Frequency Of Transverse Vibration Research Articles

Coupling between Transverse Vibrations and Instability Phenomena of Plates Subjected to In-Plane Loading

As it is known, the problems of free transverse vibrations and instability under in-plane loads of a plate are two different technological situations that have similarities in their approach to elastic solution. In fact, they are two eigenvalue problems in which we analyze the equilibrium situation of the plate in configurations which differ very slightly from the original, undeformed configuration. They are coupled in the event where in-plane forces are applied to the edges of the transversely vibrating plate. The presence of forces can have a significant effect on structural and mechanical performance and should be taken into account in the formulation of the dynamic problem. In this study, distributed forces of linear variation are considered and their influence on the natural frequencies and corresponding normal modes of transverse vibration is analyzed. It also analyzes their impact for the case of vibration control. The forces' magnitude is varied and the first natural frequencies of transverse vibration of rectangular thin plates with different combinations of edge conditions are obtained. The critical values of the forces which cause instability are also obtained. Due to the analytical complexity of the problem under study, the Ritz method is employed. Some numerical examples are presented.

基于质心体系稳态振动理论的高速列车蛇形运动研究

本文通过分析车体各个自由度与车体质心横向振动之间的关系，建立了车体质心横向振动分析的简化模型，在此基础上，运用稳定平衡体系的振动条件，证明重力和轨面支撑力是导致车体质心在轨面上发生横向振动的根本原因，并由此推导出车体质心横向振动频率与车轮踏面锥度之间的关系，发现当车轮踏面锥度 ≥ 1/40时，车体质心的横向振动是稳定的。在此基础上，讨论了车体在不同横向振动频率和不同行驶速度情况下的蛇形运动波长以及因蛇形运动而作用于轨道上的横向作用力。而有关横向作用力的计算表明，车体对轨道的横向作用力在车体重量的5%~2%之间，而规范给出的数据敲好处于这个范围内。 By analyzing the relationship between the various degrees of freedom of the body and the car body mass center transverse vibration, the establishment of a simplified model of the vehicle center of mass lateral vibration analysis, and on this basis, the use of the vibration condition of stable equilibrium system to prove that the support of gravity and track surface power is the root cause of the car center of mass in the lateral vibration of rail surface, and thus derive the relationship between the turnout center of mass transverse vibration frequency of the wheel tread taper, found that when the wheel tread taper ≥ 1/40, vehicle physical the lateral vibration of the heart is stable. Based above and combined with different speed and different lateral vibration frequency, the snake-like movement wavelength of the train vehicle was discussed, as the further step, the lateral force induced by snake-like movement and effected on the orbit was discussed deeply, it is found that the value of the force is in the range of 5% to 20% of the vehicle weight, the given specification (10% of the vehicle weight) is just located in this range.

Long reach cantilevers for sub-cellular force measurements

Maneuverable, high aspect ratio poly(3,4-ethylene dioxythiophene) (PEDOT) fibers are fabricated for use as cellular force probes that can interface with individual pseudopod adhesive contact sites without forming unintentional secondary contacts to the cell. The straight fibers have lengths between 5 and 40 μm and spring constants in the 0.07–23.2 nN μm−1 range. The spring constants of these fibers were measured directly using an atomic force microscope (AFM). These AFM measurements corroborate determinations based on the transverse vibrational resonance frequencies of the fibers, which is a more convenient method. These fibers are employed to characterize the time dependent forces exerted at adhesive contacts between apical pseudopods of highly migratory D. discoideum cells and the PEDOT fibers, finding an average terminal force of 3.1 ± 2.7 nN and lifetime of 23.4 ± 18.5 s to be associated with these contacts.

Free transverse vibration of single-walled carbon nanocones

Free transverse vibrations of single-walled carbon nanocones (SWCNCs) are investigated through beam model and molecular dynamics (MD) simulations. The fundamental frequencies of transverse vibrations of cantilevered SWCNCs with different apex angles, top radii and lengths are obtained from the MD simulations. The Timoshenko beam model provides a better prediction of the frequencies than the Euler–Bernoulli beam model. MD results indicate that apex angles have significant effects on the frequencies of SWCNCs with same lengths. It is found from the MD that the fundamental frequency of SWCNC is higher than an equivalent SWCNT. The effect of different top radii of SWCNC on the frequency is also examined.

Free transverse vibration of rotating blades in a bladed disk assembly

This paper investigates the natural frequency of free transverse vibration of blades in rotating disks to examine the relationship of natural frequencies, blade stiffness and nodal diameters to study how neighboring blades react upon each other and affect blade natural frequency. With the use of elastic hinge theory and a cantilever beam model subjected to either a transverse concentrated force or a bending moment at the free end, the force-deflection stiffness/moment-rotation stiffness of the beam have been developed. Thereafter, the reaction forces and moments from the neighboring blades have been determined without the need for an exact solution of large deformation of cantilever beams including geometrical nonlinearity effects. With the use of the energy conservation principle and modal theory, the natural frequency of free transverse vibration of blades in rotating disks has been determined for any nodal diameter. A comparison of the analytical and finite element solutions for a bladed disk with uniform aerofoils shows that the analytical method presented in this paper is accurate.

Modal Analysis of Transverse Vibrations of a Thin Rectangular Plate with a Bonded Piezoelectric Patch

Present problem deals with a rectangular plate with a PZT patch bonded to it. The plate is considered to be simply supported at its edges. Since PZT possess electromechanical properties, electrical properties along with mechanical properties are considered while deriving the equations of motion for transverse vibration of the plate with patch. The primary focus in this paper is how these electrical properties affect the plate behaviour in terms of transverse vibration frequencies. Transverse displacement has been represented by a double Fourier series. Open circuit boundary condition has been applied to the PZT patch. Results have been obtained for a plate covered fully by the patch and also for a plate covered partially by the patch. It has been found in the present investigation that electrical properties affect modal frequencies significantly.

Orbiting response in vortex-induced vibrations of a two-degree-of-freedom pivoted circular cylinder

Vortex-induced vibrations of a pivoted, rigid, circular cylinder were investigated experimentally. A cylinder with a mass ratio of 15.9 and a moment of inertia ratio of 66.8 was investigated at a constant Reynolds number of 2100 for a range of reduced velocities, 3.4≤ U ⁎≤11.3, and damping ratios, 0.4%≤ ζ≤1.1%. A novel experimental set-up was designed to reproduce the orbiting response observed in some engineering applications involving vortex induced vibrations of cylindrical structures. The results show that, in the synchronization region, the frequencies of transverse and streamwise vibrations lock onto the natural frequency of the structure, and the cylinder traces elliptic trajectories. A mathematical model is introduced to investigate the mechanism responsible for the occurrence of the elliptic trajectories or the figure-8 type trajectories observed in previous laboratory studies. The results show that the occurrence of either elliptic or figure-8 type trajectory is governed primarily by structural coupling between vibrations in streamwise and transverse directions. Based on the experimental results, four distinct types of orbiting motion are identified in the synchronization region. Each of these four types corresponds to a specific range of phase angles between the streamwise and transverse vibrations defining the orientation of the trajectory and the direction of orbiting. The results indicate that the identified four types of elliptic trajectories are associated with four distinct ranges of a dimensionless parameter used to quantify structural coupling.

A simplified nonlinear dynamic model for the analysis of pipe structures with bolted flange joints

Bolted flange joints are widely used in engineering structures; however, the dynamic behavior of this connection is complex in nature. In this paper, a simplified nonlinear dynamic model with bi-linear springs is proposed and validated for pipe structures with bolted flange joints. First, static mechanical properties of the bolted flange joint are investigated. The analytical solution reveals that the axial stiffness of the bolted flange joint is different in tension and compression. Then, nonlinear springs with different stiffness in tension and compression are employed to represent the bolted flange joint. A special type of dynamic behavior, coupling vibration in the transverse and longitudinal directions, is observed in analytical derivation. Finally, relevant physical experiments and numerical simulations are performed. The physical experiments confirm the existence of the coupling vibration behavior. The relationship of longitudinal and transverse vibration frequencies is discussed. The numerical solutions reveal that the simplified nonlinear dynamic model better fits the physical response than conventional reduced linear beam model.

Analysis on Mechanics and Reliability of Drill String during Deep Drilling

The deep drill string is subjected to many kinds of loading under the condition of vibration and precession, such as tension, compression, bending and torsion, while the temperature and press are very high. Under this circumstance, the shallow drill string is more likely to failure. Based on the force analysis of the drill string, the drilling process of the deep drill string is simulated using finite element software. The stress distribution and displacement of the drill string is obtained under the interaction of drilling pressure, torque and temperature. At the same time, the effect of transverse vibration, longitudinal vibration and torsional vibration, on the stress and displacement of the drill string, is compared. The change law of the natural frequency of transverse vibration varying with the length of drill string, rotational speed and the hole size is discussed. Connected with concrete examples, the reliability and sensitivity of some influencing factors such as external diameter, wall thickness, the minimum yield strength, temperature, elastic modulus, Poisson’s ratio, axial loading and torque is obtained. The main factors that influence the reliability of the drill string are the yield strength and torque. The reliability of the drill string increases as the increase of yield strength, and decreases as the increase of the torque.

Research on Numerical Computation of Natural Frequency of Transverse Vibration for Simply Supported Beam of Non-Uniform

Recursive and inexplicit differential equation of the second order with variable coefficients is derived from the fourth order linear homogeneous differential equation with variable coefficients of transverse vibration of non-uniform beam, which is about deflection and bending moment according to boundary conditions and order reduction. By finite difference method, numerical computation and accuracy are studied for natural frequency of transverse vibration for simply supported beam of non-uniform. Theoretical analysis and orthogonal computation examples show that numerical computation algorithm is very simple, and accuracy of computation depends on variety rate of gradually changed cross section in vertical direction and numbers of computation step, which is independent of width and length of beam; numerical accuracy of computation is estimable for given length or numbers of computation step; and reasonable length or numbers of computation step is determinable for given accuracy demand.

Mathematical analysis of transverse vibration of conical spiral tube bundle with external fluid flow

The conical spiral tube bundle is a new type of heat transfer elements used to enhance heat transfer through flow-induced vibration. The effect of the external fluid flow on the transverse vibration of the conical spiral tube bundle is investigated with a mathematical method proposed in this article. Firstly, the natural vibration of the tube bundle is obtained by the hammering excitation method and the mode shapes of the transverse vibration are discussed. Then the effect of the external fluid flow on the transverse vibration of tube bundle is analyzed by a combination of experimental data, empirical correlations and FEM. The results show that in the frequency range from 0 Hz to 50 Hz, there exist six transverse vibrations. The external fluid flow has a significant effect on the frequency of the tube's transverse vibration, which are decreased by about 18% to 24% when the external fluid flow speed is 0.3 m/s.

VIBRATION AND STABILITY OF A HEAVY AND HEATED VERTICAL CIRCULAR PLATE

This paper is concerned with the vibration and stability of a standing, heavy, and circular plate when heated. This investigation also deals with the plate being exposed to inertial forces due to uniform acceleration. The plate edge is clamped. Natural frequencies of transverse vibrations depending on the plate weight and temperature were determined using the Galerkin's method. Mode shapes are given for some frequencies including the influence of weight parameter on changes in mode shapes. It is shown that frequencies split for the asymmetric mode shapes, so that there are two different frequencies in those cases. Critical weight parameter values where plate stability ceases were determined. Critical values of the weight parameter depending on Poisson's ratio are also presented herein.

Natural frequencies of nonlinear vibration of axially moving beams

Axially moving beam-typed structures are of technical importance and present in a wide class of engineering problem. In the present paper, natural frequencies of nonlinear planar vibration of axially moving beams are numerically investigated via the fast Fourier transform (FFT). The FFT is a computational tool for efficiently calculating the discrete Fourier transform of a series of data samples by means of digital computers. The governing equations of coupled planar of an axially moving beam are reduced to two nonlinear models of transverse vibration. Numerical schemes are respectively presented for the governing equations via the finite difference method under the simple support boundary condition. In this paper, time series of the discrete Fourier transform is defined as numerically solutions of three nonlinear governing equations, respectively. The standard FFT scheme is used to investigate the natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results are compared with the first two natural frequencies of linear free transverse vibration of an axially moving beam. And results indicate that the effect of the nonlinear coefficient on the first natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results also illustrate the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters.

Vibration analysis of rotating Timoshenko beams by means of the differential quadrature method

Vibration analysis of rotating beams is a topic of constant interest in mechanical engineering. The differential quadrature method (DQM) is used to obtain the natural frequencies of free transverse vibration of rotating beams. As it is known the DQM offers an accurate and useful method for solution of differential equations. And it is an effective technique for solving this kind of problems as it is shown comparing the obtained results with those available in the open literature and with those obtained by an independent solution using the finite element method. The beam model is based on the Timoshenko beam theory.

A Simple Experiment to Demonstrate the Effect of Axial Force on Natural Frequency of Transverse Vibration of a Beam

An axial tension (compression) increases (decreases) the natural frequency of transverse vibration of a beam. The primary objective of the present work is to demonstrate this effect using a universal testing machine, an impact hammer, an accelerometer, an oscilloscope with spectrum facility and a mild steel specimen of circular cross-section. The above equipments are among the essential facilities available in a typical material testing and vibration laboratory. Therefore the proposed experimentation demands no special specific set-up and can be performed at no extra cost.

Vibration analysis of scanning thermal microscope probe nanomachining using Timoshenko beam theory

In this paper, the effect of thermal vibration on the resonant frequency of transverse vibration of scanning thermal microscope (SThM) cantilever probe is analyzed using the Timoshenko beam theory, including the effects of rotary inertia and shear deformation. The thermal vibration effect can be considered as an axial force and is dependent of temperature distribution of the probe. In this analysis, the temperature is assumed to be distributed in accordance with the constant, linear, and quadratic models along the probe length. The Rayleigh–Ritz method is used to solve the vibration problem of the probe. The numerical results show that the frequency obtained with the constant model is the highest, while it is the lowest for the quadratic model. The frequency of vibration modes of the probe increases with increasing the temperature of the probe. As the ratio of probe length to its thickness increases, the frequency of vibration modes decreases. In addition, the effects of rotary inertia and shear deformation on the frequency are significant, especially in higher order modes and smaller values of the ratio of the probe length to its thickness.

Obtaining fiber stress-strain curves by recording fiber vibrations during electric-field measurements

A simple method for constructing tension curves of thin fibers is proposed which consists of determining the dependence of the frequencies of small transverse vibrations of thin fibers on their tensile strain. The fiber stress at these frequencies is calculated using the classical formula of string vibrations. Instead of force and strain, it is proposed to measure frequency and strain. This method has a number of advantages, in particular, it is more accurate. Resonant frequencies are determined by recording the accompanying electric field resulting from the variation in the charge distributed over the fiber surface. The effectiveness of the method is demonstrated by constructing copolymer fibers of various diameters.

Vibration Mode Analysis of a Rotating Circular Membrane under Transverse Distributed Load

Vibration modes of an extremely thin rotating circular membrane subjected to transverse distributed load are investigated. In the previous paper, the author proposed an analytical method to obtain equilibrium states with large transverse deformations employing the von Karman theory and taking account of buckling under the assumptions of rotationally symmetric deformations. In this paper, transverse vibration equation around the equilibrium state under transverse load is derived and modal equation is formulated. The equation is numerically solved and modal frequencies and modal shapes are obtained. Typical vibration modes are illustrated. In order to confirm the validity of the analysis, eigenvalue analysis of a spring-mass system model for the membrane are performed to obtain vibration modes. A fairly good agreement is found between the theoretical and numerical results. Experiments of thin rotating circular membranes under gravity in vacuum are also conducted and transverse vibration frequencies are measured for a variety of rotation speed and air pressure. Analytical results are compared with the experimental results to verify the validity of the present analysis.

Electronic basis of hardness and phase transformations (covalent crystals)

Several electronic parameters measure the stabilities of covalent crystals, including minimum energy band-gap densities, inverse polarizabilities, plasma frequencies, transverse vibrational frequencies and elastic shear moduli. Convenient is the band-gap density (energy/volume; called the ‘bond modulus’). For a given bonding type, the indentation hardness is proportional to the bond modulus. Examples are the group IV elements, III–V compounds; and II–VI compounds. The motion of dislocation kinks requires the excitation of bonding electrons into anti-bonding states. The bond modulus measures this together with the work done by the applied stress when a kink moves.In addition to hardness, the bond modulus measures the compressive strain (pressure) needed to transform an ambient structure into a more dense structure. Activation of such transformations also requires the excitation of bonding electrons into anti-bonding states together with the work done by the compressive stress.

Research on Dynamic Characteristic of Concrete Box-girder with Corrugated Steel Webs

AbstractAn interspaced calculation model of a concrete box-girder with corrugated steel webs was built by sap2000, and the applicability of FEM was proved according to the comparison between the test value and FEM value of concrete box-girder with corrugated steel webs. The influence of structural parameters of corrugated steel webs on dynamic characteristic was analyzed. The results of the research indicates that vibration frequency of box-girder especially torsion vibration frequency can be improved by the augment of corrugated steel webs’ thickness to some extent; vertical and transverse vibration frequency of box-girder is affected less than torsion vibration frequency by the augment of corrugated steel webs’ folded angle; vertical, transverse and torsion vibration frequency increase and then decrease under the change of horizontal face plate width of corrugated steel webs, so the best horizontal face plate width of corrugated steel webs do exist but not too big.