Free Response of an Array of Mono-Coupled Elements Terminating at General Boundaries

1996 ◽  
Vol 15 (2) ◽  
pp. 89-98 ◽  
Author(s):  
A.S. Bansal
Keyword(s):  
General Theory ◽  
Natural Frequencies ◽  
Free Response ◽  
Frequency Dependent ◽  
Periodic Arrays ◽  
Vibrational Response ◽  
End Conditions ◽  
Mass Damper ◽  
Simple Supports ◽  
Set Up

Receptance methods have been used to set up general equations that govern the vibrational response of a finite array of N mono-coupled elements terminating at general boundaries. The equations have been modified to introduce ideal and the frequency dependent boundary conditions offered by semi-infinite periodic arrays attached at its ends. The general theory has been adapted to determine the natural frequencies of some finite 5-span beams on simple supports with their ends having various combinations of ideal and frequency dependent end conditions. Lowest group of natural frequencies of the finite beams having different disorders and different combinations of ideal, elastic and dissipative boundaries have been computed and discussed. The conditions under which the undamped combined systems can behave like spring-mass systems and spring-mass-damper systems have also been identified and explained.

scholarly journals Robust H∞ Control of STMDs Used in Structural Systems by Hardware in the Loop Simulation Method

Actuators ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 55
Author(s):  
Huseyin Aggumus ◽  
Rahmi Guclu
Keyword(s):  
Natural Frequencies ◽  
Experimental Studies ◽  
Mr Damper ◽  
Simulation Method ◽  
Control Element ◽  
Structural Systems ◽  
Hardware In The Loop ◽  
Building Model ◽  
Mass Damper ◽  
Set Up

This paper investigated the performance of a semi-active tuned mass damper (STMD) on a multi-degree of freedom (MDOF) building model. A magnetorheological (MR) damper was used as a control element that provided semi-activity in the STMD. The Hardware in the Loop Simulation (HILS) method was applied to mitigate the difficulty and expense of experimental studies, as well as to obtain more realistic results from numerical simulations. In the implementation of this method for the STMD, the MR damper was set up experimentally, other parts of the system were modeled as computer simulations, and studies were carried out by operating these two parts simultaneously. System performance was investigated by excitation with two different acceleration inputs produced from the natural frequencies of the MDOF building. Additionally, a robust H ∞ controller was designed to determine the voltage transmitted to the MR damper. The results showed that the HILS method could be applied successfully to STMDs used in structural systems, and robust H ∞ controls improve system responses with semi-active control applications. Moreover, the control performance of the MR damper develops with an increase in the mass of the STMD.

Receptances and Natural Frequencies of Finite Beams on Non-Uniformly Spaced Supports

1996 ◽  
Vol 15 (3) ◽  
pp. 115-124 ◽  
Author(s):  
A.S. Bansal
Keyword(s):  
Natural Frequencies ◽  
Finite Systems ◽  
Beam Elements ◽  
Resonance Frequencies ◽  
End Conditions ◽  
Real Functions ◽  
Simple Supports

Receptance functions for multi-supported finite beams have been derived in terms of the end receptances of individual beam elements. Receptances of some multi-supported beams have been studied as they vary with frequency over the range fully covering the lowest group of natural frequencies. Effect of variation of support spacing on the receptances and natural frequencies of the beam has also been studied. The results have been compared to a beam on equally spaced (periodic) simple supports. The receptances of undamped systems, as considered in this paper are real functions, and the frequencies at which they can be spring-like or mass-like, have been discussed. The receptances of finite beams have been found to be very useful in determining the resonance frequencies of finite systems having ideal or any other end conditions.

Free Vibration and Instability Analysis of Sandwich Plates with Carbon Nanotubes-Reinforced Composite Faces and Honeycomb Core

2021 ◽  
Author(s):  
Sushila Chowdhary ◽  
Mesfin Kebede Kassa ◽  
Yitbarek Gashaw Tadesse ◽  
Ananda Babu Arumugam ◽  
Rajeshkumar Selvaraj
Keyword(s):  
Finite Element ◽  
Glass Fiber ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Element Formulation ◽  
The Core ◽  
Glass Fiber Reinforced ◽  
End Conditions ◽  
Honeycomb Sandwich ◽  
Instability Regions

In this study, the instability regions of a honeycomb sandwich plate are investigated for different end conditions under periodic in-plane loading. The core layer of the sandwich plate is made of carbon nanotube (CNT)/glass fiber-reinforced honeycomb and the face layers of CNT/glass fiber- reinforced laminated composite. The governing equations are derived using classical laminated plate theory (CLPT) and solved numerically by using finite element formulation. The effectiveness of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies with those available in the literature. The effects of CNT wt.% on the core material, CNT wt.% on the skin material, ply orientation and various end conditions on the variation of natural frequencies, loss factors and instability regions are studied. Finally, some inferences for the effects of CNT reinforcement on the honeycomb sandwich plate subjected to the periodic in-plane loads are discussed.

Non-Destructive Testing of Mass Produced Components by Natural Frequency Measurements

1985 ◽  
Vol 199 (3) ◽  
pp. 161-168 ◽  
Author(s):  
P Cawley
Keyword(s):  
Natural Frequencies ◽  
Production Quality ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Production Quality Control ◽  
Cross Sectional ◽  
Dimensional Changes ◽  
Single Section ◽  
Set Up ◽  
Non Destructive

Vibrations in engineering components may be excited by a light tap and the vibration response may be measured with a microphone and displayed as a frequency spectrum from which the natural frequencies of the component can be extracted. Changes in the natural frequencies of the various modes are observed when small defects such as cracks are present. The use of this technique for the production quality control of mass produced components has been investigated. Tests have been carried out on a cantilever beam, a piston-shaped component and a pulley wheel. It has been shown that, in the absence of dimensional variations, defects removing between 0.5 and 2 per cent of the cross-sectional area of the component at a single section may be detected, the precise size depending on the geometry of the component and the location of the defect. Dimensional variations reduce this sensitivity, but a method has been developed for correcting the results for dimensional changes, without the need for more measurements to be taken. The results show that, unless the likely location of a defect is known in advance, it is essential to measure the natural frequencies of more than one mode of vibration. The test takes less than ten seconds to set up, about one second to carry out and is amenable to automation.

scholarly journals Detection of multiple cracks in a beam by means natural frequencies of transverse vibrations

2020 ◽  
pp. 19-26
Author(s):  
Иван Михайлович Лебедев ◽  
Ефим Ильич Шифрин
Keyword(s):  
Arbitrary Number ◽  
Natural Frequencies ◽  
Multiple Cracks ◽  
Transverse Cracks ◽  
Numerical Examples ◽  
Transverse Vibrations ◽  
End Conditions

Рассматривается задача обнаружения множественных, поперечных трещин в стержне с помощью собственных частот поперечных колебаний. В недавней статье авторов доказано, что любое количество трещин однозначно восстанавливается по трем спектрам, отвечающим трем различным типам краевых условий. В статье также предложен алгоритм идентификации повреждений, вносимых трещинами. Помимо этого, высказано предположение, что для однозначной идентификации трещиноподобных дефектов на самом деле достаточно знать два спектра. Для проверки этого предположения разработана модификация предложенного ранее численного алгоритма. Рассмотрены численные примеры. Полученные результаты дают основание полагать, что высказанное предположение справедливо. A problem of detection of multiple transverse cracks in a beam by means of natural frequencies of transverse vibrations is considered. It is proved in the recent paper of the authors that an arbitrary number of cracks can be uniquely determined by three spectra corresponding to three types of the end conditions. An algorithm of reconstruction the damages corresponding the cracks is also developed. In addition, it was assumed that the cracks can be detected using only two spectra. To verify this supposition a modification of the previously developed algorithm is proposed. Numerical examples are considered. The obtained results confirm the assumption.

A Method for Determining the Flexural Effects of Statically Loaded Beams on Multiple Elastic Supports

1956 ◽  
Vol 23 (4) ◽  
pp. 503-508
Author(s):  
R. A. Di Taranto
Keyword(s):  
Beam Theory ◽  
Elastic Supports ◽  
Electronic Digital Computer ◽  
Simply Supported ◽  
Influence Coefficients ◽  
End Conditions ◽  
Desk Calculator ◽  
Simple Supports ◽  
Fixed End ◽  
Nonuniform Beam

Abstract Herein is presented a means for calculating the static deflections, slopes, moments, and shears of a nonuniform beam on two supports for any end conditions and on three simple supports when subjected to concentrated loads and/or concentrated moments. The method is an extension of a simple tabular procedure as used by Myklestad (1) for use on a desk calculator or electronic digital computer. The procedure is such that it may be easily carried out by one who need not have any knowledge of beam theory. Influence coefficients may be easily and directly calculated for nonuniform beams on two and three elastic supports. The two-support beam is formulated for simply supported one overhang, two supports with linear and torsional springs, and fixed-fixed end conditions. Extensions of this method to any other boundary conditions are indicated.

‘No One in Our Age was Cleverer …’

2019 ◽  
pp. 99-136
Author(s):  
Alan Bollard
Keyword(s):  
Soviet Union ◽  
General Theory ◽  
John Maynard Keynes ◽  
Bretton Woods ◽  
The Soviet Union ◽  
Set Up ◽  
The Imf

As troops massed on the border, John Maynard Keynes had to hastily cut short a holiday in France. A government advisor, academic, journalist, and polymath, he spent the next few years working on pioneering and highly innovative economic ideas: how to pay for the war, how to apply his ground-breaking ‘General Theory’ to policy, how to avoid repeating the mistakes of Versailles, and how to set up an international clearing exchange at Bretton Woods that would eventually become the IMF. As Germany turned on the Soviet Union, Keynes became very worried about his Russian in-laws caught up in the terrible siege of Leningrad.

Interaction Between Wind Loading and Japanese Slates: Effect on Vibration and Scattering

2008 ◽  
Author(s):  
Satoru Okamoto
Keyword(s):  
Wind Tunnel ◽  
High Speed ◽  
Natural Frequencies ◽  
Basic Mechanism ◽  
Video Camera ◽  
Flow Speed ◽  
Test Method ◽  
Wind Loading ◽  
Natural Mode ◽  
Set Up

A series of wind tunnel tests was conducted on the vibration and scattering behavior of full-sized model of roof tiles, which were used widely for roofings of Japanese wooden dwellings. This study has investigated the nature and source of the vibrating and scattering behavior of roof tiles with the aim of providing a better insight to the mechanism. The roof tiles were set up on the pitched roof in the downstream of the flow from the wind tunnel. The vibrations for the roof tiles were measured by the Laser Doppler Vibrometry and the accelerometer, and the practical natural frequencies of the roof tiles were analyzed by the impulse force hammer test method. The motions of the vibration and scattering were observed by the high-speed video camera. Based on the consideration on the results of the measurements, there is a basic mechanism which can lead to flow-induced vibrations of the roof tiles. This mechanism is similar to that of the so-called fluttering instability, which appears as the self-excited oscillation in the natural mode of the structure at the certain critical flow speed. The values of the frequencies for the oscillating relate to the values of natural frequencies of the vibration.

An Original Setup Test Rig for Analysing Lubricated Contact Under Dynamic Normal Excitation Forces

2003 ◽  
Author(s):  
Toufiq El Kilali ◽  
Joe¨l Perret-Liaudet ◽  
Denis Mazuyer
Keyword(s):  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Normal Load ◽  
Point Of View ◽  
Test Rig ◽  
Dynamic Excitation ◽  
Lubricated Contacts ◽  
Lubricated Contact ◽  
Set Up ◽  
New Machine

This paper concerns a new experimental set-up based on an optical EHL machine fitted with a dynamic excitation system. The test rig has been built and presented in this paper. Apparatus design derives from two previously defined experimental test rig. With this new machine, we can study the dynamic behaviour of lubricated contacts under sliding conditions on the both tribological and dynamical point of view. It allows to measure the oil film thickness and to visualise the lubricated dynamically loaded contact under sliding condition. It allows also to measure the dynamic response (acceleration) of the loaded contact under harmonic or random external normal load excitation superimposed on a static one. Capabilities of the apparatus are given in this paper. In particular, theoretical and experimental results concerning the system natural frequencies.

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