convergences of the nonlinear solutions are performed to verify the proposed method. The effects of vibration amplitude and leakage size are studied and discussed. It is found that （1） the edge leakages in a panel cavity system significantly affect the natural frequency properties, and （2） the edge leakages induce a low frequency acoustic resonance.

Numerical study on influence of structural vibration on cavitating flow around axisymmetric slender body

The unsteady behaviors of cloud cavitating flow would lead to structural vibration and deformation that conversely affect its development. The present paper aims to preliminarily discuss the influences of structural vibration on the development of the cavitating flow. Simulations of a slender body are carried out under different vibration amplitudes and frequencies. The results show that the structural vibration causes alternate variation of local attack angle at the head of the body, and thus changes the development of cavitation and re-entrant jet. On the downstream side, the length and thickness of the cavity are larger than that on the upstream side due to larger area of negative pressure. For a large vibration amplitude, alternate variations of the local attack angle change the adverse pressure gradient at the closure of the cavity, and then affect the development of the re-entrant jet, so that the phenomena of local shedding of the cavitation happen, compared with global shedding in the case of no structural vibration. For a frequency larger than 0.05, transverse speed of the vibration is suggested to be a dominant factor in controlling the behavior of the cavitating flow besides the local attack angle, since it causes local cavitating phenomena.

Experimental-based study of gear vibration characteristics incorporating the fractal topography of tooth surface

Microscopic roughness is inevitable on the gear meshing surface,which is also a key parameter affecting the dynamic response.The surface roughness exhibits self‐affine characteristics across multiscales.To explore the influence of surface fractal topography on the vibration amplitude of the gear system under different rotational speeds and loads,an experimental setup of spur gear transmission is devised.The fractal dimension and fractal roughness of the meshing surface are calculated by the power spectral density method.The relationships between gear response and fractal parameters are revealed experimentally.Results indicate that a rougher tooth surface,that is,a smaller fractal dimension or larger fractal roughness,corresponds to an intense vibration amplitude.The sensitivity of dynamic response to the tooth surface topography varies at different rotational speeds and loads.Under low speed and light load conditions,the fractal dimension and fractal roughness have a more obvious influence on the dynamic response of the gear transmission system.With the increase of speed and load,the macroworking conditions gradually become the main factor attributed to vibration amplitude.

Numerical investigation on dynamic response of the screen mesh in vibrating screening through DEM-FEM co-simulation

Dynamic response of the screen mesh is of great significance in the optimum vibrating screen design.In this paper,based on the DEM-FEM co-simulation method,the effect of screening parameters on the dynamic response of the screen mesh is explored and the mechanism is revealed on the particle level.Firstly,a virtual experiment on a linear vibrating screen was carried out to analyze the screening pa-rameters'effect with both impact load and sustained stress inflicted on the screen mesh.Then,the time-domain evolution regularity of the screen mesh LVA(Local Vibration Amplitude)under different particle plugging conditions was investigated based on the co-simulation.Finally,the influence of screening parameters on LVA and its distribution was discussed.The results show that the screening parameters can greatly affect the screen mesh LVA and its distribution by changing the movement of the granular material and the particle penetration probability,which provides an important basis for the optimal design of the screen mesh and its supporting structure.

Some studies on mechanics of continuous mediums viewed as differential manifolds

The continuous mediums are divided into two kinds according to their geometrical configurations,the first one is related to Euclidian manifolds and the other one to Riemannian manifolds/surfaces in the point of view of the modern geometry.Two kinds of finite deformation theories with respect to Euclidian and Riemannian manifolds have been developed in the present paper.Both kinds of theories include the definitions of initial and current physical and parametric configurations,deformation gradient tensors with properties,deformation descriptions,transport theories and governing equations of nature conservation laws.The essential property of the theory with respect to Euclidian manifolds is that the curvilinear coordinates corresponding to the current physical configurations include time explicitly through which the geometrically irregular and time varying physical configurations can be mapped in the diffeomorphism manner to the regular and fixed domains in the parametric space.It is quite essential to the study of the relationships between geometries and mechanics.The theory with respect to Riemannian manifolds provides the systemic ideas and methods to study the deformations of continuous mediums whose geometrical configurations can be considered as general surfaces.The essential property of the theory with respect to Riemannian manifolds is that the thickness variation of a patch of continuous medium is represented by the surface density and its governing equation is rigorously deduced.As some applications,wakes of cylinders with deformable boundaries on the plane,incompressible wakes of a circular cylinder on fixed surfaces and axisymmetric finite deformations of an elastic membrane are numerically studied.

ACOUSTIC ANALYSIS OF HYDRODYNAMIC AND ELASTO-HYDRODYNAMIC OIL LUBRICATED JOURNAL BEARINGS

The purpose of the present paper is to investigate the effect of elastic deformation of bearing liner on the acoustic behavior of oil lubricated journal bearings.Analysis is performed for hydrodynamic（HD） and elasto-hydrodynamic （EHD） lubrications.Dynamic behavior and acoustical properties are investigated through an analysis of pressure fluctuation calculated from the Reynolds equation governing the flow in the clearance space of the journal bearing.This is solved numerically using the finite difference method with the successive over relaxation technique.In elasto-hydrodynamic lubrication,the finite element method with in iteration scheme is adopted to solve both Reynolds equation and the three-dimensional elasticity equation representing the displacement field in the bearing shell.The results show that the sound pressure level of the bearing is markedly influenced by the flexibility of the bearing liner,the viscosity of lubricant and the load applied to journal.HD analysis shows that the journal centre＇s orbit,from a disturbed position,converges to the static equilibrium position faster than EHD lubrication.The results of the present paper could aid in the design of low-noise rotor-bearing systems supported by oil lubricated journal bearings.