Higher Mode Frequency Effects on Resonance in Machinery Structures

2010 ◽  
Author(s):  
Robert A. Leishear
Keyword(s):  
Cyclic Load ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Cyclic Loads ◽  
Comprehensive Description ◽  
Single Degree Of Freedom ◽  
Frequency Effects ◽  
Single Degree ◽  
Near Resonance ◽  
Mass Damper

The complexities of resonance in multi-degree of freedom systems (multi-DOF) may be clarified using graphic presentations. Multi-DOF systems represent actual systems, such as beams or springs, where multiple, higher order, natural frequencies occur. Resonance occurs when a cyclic load is applied to a structure, and the frequency of the applied load equals one of the natural frequencies. Both equations and graphic presentations are available in the literature for single degree of freedom (SDOF) systems, which describe the response of spring-mass-damper systems to harmonically applied, or cyclic, loads. Loads may be forces, moments, or forced displacements applied to one end of a structure. Multi-DOF systems are typically described only by equations in the literature, and while equations certainly permit a case by case analysis for specific conditions, graphs provide an overall comprehension not gleaned from single equations. In fact, this collection of graphed equations provides novel results, which describe the interactions between multiple natural frequencies, as well as a comprehensive description of increased vibrations near resonance.

Effects of human-induced load models on tuned mass damper in reducing floor vibration

2019 ◽  
Vol 22 (11) ◽  
pp. 2449-2463
Author(s):  
Jun Chen ◽  
Ziping Han ◽  
Ruotian Xu
Keyword(s):  
Response Spectra ◽  
Tuned Mass Damper ◽  
Design Guidelines ◽  
Degree Of Freedom ◽  
Dynamic Responses ◽  
Single Degree Of Freedom ◽  
Load Model ◽  
Load Models ◽  
Single Degree ◽  
Mass Damper

Dozens of human-induced load models for individual walking and jumping have been proposed in the past decades by researchers and are recommended in various design guidelines. These models differ from each other in terms of function orders, coefficients, and phase angles. When designing structures subjected to human-induced loads, in many cases, a load model is subjectively selected by the design engineer. The effects of different models on prediction of structural responses and efficiency of vibration control devices such as a tuned mass damper, however, are not clear. This article investigates the influence of human-induced load models on performance of tuned mass damper in reducing floor vibrations. Extensive numerical simulations were conducted on a single-degree-of-freedom system with one tuned mass damper, whose dynamic responses to six walking and four jumping load models were calculated and compared. The results show a maximum three times difference in the acceleration responses among all load models. Acceleration response spectra of the single-degree-of-freedom system with and without a tuned mass damper were also computed and the response reduction coefficients were determined accordingly. Comparison shows that the reduction coefficient curves have nearly the same tendency for different load models and a tuned mass damper with 5% mass ratio is able to achieve 50%–75% response reduction when the structure’s natural frequency is in multiples of the walking or jumping frequency. All the results indicate that a proper load model is crucial for structural response calculation and consequently the design of tuned mass damper device.

Three-Element Vibration Absorber–Inerter for Passive Control of Single-Degree-of-Freedom Structures

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Abdollah Javidialesaadi ◽  
Nicholas E. Wierschem
Keyword(s):  
Passive Control ◽  
Translational Motion ◽  
Tuned Mass Damper ◽  
Degree Of Freedom ◽  
Superior Performance ◽  
Underlying Structure ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Mass Damper

In this study, a novel passive vibration control device, the three-element vibration absorber–inerter (TEVAI) is proposed. Inerter-based vibration absorbers, which utilize a mass that rotates due to relative translational motion, have recently been developed to take advantage of the potential high inertial mass (inertance) of a relatively small mass in rotation. In this work, a novel configuration of an inerter-based absorber is proposed, and its effectiveness at suppressing the vibration of a single-degree-of-freedom system is investigated. The proposed device is a development of two current passive devices: the tuned-mass-damper–inerter (TMDI), which is an inerter-base tuned mass damper (TMD), and the three-element dynamic vibration absorber (TEVA). Closed-form optimization solutions for this device connected to a single-degree-of-freedom primary structure and loaded with random base excitation are developed and presented. Furthermore, the effectiveness of this novel device, in comparison to the traditional TMD, TEVA, and TMDI, is also investigated. The results of this study demonstrate that the TEVAI possesses superior performance in the reduction of the maximum and root-mean-square (RMS) response of the underlying structure in comparison to the TMD, TEVA, and TMDI.

A Probabilistic Analysis of Single-Degree-of-Freedom Blade Vibration

1993 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
Mehmet Imregun ◽  
David J. Ewins
Keyword(s):  
Natural Frequencies ◽  
Probabilistic Approach ◽  
Substantial Reduction ◽  
Forced Response ◽  
Degree Of Freedom ◽  
Cumulative Probability ◽  
Blade Vibration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stiffness And Damping

The effects of random stiffness and damping variations on damped natural frequencies and response levels of turbomachinery blades are investigated by employing probabilistic approach using a single-degree-of-freedom (SDOF) model. An important feature of this study is the determination of the cumulative probability distributions for damped natural frequencies and receptance frequency response functions without having to compute their probability density distributions since it is shown that those of stiffness and damping can be used directly. The advantage of this approach is not only in the simplicity of problem formulation but also in the substantial reduction of computational requirements. Furthermore, results suggest that both stiffness and damping properties should be considered as random parameters in statistical analyses of forced response.

Effect of Intermolecular Forces on the Dynamic Response of a Slider

2006 ◽  
Vol 129 (1) ◽  
pp. 177-180 ◽  
Author(s):  
Saurabh K. Deoras ◽  
Frank E. Talke
Keyword(s):  
Dynamic Response ◽  
Impulse Response ◽  
Magnetic Recording ◽  
Intermolecular Forces ◽  
Degree Of Freedom ◽  
Flying Height ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Mass Damper

A single-degree-of-freedom spring-mass-damper model has been developed to simulate the dynamic response of a typical magnetic recording slider under the effect of intermolecular forces. Thornton and Bogy (2003, IEEE Trans. Magn., 39(5), pp. 2420–2422) have previously reported that the slider “snaps” to the surface of the disk, below a certain “critical” flying height, due to the intermolecular forces. We have studied impulse response of the model to show that the slider can snap even at flying heights greater than the critical flying height and that the occurrance of snapping also depends on the magnitude of the applied impulse.

scholarly journals Quality-Factor Enhancing Locations for Substrate Mounted Resonators

2020 ◽  
Vol 25 (3) ◽  
pp. 318-326
Author(s):  
Allen Anilkumar ◽  
Arun George ◽  
Gireesh Sharma N.
Keyword(s):  
Eigenvalue Problem ◽  
Quality Factor ◽  
Characteristic Equation ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Structural Interaction ◽  
Single Degree ◽  
Lookup Tables

An important but often overlooked factor that affects the performance of a meso/micro electro mechanical vibratory sensor is the structural interaction between the sensor's resonator and the substrate on which it is mounted. Situating resonators at node points eliminates this interaction and thereby helps to improve a resonator's quality-factor for a particular mode of vibration. This paper addresses the problem of locating a single degree of freedom spring-mass resonator on a generic cantilever substrate. The loci of natural frequencies obtained when the resonator's mounting location is varied are developed, and the nodal locations are identified. Thereafter a method to obtain these locations from the characteristic equation without solving the associated eigenvalue problem is described. Lookup tables detailing the nodal locations and the corresponding natural frequencies for various resonator parameters are presented. It is found that at these special nodal locations, the magnitude of the power transmitted through anchors is negligible, which ensures minimal structural interaction between the resonator and the substrate.

Effects of Clearance on Normal Mode Frequencies of a Nonsmooth System

1999 ◽  
Author(s):  
Eric A. Butcher
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Normal Mode ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Nonsmooth System ◽  
Single Degree ◽  
Equivalent Linear ◽  
Frequency Relation

Abstract The effects of a clearance or interference on the normal mode frequencies of a two-dof system with bilinear stiffness and without damping are investigated through various modifications of the bilinear frequency relation. First, the exact bilinear natural frequencies of a single degree-of-freedom system are analytically obtained in terms of the amount of clearance and the strength of nonlinearity, and an equivalent linear system is derived. These results are in turn used to construct three methods which approximate the bilinear frequencies for the 2-dof system in which the resulting approximate frequencies are compared with those obtained from numerical simulations. The results demonstrate how these bilinear normal mode frequencies vary with the magnitude of the clearance/interference and thus point toward the need of including such effects in methods which utilize the bilinear frequency relation.

Application of Viscoelastic Material for a Dynamic Damper

1986 ◽  
Vol 108 (3) ◽  
pp. 378-381 ◽  
Author(s):  
K. J. Kim ◽  
T. I. Yeo
Keyword(s):  
Resonance Frequency ◽  
Viscoelastic Material ◽  
Optimization Procedure ◽  
Degree Of Freedom ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Dynamic Damper ◽  
Single Degree ◽  
Mass Damper

An optimization procedure in the design of a viscoelastic dynamic damper is proposed for a single-degree-of-freedom primary system with the effects of prestrain taken into account. The performance is compared with that by a conventional spring-dashpot-mass damper. Applicability of the proposed procedure to a resonance-frequency-varying system is also shown.

scholarly journals Experimental study of a passive inverted pendulum control system

2018 ◽  
Vol 211 ◽  
pp. 02005 ◽  
Author(s):  
Diogo V. Resende ◽  
Marcus V. G. de Morais ◽  
Suzana M. Avila
Keyword(s):  
Experimental Study ◽  
Inverted Pendulum ◽  
Degree Of Freedom ◽  
3D Printer ◽  
Single Degree Of Freedom ◽  
Response Data ◽  
Single Degree ◽  
Mass Damper ◽  
Base Displacement ◽  
The Time Domain

This work presents the results obtained by an experimental study of vibration control for a system with a single degree of freedom, composed by a sliding base on an air track. An inverted pendulum-type tuned mass damper (TMD-IP) is installed on the sliding base to reduce its displacements. First, a reduced model is built using a 3D printer. The experimental model consists of two parts: the mains system, which is the sliding base; and the inverted pendulum (TMD-IP). The model can be tested as a one-degree-of-freedom system using only the base or as a two-degree system of freedom system after connecting the TMD-IP to the sliding base. The CIDEPE air rail is used to provide the sliding base displacement, which will receive the TMD-IP. The acquisition of the response data in the time domain is done through the software CvMob, which performs image acquisition and was produced by the Nucleus of Technological Innovation in Rehabilitation - NITRE, Federal University of Bahia.

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