SIMULATION OF VIBRATION STRESS RELIEF AFTER WELDING BASED ON FEM

A finite element model is developed for the simulation of vibration stress relief （VSR） after welding. For the nonresonant vibration, the reduction in stress strongly depends on the amplitude of vibration. For the resonant vibration, the vibration frequency is the key for stress relief. The vibration frequency should be close to the structure natural frequency for the desired vibration mode. Only small vibration amplitude is required, which will be amplified during vibration. Vibration time does not have a major impact on vibration stress relief. When the amplitude of vibration stress relief is large, the treatment will be more effective.

Effect of residual stress on the vibration failure of dissimilar steels joint

Elasto-plastic finite element method is used for the welding residual stress calculation in butt welded joint of carbon steel and stainless steel, fluctuating pressure on the ship hull induced by a propeller is calculated from the actual measurement data. As the result of the superposition of vibration load and welding residual stress, the stress amplitude is reduced slightly in high stress area near the welding line, while the value of stress reduction becomes larger when the welding current increases. On the contrary, the stress amplitude is increased clearly far from the welding line. The welding residual stress obviously reduced the fatigue life of ship structure with the vibration load. The fatigue lives of ship structures under vibration are - 1.75 × 105 （ 110 000 ton product carrier） and - 2.43 × 105 （52 000 ton all-purpose cargo ship） without welding residual stress, while the residual stress exists, the fatigue life is down to - 3 × 104.

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.

Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory

The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton＇s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method （HAM）. This method is based on the Taylor series with an embedded parameter and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.

Size-dependent thermomechanical vibration characteristics of rotating pre-twisted functionally graded shear deformable microbeams

A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).

Vibration Response and Stress Analysis of Planar Elastic Tube Bundle Induced by Fluid Flow

Flow?induced vibration plays a positive role on heat transfer enhancement. Meanwhile, it is also a negative factor for fatigue strength. Satisfying the fatigue strength is the primary prerequisite for heat transfer enhancement. This paper numerically studied the flow?induced vibration of planar elastic tube bundle based on a two?way fluid–structure interaction(FSI) calculation. The numerical calculation involved the unsteady, three?dimensional incompressible governing equations solved with finite volume approach and the dynamic balance equation of planar elastic tube bundle solved with finite element method combined with dynamic mesh scheme. The numerical approach was verified by comparing with the published experimental results. Then the vibration trajectory, deformation and stress contour of planar elastic tube bundle were all studied. Results show that the combined movement of planar elastic tube bundle represents the agitation from inside to outside. The vibration of out?of?plane is the main vibration form with the typically sinusoidal behavior because the magnitude of displacement along the out?of?plane direction is the 100 times than the value of in?plane direction. The dangerous point locates in the innermost tube where the equivalent stress can be utilized to study the multiaxial fatigue of planar elastic tube bundle due to the alternating stress concentration. In the velocity range of 0.2-3 m/s, it is inferred that the vibration amplitude plays a role on the stress response and the stress amplitude is susceptible to the fluid velocity. This research paves a way for studying the fatigue strength of planar elastic tube bundle by flow?induced vibration.

Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model

Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton＇s principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.

Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect

Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.

The Interface Stress Field in the Elastic System Consisting of the Hollow Cylinder and Surrounding Elastic Medium Under 3D Non-Axisymmetric Forced Vibration

The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.

Forced and Natural Vibrations of an Orthotropic Pre-Stressed Rectangular Plate with Neighboring Two Cylindrical Cavities

Forced and natural vibrations of a rectangular pre-stressed orthotropic compositeplate containing two neighboring cylindrical cavities whose cross sections are rectangularwith rounded-off corners are investigated numerically. It is assumed that all the end surfacesof the rectangular pre-stressed composite plate are simply supported and subjected to auniformly distributed normal time-harmonic force on the upper face plane. The consideredproblem is formulated within the Three-Dimensional Linearized Theory of Elastic Waves inInitially Stressed Bodies (TDLTEWISB). The influence of mechanical and geometricalparameters as well as the initial stresses and the effect of cylindrical cavities on the dynamicalcharacteristics of the rectangular orthotropic composite plate are analyzed and discussed.

Stress-strain State and Vibration Frequencies of Blades of the Main Mine Fan Impeller

The paper discusses geometrical characteristics and strength parameters of fan blades equipped with replaceable active part it end ended to improve the fan adjustability owing to replacement or removal of the active part, which allows the fan to maintain a wide range of ventilation modes.

Evaluation of residual stress relief of aluminum alloy 7050 by using crack compliance method

High strength aluminum alloys of 7xxx series have unacceptable levels of quenching residual stresses from solution heat treatment. The residual stress not only results in machining distortion and dimensional instability, but also increases the possibility of stress corrosion cracks. Therefore, it is necessary to reduce the residual stress to an acceptable level. The crack compliance method was adopted to study the influences of various stress relief methods on residual stress patterns in 7050 aluminum alloy. The results show that 90% residual stress can be eliminated by the cold stretching(Tx51) method. And a lower level of residual stress can be achieved by the uphill quenching(Tx53) method or the cold compression(Tx52). However, there is a very steep residual stress gradient normal to exterior surfaces.

Vibration of a Two-Layer“Metal+PZT”Plate Contacting with Viscous Fluid

The present work investigates the mechanically forced vibration of the hydro-elasto-piezoelectric system consisting of a two-layer plate“elastic+PZT”,a compressible viscous fluid,and a rigid wall.It is assumed that the PZT(piezoelectric)layer of the plate is in contact with the fluid and time-harmonic linear forces act on the free surface of the elastic-metallic layer.This study is valuable because it considers for the first time the mechanical vibration of the metal+piezoelectric bilayer plate in contact with a fluid.It is also the first time that the influence of the volumetric concentration of the constituents on the vibration of the hydro-elasto-piezoelectric system is studied.Another value of the present work is the use of the exact equations and relations of elasto-electrodynamics for elastic and piezoelectric materials to describe the motion of the plate layers within the framework of the piecewise homogeneous body model and the use of the linearized Navier-Stokes equations to describe the flow of the compressible viscous fluid.The plane-strain state in the plate and the plane flow in the fluid take place.For the solution of the corresponding boundary-value problem,the Fourier transform is used with respect to the spatial coordinate on the axis along the laying direction of the plate.The analytical expressions of the Fourier transform of all the sought values of each component of the system are determined.The origins of the searched values are determined numerically,after which numerical results on the stress on the fluid and plate interface planes are presented and discussed.These results are obtained for the case where PZT-2 is chosen as the piezoelectric material,steel and aluminum as the elastic metal materials,and Glycerin as the fluid.Analysis of these results allows conclusions to be drawn about the character of the problem parameters on the frequency response of the interfacial stress.In particular,it was found that after a certain value of the vibration frequency,the presence of the metal layer in the two-layer plate led to an increase in the absolute values of the above interfacial stress.

Vibration analysis of axisymmetric functionally graded viscothermoelastic spheres

The present study focuses on the analysis of free vibrations of axisymmetric functionally graded hollow spheres. The material is assumed to be graded in radial di- rection with a simple power law. Matrix Frrbenious method of extended power series is employed to derive the analytical solutions for displacement, temperature, and stresses. The dispersion relations for the existence of various types of pos- sible modes of vibrations in the considered hollow sphere are derived in a compact form. In order to explore the character- istics of vibrations, the secular equations are further solved by using fixed point iteration numerical technique with the help of MATLAB software. The numerical results have been presented graphically for polymethyl methecrylate materials in respect of natural frequencies, frequency shift, inverse quality factor, displacement, temperature change, and radial stress.

APPLICATION OF THE MODIFIED ITERATION METHOD TO NONLINEAR VIBRATION OF CORRUGATED CIRCULAR PLATES

In this paper, the modified iteration method is successfully extended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequency response of corrugated circular plates is obtained and discussions on the influences of geometrical parameters on vibration behaviours of corrugated circular plates are made. The present results are practically important in the design of elastic elements in precision instruments.

TORSIONAL VIBRATIONS OF A RIGID CIRCULAR PLATE ON SATURATED STRATUM OVERLAYING BEDROCK

The torsional vibration of a rigid plate resting on saturated stratum overlaying bedrock has been analysed for the first time. The dynamic governing differential equations for saturated poroelastic medium are solved by employing the technology of Hankel transform. By taking into account the boundary conditions, the dual integral equations of torsional vibration of a rigid circular plate are established, which are further converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficients of the foundation on saturated stratum, the contact shear stress under the foundation and the angular amplitude of the foundation are evaluated. Numerical results indicate that, when the dimensionless height is bigger than 5, saturated stratum overlaying bedrock can be treated as saturated half space approximately. When the dimensionless frequency is low, the permeability of the soil must be taken into account. Furthermore, when the vibration frequency is a constant, the height of the saturated stratum has a slight effect on the dimensionless contact shear stress under the foundation.

Vortex-Induced Vibrations of A Free-Spanning Pipe Based on A Nonlinear Hysteretic Soil Model at the Shoulders

The pipe-soil interactions at shoulders can significantly affect the vortex-induced vibrations (VIV) of free-spanning pipes in the subsea. In this paper, the seabed soil reacting force on the pipe is directly calculated with a nonlinear hysteretic soil model. For the VIV in the middle span, a classic van der Pol wake oscillator is adopted. Based on the Euler-Bernoulli beam theory, the vibration equations of the pipe are obtained which are different in the middle span and at the two end shoulders. The static configuration of the pipe is firstly calculated and then the VIV is simulated.The present model is validated with the comparisons of VIV experiment, pipe-soil interaction experiment and the simulation results of VIV of free-spanning pipes in which the seabed soil is modelled with spring-dashpots. With the present model, the influence of seabed soil on the VIV of a free-spanning pipe is analyzed. The parametric studies show that when the seabed soil has a larger suction area, the pipe vibrates with smaller bending stresses and is safer.While with the increase of the shear strength of the seabed soil, the bending stresses increase and the pipe faces more danger.

Thermoelastic vibrations in a thin elliptic annulus plate with elastic supports

In this study, integral operational methods are used to investigate the thermally induced transverse vibration of a thin elliptic annulus plate with elastic supports at both radial boundaries.The axisymmetric temperature distribution is determined by the heat conduction differential equation and its corresponding boundary conditions by employing a unified integral transform technique by use of Mathieu functions and modified Mathieu functions. The solution of thermally induced vibration of the plate with both ends encased with elastic supports is obtained by employing an integral transform for double Laplace differential equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained based on resultant bending moments per unit width. The numerical calculations of the distributions of the transient temperature and its associated stress distributions are shown in the figures.

TORSIONAL VIBRATIONS OF RIGID CIRCULAR PLATE ON TRANSVERSELY ISOTROPIC SATURATED SOIL

An analytical method was presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil. By Hankel transform, the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established. By appropriate transform, the dual integral equations were converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficient, the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly. Selected examples were presented to analyse the influence of saturated soil＇s anisotropy on the foundation＇s vibrations.

Bending and Vibrations of a Thick Plate with Consideration of Bimoments

The paper is dedicated to the development of the theory of orthotropic thick plates with consideration of internal forces, moments and bimoments. The equations of motion of a plate are described by two systems of six equations. New equations of motion of the plate and the boundary conditions relative to displacements, forces, moments, and bimoments are given. As an example, the problems of free and forced oscillations of a thick plate are considered under the effect of sinusoidal periodic load. The problem is solved by Finite Difference Method. Eigenfrequencies of the plate are determined, numeric maximum values of displacements, forces and moments of the plate are obtained depending on the frequency of external force. It is shown that when the value of the frequency of external effect approaches the eigenfrequency, there occurs an increase in displacement, force and moment values;that testifies a gradual transition of the motion of plate points into the resonant mode.