Steady Vibration Research Articles

Parametric excitation of a micro Coriolis mass flow sensor

We demonstrate that a micro Coriolis mass flow sensor can be excited in its torsional movement by applying parametric excitation. Using AC-bias voltages for periodic electrostatic spring softening, the flow-filled tube exhibits a steady vibration at suitable voltage settings. Measurements show that the sensor for this type of excitation can be used to measure water flow rates within a range of 0 ± 500 μl/h with an accuracy of 1% full scale error.

Active Dynamic Vibration Absorber for Broadband Control of a Multi-Mode System: Simulation and Experimental Verification

The control of broadband steady state vibration amplitude of a multi-mode system is presented. This objective is achieved using an Active Dynamic Vibration Absorber (ADVA). The stiffness property of the ADVA is adaptively tuned to attenuate the vibration of the multi-mode system at resonance. The ADVA detects the excitation frequency of the multi-mode system and calibrates its stiffness property to give the required stiffness for that mode. To implement the ADVA, a prototype model with low modal frequencies is designed. The equations of the steady state response of the multi-mode system with the attached ADVA are derived. The behavior of the prototype model when the ADVA is attached to different locations is used to determine the optimal location of the ADVA. The simulation result shows a reduction in the broadband of the multi-mode system. The result of the implementation of the ADVA reveals a 46%, 73% and 97% vibration amplitude reduction at first, second and third mode of the multi-mode system respectively.

Fatigue life of vehicle components

A method is developed for strength calculations of the supporting system of a vehicle (for the example of a trolleybus) with random steady vibration, in terms of fatigue life. The spectral method derived in the statistical dynamics of machines is employed.

Frequency Conversion Control for Vibration Mill with High Vibration Intensity Based on Multi-Wave Variable Sinusoid

The key technology of vibration machine to finish deaggregation and powder refinement is both high vibration Intensity with a certain frequency and steady vibration of frequency conversion control. A frequency conversion control for vibration mill system based on multi-wave variable sinusoidal frequency ascending and descending cycle curve was developed. The frequency conversion control test of vibration mill was finished through sensing signal amplification, analog digital conversion and on line detection. The results show that the high and super-high vibration intensity with certain action time is produced and the effect of multi-amplitude and multi-frequency is acquired. The experimental data show that the super micro grinding of superfine particles is achieved, energy consumption is reduced, the useful life of wearing parts such as bearing is extended, and engineering effects of deaggregation and refinement of super-hard superfine powder are obtained by frequency conversion control.

Plane Waves and Boundary Value Problems in the Theory of Elasticity for Solids with Double Porosity

This paper concerns with the dynamical theory of elasticity for solids with double porosity. This theory unifies the earlier proposed quasi-static model of Aifantis of consolidation with double porosity. The basic properties of plane waves are established. The radiation conditions of regular vectors are given. The basic internal and external boundary value problems (BVPs) of steady vibrations are formulated. The uniqueness theorems are proved. The basic properties of elastopotentials are given. The existence of regular (classical) solution of the external BVP by means of the potential method (boundary integral method) and the theory of singular integral equations are proved.

Investigation of Vibration Mitigation of Flexibly Support Rigid Rotors Equipped with Controlled Elements

Abstract The subject of investigations presented in this article is achieving the optimum attenuation of lateral vibration of rotors by means of two design variants of constraint elements: semiactive magnetorheological squeeze film dampers and actively controlled hydrodynamic bearings. The damping effect of magnetorheological dampers is controlled by the change of magnetic flux generated in electric coils and of the hydrodynamic bearings by the change of magnitude of the proportional gain of a feedback controller exciting movement of the bearing housings. In the developed mathematical models the rotor is considered as absolutely rigid and the controllable constraint elements are represented by force couplings. The rotor turns at constant angular speed, is loaded by its weight and in addition it is excited by a centrifugal force caused by the disc unbalance. In both design cases its lateral vibration is governed by a nonlinear equation of motion. The pressure distribution in the lubricating film in the magnetorheological squeeze film damper is described by a Reynolds equation modified for Bingham fluid whose yield shear stress depends on magnetic induction. The hydraulic forces acting in the hydrodynamic bearings are determined for the case of π-film cavitation and position of the bearing housings is adjusted by actuators activated by a proportional feedback controller. The aim of the analysis is to deal with approaches leading to minimizing amplitude of the rotor steady state vibration and magnitude of the force transmitted into the rotor casing and to compare efficiency of both design variants. The performed computer simulations show that the arrangement with the magnetorheological squeeze film damper gives better results in reducing magnitude of the transmitted force than those when the rotor is supported by hydrodynamic bearings with actively controlled position of the bearing housings.

Boundary value problems of steady vibrations in the theory of thermoelasticity with microtemperatures

AbstractIn this paper the linear theory of steady vibrations of thermoelasticity with microtemperatures for isotropic solids with microstructure is considered. The uniqueness and existence theorems of solutions of the internal and external second boundary value problems (BVPs) by means of the boundary integral method (potential method) and the theory of singular integral equations are proved. The existence of eigenfrequencies of the internal homogeneous BVP of steady vibrations is studied. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The process of getting stable self-excited oscillations in system of low-voltage circuits of regulation with electric potential of locomotive VL8

The possibility of construction of a steady natural vibration system by introduction of successive correction link as an aperiodic link of the first-order is considered.

Investigation on steady state deformation and free vibration of a rotating inclined Euler beam

The steady state deformation and infinitesimal free vibration around the steady state deformation of a rotating inclined Euler beam at constant angular velocity are investigated by the corotational finite element method combined with floating frame method. The element nodal forces are derived using the consistent second order linearization of the nonlinear beam theory, the d'Alembert principle and the virtual work principle in a current inertia element coordinates, which is coincident with a rotating element coordinate system constructed at the current configuration of the beam element. The rotating element coordinates rotate about the hub axis at the angular speed of the hub. The equations of motion of the system are defined in terms of an inertia global coordinate system, which is coincident with a rotating global coordinate system rigidly tied to the rotating hub. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady state deformation and natural frequency of the rotating inclined beam.

Identification of structural damage based on locally perturbed dynamic equilibrium with an application to beam component

In recognition of the obvious limitations of most global vibration-based and local guided-wave-based damage detection techniques, a novel inverse identification approach was developed by canvassing the local perturbance to equilibrium characteristics of the structural component under inspection. Characterized by high-order spatial derivatives, this approach has in particular proven sensitivity to structural damage. Most importantly, it requires neither benchmark structures nor baseline signals; neither global models nor additional excitation sources as long as the structure undergoes steady vibration under its normal operation. Independent of a global model, prior knowledge on structural boundary conditions is not compulsory. To minimize unavoidable influence of measurement noise on high-order spatial derivatives, various de-noising treatments, including wavenumber filtering, optimal selection of measurement configuration and hybrid information fusion were introduced independently. Using a simple beam as a representative structural component for illustration, relationships among vibration frequency, density of measurement points and size of detectable damage were explored, facilitating a judicious selection of measurement parameters. Proof-of-concept validation was numerically conducted, and then experimentally demonstrated using a scanning laser vibrometer. In principle, this proposed methodology is applicable to a complex system comprising various structural components, provided that the local equilibrium relationships of the components are known a priori.

Vibration Cosine Solutions of Free Orthotropic Rectangular Plates on the Elastic Half-Space

In this paper, the analytic solutions of steady vibration of free orthotropic rectangular plate loaded with vertical steady loading on the elastic half-space was given by combining the general solution of double trigonometrically cosine series with supplementary terms with dynamic integral representations for displacements of the elastic half-space loaded with arbitrary vertical steady loading. This solution not only is four-order derivative, but also has less undetermined coefficients. It can be used to solve the problems of bending and steady vibration of orthotropic rectangular plates on the elastic half-space without be classified and be superimposed. This causes this kind of things, bending and steady vibration of orthotropic rectangular plates with four free edges on the elastic half-space, unionization, simplification and systematization. When the material is isotropic, the solutions are turned into analytic solutions of steady vibration of free rectangular plate on the elastic half-space. At last some computational examples are presented and the results are coincided with those in literatures. Then the method in this paper will be of important practical applications.

Analytical Solution of Bending and Vibration of a Rectangular Plate on the Elastic Foundation

The analytic solutions of steady vibration of a rectangular plate loaded with vertical force on the semi-infinite elastic foundation were given by combining the general solution of double trigonometrically sine series with supplementary terms with the dynamic integral representations for displacements of the semi-infinite elastic foundation loaded with arbitrary vertical force. Some computational results were presented. The agreements were found to be satisfactory which proved the validity of the new method in solving the problem. This new method would be feasible in practical applications.

A computational investigation on the reducing lateral vibration of rotors with rolling-element bearings passing through critical speeds by means of tuning the stiffness of the system supports

Since there are manufacturing and assembling inaccuracies rotors are always slightly imbalanced. Their rapid angular acceleration leads to an increase in the magnitude of the tangential component of the imbalance forces. The slow acceleration enables the development of an almost steady state vibration. In both cases the amplitude of their oscillation is high. The frequency tuning achieved by changing the stiffness of the rotor supports represents one approach to its attenuation. Stiffness decreases shortly before reaching the critical speed, and after crossover, the stiffness increases again. As almost all publications and computer procedures from the field of rotor dynamics deal only with the case when the rotor turns at a constant angular speed, derivation of the equations of motion of the rotor rotating at variable velocities and investigation of the operating conditions and individual parameters of the supports on the vibration of the rotor passing critical speeds represent the fully new contribution of this paper. The critical revolutions are determined from the Campbell diagram. To solve the equations of motion the Newmark method has been proposed and tested.

On the steady vibrations problem in linear theory of micropolar solid–fluid mixture

Abstract In this paper we study the steady vibrations problem in linear theory of isothermal micropolar solid–fluid mixture. With the help of fundamental solution we establish representations of Somigliana type. Then, using the potentials of single layer and double layer, we reduce the boundary value problems to singular integral equations for which the Fredholm’s theorems are valid. Existence and uniqueness results for interior and exterior problems are presented.

Representations of Solutions in the Theory of Thermoelasticity with Microtemperatures for Microstretch Solids

Here, the linear theory of thermoelasticity with microtemperatures for isotropic microstretch solids is considered. First, the representation of Galerkin type solution of equations of motion is obtained. Then, the representation theorem of Galerkin type for the system of equations of steady vibrations is presented. Finally, the representation formula for general solution of the system of homogeneous equations of steady vibrations in terms of 10 metaharmonic functions is established.

Reducing Fatigue in Wind-Excited Support Structures of Traffic Signals with Innovative Vibration Absorber

Support structures of traffic signals are flexible, lightly damped structures that are highly susceptible to wind-induced vibration. The sustained large-amplitude deflections caused by these dynamic vibrations can result in fatigue cracking and failure. The proposed innovative vibration absorber reduces fatigue in support structures of traffic signals with the use of the mass of the signal head as a damped-vibration absorber. This novel concept, referred to as a signal head vibration absorber (SHVA), provides energy absorption in the form of increased damping to the lightly damped signal support structure. A prototype smart vibration absorber, envisioned as an inexpensive retrofit to signal support structures that were experiencing excessive wind-induced vibration, was tested in a full-scale laboratory experiment at the University of Connecticut. The SHVA was experimentally shown to have increased the damping in the signal support structure from 0.2% of the critical damping ratio to 10.1%. For steady state vibration, this difference is equivalent to a 98.3% reduction in the response and virtually eliminates any deflections. A single SHVA can be applied to a wide range of signal support structures while still achieving reasonable performance. The SHVA can change the way vibration in traffic signal support structures is mitigated.

Analysis of Steady Collision Vibration in Simply-Supported-Beam Having an Attached Mass with Restoring Force of Hysteresis Loops

This paper deals with the collision vibration in continuous system excited by periodic displacement with arbitrary functions. The analytical model is steady collision vibration in simply-supported-beam having an attached mass which collides elastically to symmetric faces with restoring force of hysteresis loops. In order to clarify the main resonance of the system subjected to excitation by displacement, the resulting vibration is analyzed applying the Fourier series method for this system. Following this theoretical analysis, the numerical calculations are also performed, and the resonance curves are constructed using the resulting vibrations. Effects of the stiffness of clamped spring, the ratio of attached mass and the amplitude of excitation on the resonance curves are shown as an example of numerical results.

Damping Characteristics of Bladed Disk with Continuous Ring Type Structure (Effects of Friction Damping on Self-Excited Vibration)

Recently, bladed disks with continuous ring type structure have been used in many kinds of turbomachinery due to its high reliability. The vibration characteristics of the bladed disk with continuous ring type structure have been studied extensively, and the effect of the friction damping on the forced vibration is almost clarified. On the other hand, few studies have been done on the effect of the friction damping on the blade flutter. In this paper, the stability analysis of the bladed disk with continuous ring type structure is carried out using the equivalent spring-mass model, and the effect of the friction damping on the blade flutter is clarified. From the results of the analysis, it is concluded that the stable steady vibration or the flutter always occurs when the aerodynamic damping of the blade becomes negative. Whether the blade vibration is stable or unstable depends on the magnitude of the aerodynamic damping and the initial condition. In other words, when the friction damping cannot suppress the self-excited vibration due to the large aerodynamic damping and the large initial amplitude, the amplitude of the blade vibration becomes larger and the flutter occurs.

Damping Characteristics of Bladed Disk with Continuous Ring Type Structure (Effects of Friction Damping on Self-Excited Vibration)

Recently, bladed disks with the continuous ring type structure have been used in many kinds of turbomachinery due to its high reliability. The vibration characteristics of the bladed disk with continuous ring type structure have been studied extensively, and the effect of the friction damping on the forced vibration is almost clarified. On the other hand, few studies have been done on the effect of the friction damping on the blade flutter. In this paper, the stability analysis of the bladed disk with the continuous ring type structure is carried out using the equivalent spring mass model, and the effect of the friction damping on the blade flutter is clarified. From the results of analysis, it is concluded that the stable steady vibration or the flutter occurs when the aerodynamic damping of the blade becomes negative. Whether the blade vibration is stable or unstable depends on the magnitude of the aerodynamic damping and the initial condition. In other words, when the friction damping can not suppress the self-excited vibration due to the large aerodynamic damping and the large initial amplitude, the amplitude of the blade vibration becomes larger and the flutter occurs.

An adaptive tuned mass damper based on the emulation of positive and negative stiffnesswith an MR damper

This paper presents a new adaptive tuned mass damper (TMD) whose stiffness anddamping can be tuned in real-time to changing frequencies of a target structure. Theadaptive TMD consists of a tuned mass, a tuned passive spring and a magnetorheological(MR) damper. The MR damper is used to emulate controlled friction–viscous damping andcontrolled stiffness. The controlled positive or negative stiffness emulated by the MRdamper works in parallel to the stiffness of the passive TMD spring. The resulting overallTMD stiffness can therefore be varied around the passive spring stiffness using the MRdamper. Both the emulated stiffness and friction–viscous damping in the MR damper arecontrolled such that the resulting overall TMD stiffness and damping are adjustedaccording to Den Hartog’s formulae. Simulations demonstrate that the adaptive TMD witha controlled MR damper provides the same reduction of steady state vibration amplitudesin the target structure as a passive TMD if the target structure vibrates at thenominal frequency. However, if the target structure vibrates at different frequencies,e.g. due to changed service loads, the adaptive TMD with a controlled MR damperoutperforms the passive TMD by up to several 100% depending on the frequencychange.