THE DESIGN AND ANALYSIS OF VIBRATION STRUCTURE OF VERTICAL DYNAMIC BALANCING MACHINE

A new type of vibration structure (i.e. supporting system, called swing frame cus- tomarily) of vertical dynamic balancing machine has been designed, which is based on an analysis for the swing frame of a traditional double-plane vertical dynamic balancing machine. The static unbalance and couple unbalance can be e?ectively separated by using the new dynamic balancing machine with the new swing frame. By building the dynamics model, the advantages of the new structure are discussed in detail. The modal and harmonic response are analyzed by using the ANSYS7.0. By comparing the ?nite element modal analysis with the experimental modal analy- sis, the natural frequencies and vibration modes are found. There are many spring boards in the new swing frame. Their sti?nesses are di?erent and assorted with each other. Furthermore, there are three sensors on the measuring points. Therefore, the new dynamic balancing machine can measure static unbalance and coupling unbalance directly, and the interaction between them is faint. The result shows that the new vertical dynamic balancing machine is suitable for inertial measurement of ?ying objects, and can overcome the shortcomings of traditional double-plane vertical dynamic balancing machines, which the e?ect of plane-separation is inferior. The vertical dynamic balancing machine with the new vibration structure can ?nd wide application in the future. The modelling and analysis of the new vibration structure will provide theoretical basis and practical experience for designing new-type vertical dynamic balancing machines.

SEISMIC RANDOM VIBRATION ANALYSIS OF STOCHASTIC STRUCTURES USING RANDOM FACTOR METHOD

Seismic random vibration analysis of stochastic truss structures is presented. A new method called random factor method is used for dynamic analysis of structures with uncertain parameters, due to variability in their material properties and geometry. Using the random factor method, the natural frequencies and modeshapes of a stochastic structure can be respectively described by the product of two parts, corresponding to the random factors of the structural parameters with uncertainty, and deterministic values of the natural frequencies and modeshapes obtained by conventional finite element analysis. The stochastic truss structure is subjected to stationary or non-stationary random earthquake excitation. Computational expressions for the mean and standard deviation of the mean square displacement and mean square stress are developed by means of the random variable＇s functional moment method and the algebra synthesis method. An antenna and a truss bridge are used as practical engineering examples to illustrate the application of the random factor method in the seismic response analysis of random structures under stationary or non-stationary random earthquake excitation.

An off-and-towards-equilibrium strategy for vibrational control of structures

Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardsequilibrium （OTE） strategy combined with fuzzy control is presented in this paper to overcome these difficulties. According to the OTE strategy, the control force is designed from the viewpoint of a mechanical relationship between the motions of the structure, the exciting force and the control force. The advantage of the OTE strategy is that it can be used for a variety of control systems. In order to evaluate the performance of the proposed strategy, the seismic performance of a three-story shear building with an Active Tendon System （ATS） using a Fuzzy Logic Controller （FLC） is studied. The main advantage of the fuzzy controller is its inherent robustness and ability to handle any nonlinear behavior of structures. However, there are no design guidelines to set up the corresponding control rule table for a FLC. Based on the proposed strategy for the FLC, a control rule table associated with the building under study is developed, which then allows formation of a detailed algorithm. The results obtained in this study show that the proposed strategy performs slightly better than the linear quadratic regulator （LQR） strategy, while possessing several advantages over the LQR controller. Consequently, the feasibility and validity of the proposed strategy are verified.

Structural Vibration Mode Re-Analysis of Offshore Structures

-This paper reviews the current methodology for dynamic reanalysis. Rayleigh-Ritz approach and receptance approach are discussed in detail. Based on a general finite element structural analysis program SAPS, an eigenproblem re-analysis prorgram ERP was compiled. With a very small change the program can be implemented readily with any general FEM program. Finally, some numerical examples show that the new algorithm is of high precision and efficiency. In the case of local modification in the offshore platform, the efficiency is raised by 20- 50 times when compared with the re-calculation of the whole model.

REDUCTION APPROACHES FOR VIBRATION CONTROL OF REPETITIVE STRUCTURES

The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way so that the control system posses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.

Ab Initio Studies of Radicals HBX(X=H, F, Cl, Br): Molecular Structure,Vibrational Frequencies and Potential Energy

We describe high-level ab initio calculations on the BH_2, HBF, HBCl and HBBr radicals. Molecular structure,vibrational frequencies and potential energy curves of the ground state and the first excited state, which are two Renner-Teller components for a^2Π state at linearity, are studied using the basis sets aug-cc-pVTZ and icMRCI＋Q technique. On the basis of the potential energy curves, a reliable potential energy barrier to dissociation HB＋X（X=F, Cl, Br） fragments and to linearity are given. The ab initio results will add some understanding on the spectrum and the photo-dissociation dynamics of the series of radicals.

Statistical analysis on the influence of mechanical parameters in the vibration of pylons

We present a statistical investigation of the degree of influence that assumptions made in relation to the mechanical parameters of a pylon have on its ground-induced vibrations.The study is set up by using as a key kinematic variable the displacement at the top of a reference,a stand-alone pylon with a uniform cross-section and fixity at its base.Next,statistics are produced using a dimensionless displacement ratio defined between the‘parental’and the‘subsidiary’cases,the latter defined for the pylon(a)resting on compliant soil,(b)having an attached top mass,and(c)being non-uniform with height.Furthermore,two materials are examined,namely,steel and reinforced concrete(R/C).More specifically,this displacement ratio is independent of the excitation and plays the role of a transfer function between the base and the top of the pylon.Both horizontal and vertical motions are considered,and the equations of motion are solved in the frequency domain.The ensuing statistical analysis is conducted for the following parameter combinations:(a)pylon founded on soft,intermediate,and stiff soil;(b)low,intermediate,and high-mass ratios of the attached mass to the pylon′s mass;(c)a constant and quadratic degree of pylon tapering with height.Spearman correlation coefficients are calculated for all the above combinations to arrive at statistical results that establish validity bounds and quantify the degree of influence of each assumption on the pylon′s response.

H∞ Control for Externally Excited Building Structures with Active Mass Damper under Actuator Saturation

This paper investigates the application of active mass dampers to mitigate the vibrations of building structures subjected to unknown external excitations under controller saturation conditions. By utilizing an H∞ control strategy, the optimal state feedback controller is derived by solving the linear matrix inequality problem for controller saturation. Case studies show that the proposed controller is capable of stabilizing the closed-loop system with good control performance and effectively suppressing vibrations in building structures under unknown external excitation. When compared to controllers that do not consider saturation, the proposed controller requires lower gain and results in reduced energy consumption. The research findings provide valuable insights for addressing real-world building structure control problems, contributing to both theoretical significance and practical applications.

Optical Evaluation of Vibrations in a Concrete Column by the LPD Method

In this work we present the results of the optical evaluation of vibrations of a conventional concrete column with a metal frame.In a previous work[1]we reported the optical evaluation of a pure concrete column,without a metal framework.In this evaluation we expected to obtain a noticeably different result,but that was not the case,then the obtained results are surprisingly similar.From the LPD evaluations,the first 12 vibration resonances were found,which fit very well with the basic applied theory(the cantilever theory).Using known average values,we estimate the corresponding column effective length,obtaining an average value of 2.5 m.As in the former case of the concrete column,we find a discrepancy with respect to the length value,measurable from the ground(1.75 m),which can be explained again by the fact that the column and its base were built on inconsistent terrain.

Suppression of Wave-Excited Vibration of Offshore Platform by Use of Tuned Liquid Dampers

This paper describes experimental and theoretical investigations of Tuned Liquid Damper (TLD) characteristics for suppressing the wave-excited structural vibration. The structural model for the experiments is scaled according to a full size offshore platform by matching their dynamic properties. Rectangular TLDs of different sizes with partially filled liquid are examined. By observing the performance and behavior of TLDs through laboratory experiments, the Study investigates the influence of a number of parameters, including container size, container shape, frequency ratio, and incident wave characteristics. In an analytical study, a mathematical model that describes the nonlinear behavior of liquid in TLD and the interaction of TLD and structure is prerequisite. The validity of the model is evaluated and simulating results can reasonably match the corresponding experimental results.

Control strategies and experimental verifications of the electromagnetic mass damper system for structural vibration control

The electromagnetic mass damper （EMD） control system, as an innovative active control system to reduce structural vibration, offers many advantages over traditional active mass driver/damper （AMD） control systems. In this paper, studies of several EMD control strategies and bench-scale shaking table tests of a two-story model structure are described. First, two structural models corresponding to uncontrolled and Zeroed cases are developed, and parameters of these models are validated through sinusoidal sweep tests to provide a basis for establishing an accurate mathematical model for further studies. Then, a simplified control strategy for the EMD system based on the pole assignment control algorithm is proposed. Moreover, ideal pole locations are derived and validated through a series of shaking table tests. Finally, three benchmark earthquake ground motions and sinusoidal sweep waves are imposed onto the structure to investigate the effectiveness and feasibility of using this type of innovative active control system for structural vibration control. In addition, the robustness of the EMD system is examined. The test results show that the EMD system is an effective and robust system for the control of structural vibrations.

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.

Vibration Control of Multi-Tuned Mass Dampers for An Offshore Oil Platform

ne purpose of this study is to investigate the effectiveness of multi-tuned mass dampers (MTMD) on mitigating vibration of an offshore oil platform subjected to ocean wave loading. An optimal design method is used to determine the optimal damper parameters under ocean wave loading. The force on the structure is determined by use of the linearized Morison equation. Investigation on the deck motion with and without MTMD on the structure is made under design conditions. The results show that MTMD with the optimized parameters suppress the response of each structural mode. The sensitivity of optimum values of MTMD to characteristic wave parameters is also analyzed. It is indicated that a single, TMD on the deck of a platform can have the best performance, and the small the damping value of TMD, the better the vibration control.

A BOUNDARY ELEMENT METHOD FOR SMALL-AMPLITUDE VISCOUS FLUID SLOSHING IN COUPLE WITH STRUCTURAL VIBRATION

A boundary element method is presented for the coupled motionanalysis of structural vibration with small-amplitude fluid sloshingin two-dimensional space. The linearized Navier-Stokes equations areconsidered in frequency domain and transformed into boundary integralequations. An appropriate fundamental solution for the Helmholtzequation with pure imaginary constant is found. The condition ofzero-stress is imposed on the free surface, and non-slip condition offluid particles is Imposed on the walls of the container. For rigidmotion models, the expressions for added mass and Added damping tothe structural motion equations are obtained. Some typical numericalexamples are Presented.

A MODEL IDENTIFICATION METHOD OF VIBRATING STRUCTURES FROM INCOMPLETE MODAL INFORMATION

The accurate mathematical models for complicated structures are verydifficult to construct.The work presented here provides an identification method for estimating the mass, damping , and stiffness matrices of linear dynamical systems from incompleteexperimental data. The mass, stiffness, and damping matrices are assumed to be real,symmetric, and positive definite. The partial set of experimental complex eigenvalues and corresponding eigenvectors are given. In the proposed method the least squaresalgorithm is combined with the iteration technique to determine systems identified matrices and corresponding design parameters. several illustrative examples, are presented to demonstrate the reliability of the proposed method .It is emphasized thatthe mass, damping and stiffness martices can be identified simultaneously.

Mitigation of micro vibration by viscous dampers

This study proposes a micro vibration mitigation system using viscous dampers to solve the problem of vibration in a high-tech building. Due to the operating frequency of the air conditioners and fundamental mode of the floors, a resonant phenomenon is occasionally experienced at the upper levels of the structure. Several strategies were considered, and viscous dampers combined with a suspension system were chosen to mitigate this annoying situation. A theoretical analysis was first executed to determine the optimal design value of the damper and the suspension spring. An efficient reduction in floor velocity of approximately 50 % was achieved by the proposed system. Practical verifications including a performance test of the micro-vibration-oriented dampers, the pragmatic application result, and a comparison in one-third octave spectrum was then carried out. The performance of the system was demonstrated by the data measured. It alleviated more trembling than was numerically expected. The energy absorbed by the viscous dampers is illustrated by the hysteresis loops and the one-third octave spectrum. It is found that with the proposed system, the vibration can be effectively captured by the viscous damper and converted to lower frequency-content tremors. The success of this project greatly supports the proposed standard two-stage analysis procedure for mitigating micro-vibration problems in practice. This research extends the use of viscous dampers to a new field.

A MODEL IDENTIFICATION METHOD OF VIBRATING STRUCTURES FROM INCOMPLETE MODAL INFORMATION

The accurate mathematical models for complicated structures are very difficult to construct.The work presented here provides an identification method for estimating the mass.damping,and stiffness matrices of linear dynamical systems from incomplete experimental data.The mass,stiffness and damping matrices are assumed to be real,symmetric,and positive definite The partial set of experimental complex eigenvalues and corresponding eigenvectors are given.In the proposed method the least squares algorithm is combined with the iteration technique to determine systems identified matrices and corresponding design parameters.Seeveral illustative examples,are presented to demonstrate the reliability of the proposed method .It is emphasized that the mass,damping and stiffness matrices can be identified simultaneously.

Stochastic Finite Element Method of Structural Vibration Based on Sensitivity Analysis

In this paper, material properties, geometry parameters and applied loads are assumed to be stochastic and a sensitivity computation of structural vibration is presented. The vibration equation of a system is transformed to a static problem by using the Newmark method. In order to develop computational efficiency and allow for efficient storage, the Preconditioned Conjugate Gradient method （PCG） is also employed. The PCG is an effective method for solving a large system of linear equations and belongs to methods of iteration with rapid convergence and high precision. An example is given and calculated results are compared to validate the proposed methods.

Flight Dynamic Analysis of Hypersonic Vehicle Considering Liquid-Solid Coupling

With the liquid propellant making up 60%—70% of the takeoff weight of the hypersonic vehicle,the dynamic load caused by great propellant sloshing interacts with the flexible structure of the aircraft.Therefore,the dynamic model displays characteristics of strong coupling with structure/control and nonlinearity.Based on the sloshing mass dynamic simplified as a spring-mass-damping model,a rigid-flexible-sloshing model is constructed.Moreover,the effect on the dynamic performance of the coupled model is analyzed with changing frequency and damping.The results show that propellant sloshing dynamics significantly affects the rigid body motion modes,especially flexible mode and short mode.The right half plane pole(RHP)moves far from the imaginary axis with the consumption of the propellant.The flexible mode attenuates with the increase of the sloshing damping,and the coupling becomes stronger when sloshing frequency is close to the short mode frequency or the flexible frequency of the beam.

Quasi-steady aerodynamic characteristics of Terminal Sensitive Bullets with short cylindrical portion

The aerodynamic characteristics are vital for short cylindrical Terminal Sensitive Bullets(TSB)with lowaspect ratio,especially in terminal trajectory.Currently,there is little research in terms of the TSB andshort cylinder with two free ends,and particularly in this trajectory,where the scanning angleβand rollangle a vary over a broad range between 0°and 180.In this work wind tunnel experiments are firstconducted to learn the effects of Reynolds number and scanning angle on aerodynamic parameters forshort cylinder with aspect ratio L/D=1.Similar to infinite cylinder,for the short cylinder with two freeends,the drag crisis phenomenon still exists in the critical regime 1.7×10^(5)≤Re≤6.8×10^(5).Then 3Dsimulations are performed to demonstrate the aerodynamic characteristics of short cylinder and TSBover a broad range of Re,L/D,a and 6.The sensitivity analysis of time step and grid are presented as well.whenβ3=0,for short cylinder,the drag crisis phenomenon was also observed in the simulation,but notas obvious as in the wind tunnel test.In some attitudes,there is an obvious Karman vortexin the wake ofshort cylinder and TSB.The correlation between time-averaged aerodynamic coefficients and L/D,Re,a&l is discussed.The vortex shedding frequency and shear layer behavior are obtained for quasi-steadyand unsteady flow.Finally,the effect of end's shape on drag reduction and vortex shedding frequency isanalyzed.