Benndorf's formula for the dynamic magnification of an electromagnetic seismograph

1969 ◽  
Vol 59 (4) ◽  
pp. 1713-1717
Author(s):  
G. A. Bollinger
Keyword(s):  
Steady State ◽  
Natural Frequencies ◽  
At Resonance ◽  
Velocity Sensitivity ◽  
Electromagnetic Seismograph ◽  
Dynamic Velocity

Abstract The indicator equation for a seismogram from an electromagnetic seismograph is integrated under the assumption that the trace has the form of a suddenly beginning sinusoid. An expression for the velocity sensitivity is derived from the integrated result and applied to the particular case of a seismometer-galvanometer combination with natural frequencies of 2 Hertz-200 Hertz respectively. For that seismograph the dynamic velocity sensitivity at transducer—earth resonance is one-fifth of the steady-state harmonic sensitivity at resonance.

Vibration Behavior and Serviceability of Arched Prestressed Concrete Truss Due to Human Activity

2018 ◽  
Vol 18 (12) ◽  
pp. 1850146 ◽  
Author(s):  
Jiang Li ◽  
Jiepeng Liu ◽  
Liang Cao ◽  
Y. Frank Chen
Keyword(s):  
Steady State ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Current Trend ◽  
Threshold Values ◽  
Transient Vibration ◽  
Vibration Behavior ◽  
Detailed Evaluation ◽  
Floor Systems ◽  
Floor Vibration

The current trend toward longer spans and lighter floor systems, combined with reduced damping and new activities, have resulted in an increasing complaints on floor vibration from building owners and occupants. Heel-drop, jumping, and walking impacts, which may lead to discomfort problems in daily life, were imposed on a large-span arched prestressed concrete truss (APT) girder system studied. The natural frequencies, peak acceleration, average root-mean-square acceleration (ARMS), maximum transient vibration value (MTVV), and perception factor for the girder were obtained and checked against the existing codes and standards. The purpose of this paper is to provide researchers and engineers with a detailed evaluation on the vibration behavior of the APT girder under different human activities, with a comprehensive review on the relevant criteria and some suggestions. Lastly, the following threshold peak accelerations are suggested: 650[Formula: see text]mm/s2 for transient heel-drop impact, 1450[Formula: see text]mm/s2 for transient jumping impact, and 250[Formula: see text]mm/s2 for steady-state walking. In addition, the threshold values of 90[Formula: see text]mm/s2 and 50[Formula: see text]mm/s2 are suggested for MTVV and ARMS, respectively, under steady-state walking.

Non-linear free transverse vibration of thin rotating discs

2007 ◽  
Vol 221 (3) ◽  
pp. 467-473 ◽  
Author(s):  
H R Hamidzadeh
Keyword(s):  
Steady State ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Stress Distributions ◽  
Rotating Speed ◽  
Rotating Discs ◽  
Non Linear ◽  
Modes Of Vibration ◽  
Free Transverse Vibration

An analytical method is adopted to determine modal characteristics of non-linear spinning discs. The disc is assumed to be isotropic and rotating under steady-state conditions. The effects of amplitude and rotating speed on natural frequencies are determined. The developed procedure is also capable of analysing natural frequencies of linear free vibration, which is independent of amplitude. Attention is confined to determine natural frequencies, mode shapes, stress distributions, and critical speeds for different numbers of nodal diameters. The developed procedure does not consider modes of vibration corresponding to nodal circles. Validity of this procedure is verified by comparing some of the computed results with those established for certain cases.

Particularities of Blading Free Resonance Design for Heavy Duty Gas Turbines With Circumferential Rotor Grooves

2014 ◽  
Author(s):  
Igor Putchkov ◽  
Alexander Arkhipov ◽  
Valery Moskovskikh ◽  
Harald Kissel ◽  
Alexander Laqua
Keyword(s):  
Steady State ◽  
Gas Turbines ◽  
Natural Frequencies ◽  
Contact Spot ◽  
Heavy Duty ◽  
Blade Root ◽  
Lateral Contact ◽  
Start Up ◽  
Blade Frequency ◽  
Engine Start

Blades for heavy duty engines with circumferential rotor grooves are designed such that radial contact is made between the blade teeth and rotor groove at steady state operation conditions. However, sometimes circumferential contact arises between neighboring blade shanks, which is often caused by blade root /rotor thermal expansion. In this case, the radial fixation will give the lower limit of blade frequency band, and the circumferential will give the upper one. The Blade frequency difference between these two fixations might reach about 200–500 Hz depending on blade airfoil and root sizes. When some excitation source (e.g., vane passing frequencies caused by up-stream and down-stream vane counts) has a frequency level situated between blade frequencies caused by radial and circumferential contact, such a case is the subject of the proposed approach. In order to assess how strongly the blade might be fixed under different conditions and how long it might be in resonance during engine start-up and subsequent loading, a 3D elastic-plastic transient analysis and corresponding frequency calculation of blade/rotor assembly is used. At engine start-up the circumferential (lateral) contact between neighboring blade roots is insignificant, and the radial contact between the rotor and the blade is dominant. The lateral contact spot between neighboring blade attachments during start-up appears due to different rates of blade/rotor heating. Further heating leads to an increase of the lateral contact spot areas. The closing of these contact surfaces starts from the outer root edge and spreads toward the inner one, leading to an increase of assembly natural frequencies. Engine loading and further heating lead to the appearance of a circumferential gap between the surfaces, causing the lateral contact to disappear during steady state. The blade root coupling switches again to the usual radial contact state, with the corresponding reduction of natural frequencies. Because the described phenomenon might occur for some time during every start-up and shut-down (from several minutes to couple of hours), it becomes even more severe from a dynamics standpoint if some natural frequency of coupled system crosses the exciting frequency. Examples of assembly frequency tuning are presented.

The Galloping Response of a Two-Degree-of-Freedom System

1974 ◽  
Vol 41 (4) ◽  
pp. 1113-1118 ◽  
Author(s):  
R. D. Blevins ◽  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Natural Frequencies ◽  
Analytic Solutions ◽  
Degree Of Freedom ◽  
Approximate Analysis ◽  
Stability Criteria ◽  
Integer Multiple ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

The galloping response of a two-degree-of-freedom system is investigated using asymptotic techniques to generate approximate steady-state solutions. Simple closed-form analytic solutions and stability criteria are presented for the case where the two structural natural frequencies are harmonically separated. Examples of the nature of the galloping response of a particular section are presented for the case where the frequencies are harmonically separated as well as for the case where the two natural frequencies are near an integer multiple of each other. The results of the approximate analysis are compared with experimental and numerical results.

A Three-Dimensional Ring Model for Uncertainty Quantification in Natural Frequencies and Sound Radiation Characteristics of Tires

2020 ◽  
Vol 28 (02) ◽  
pp. 2050016
Author(s):  
Zhe Liu ◽  
Wenchang Zhao ◽  
Kian K. Sepahvand ◽  
Yintao Wei ◽  
Steffen Marburg
Keyword(s):  
Steady State ◽  
Natural Frequencies ◽  
Sound Radiation ◽  
Superposition Method ◽  
Sound Power ◽  
Steady State Response ◽  
Radiation Characteristics ◽  
State Response ◽  
Ring Model ◽  
Out Of Plane

Material and geometrical parameters of tires involve some degree of uncertainty mainly related to production processes. Accordingly, the associated structural responses are affected by these uncertainties. In this study, a novel theoretical ring model is presented to describe the in-plane and out-of-plane vibrations as well as the steady-state response of tires, and then to evaluate the influence of the uncertainties in structural parameters on the natural frequencies and the sound radiation characteristics under uncertain excitations. The Hamilton principle is applied here to derive the governing equations. The modal superposition method is used to calculate the steady-state response of the tire. In the sound radiation analysis, the in-plane and out-of-plane bending and torsional vibrations under a set of harmonic unit forces and moments are treated as the source of noise generation. On this basis, the generalized polynomial chaos expansion method is then adopted to evaluate the influence of the uncertainty on the natural frequencies and the sound power. To obtain the unknown coefficients of the expansions, the nonintrusive probabilistic collocation method is employed. Moreover, considering the concept of linear independence of vectors, the number of collocation points is reduced. It is applied to investigate the impacts of the elastic and structural uncertainties on the natural frequencies of the tire. This yields an efficient simulation in terms of computational costs. Finally, the distributions of the sound power due to the forced vibration under the random concentrated line forces are given.

Modal Analysis of Ballooning Strings With Small Sag

1999 ◽  
Author(s):  
Rongjun Fan ◽  
Sushil K. Singh ◽  
Christopher D. Rahn
Keyword(s):  
Steady State ◽  
High Speed ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Theoretical Predictions ◽  
Nonlinear Equations Of Motion

Abstract During the manufacture and transport of textile products, yarns are rotated at high speed and form balloons. The dynamic response of the balloon to varying rotation speed, boundary excitation, and disturbance forces governs the quality of the associated process. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three dimensional nonlinear equations of motion are simplified via small steady state displacement (sag) and vibration assumptions. Axial vibration is assumed to propagate instantaneously or in a quasistatic manner. Galerkin’s method is used to calculate the mode shapes and natural frequencies of the linearized equations. Experimental measurements of the steady state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

Simulation of the frequency split of the fundamental air cavity mode of a loaded and rolling tire by using steady-state transport analysis

2021 ◽  
Vol 263 (1) ◽  
pp. 4919-4932
Author(s):  
Won Hong Choi ◽  
J. Stuart Bolton
Keyword(s):  
Steady State ◽  
Cavity Mode ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Moving Frame ◽  
Noise Levels ◽  
Air Cavity ◽  
Frequency Split ◽  
Transport Analysis ◽  
Oscillatory Force

It has been found that when a tire deforms due to loading, the fundamental air cavity mode splits into two due to the break in geometrical symmetry. The result is the creation of fore-aft and vertical acoustic modes near 200 Hz for typical passenger car tires. When those modes couple with structural, circumferential modes having similar natural frequencies, the oscillatory force transmitted to the suspension can be expected to increase, hence causing increased interior noise levels. Further, when the tire rotates, the frequency split is enlarged owing to the Doppler effect resulting from the airflow within the tire cavity. The current research is focused on determining the influence of rotation speed on the frequency split by using FE simulation. In particular, the analysis was performed by using steady-state transport analysis which enables vibroacoustic analysis in a moving frame attached to tire in the frequency domain. The details of the modeling are described and results are given for a tire under different rotation speeds, presented in terms of dispersion curves that illustrate the interaction between structural and acoustical modes. The results are compared to those for static tires and tires spinning without translational velocity to highlight the effects of rolling.

A rapid method for calibrating Willmore seismographs

1964 ◽  
Vol 54 (5A) ◽  
pp. 1473-1477
Author(s):  
K. G. Barr
Keyword(s):  
Rapid Method ◽  
Velocity Sensitivity ◽  
Electromagnetic Seismograph

Abstract A method is described for calibrating Willmore seismographs. It could be applied to any other electromagnetic seismograph having a galvanometer period substantially shorter than the seismometer period. The method is rapid and involves very little equipment. An overall accuracy of 20% in the velocity sensitivity is easily attainable.

Experimental and Numerical Investigation of Vibration Damping Using a Thin Layer Coating

2017 ◽  
Author(s):  
Imran Aziz ◽  
Sajjad Hussain ◽  
Wasim Tarar ◽  
Imran Akhtar
Keyword(s):  
Nickel Alloy ◽  
High Cycle Fatigue ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Rotating Machinery ◽  
Forced Response ◽  
Cycle Fatigue ◽  
Damping Characteristics ◽  
At Resonance ◽  
Vibration Shaker

High cycle fatigue (HCF) is the main cause of failure in rotating machinery especially in aircraft engines which results in the loss of human life as well as billions of dollars. More than 60 percent of aircraft accidents are related to High cycle fatigue. Major reason for HCF is vibratory stresses induced in the blades at resonance. Damping is needed to avoid vibratory stresses to reach the failure level. High speed rotating machinery has to pass through the resonance in order to reach the operational speed and chances of failure are high at resonance level. It is therefore required to suppress the vibrations at resonance level to avoid any damage to the structure. Application of coating to suppress vibrations is a current area of research. Various types of coatings have been studied recently. This includes plasma graded coatings, viscoelastic dampers, piezoelectric material damping, and magnetomechanical damping. In this research, the phenomenon of damping using a coating of nickel alloy on a steel beam is studied experimentally and numerically to reduce vibratory stresses by enhancing damping characteristics to avoid aircraft engine and rotating machinery failure. For this purpose, uncoated and nickel alloy coated steel beams are fabricated. The coating procedure was performed using plasma arc method. The beams were then mounted in a cantilevered position and bump and vibration shaker tests were conducted to determine the natural frequencies and mode shapes. One of the most important parameter to measure the damping of a system is the damping ratio. In order to determine the damping ratio, vibration analyzer mode was adjusted in time domain and beam was excited by using a hammer. The vibration analyzer showed the vibration decay as a function of time. Using that decay, damping ratio was calculated by using logarithmic decrement method. In order to investigate and compare the damping characteristics of un-coated and coated beams, forced response method was employed. In this method, beams were excited at 1st and 2nd bending mode natural frequencies using vibration shaker. Results were very encouraging and showed a significant improvement in damping characteristics. The experimental results were then endorsed by numerical results which were achieved by performing modal and forced response analysis using finite element analysis techniques.

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