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.

Linearization Equations for Vibration Induced by Oscillatory Flow

1979 ◽  
Vol 46 (4) ◽  
pp. 946-948 ◽  
Author(s):  
P-T. D. Spanos ◽  
T. W. Chen
Keyword(s):  
Linear System ◽  
Oscillatory Flow ◽  
Degree Of Freedom ◽  
Approximate Determination ◽  
Equivalent Linearization ◽  
Mean Velocity ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Nonzero Mean

Equations are presented for the approximate determination through equivalent linearization of the response of a single-degree-of-freedom linear system to excitation induced by oscillatory flow with nonzero mean velocity. The reliability of the proposed methodology is examined.

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.

A Design Criterion for Avoiding Resonance in Lumped Mass Normal Mode Systems

1989 ◽  
Vol 111 (1) ◽  
pp. 48-52
Author(s):  
A. D. S. Ross ◽  
D. J. Inman
Keyword(s):  
Normal Mode ◽  
Design Criterion ◽  
Degree Of Freedom ◽  
Simple Design ◽  
Parameter System ◽  
Lumped Mass ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Lumped Parameter

A simple design criterion that determines whether a normal mode multiple degree of freedom damped linear lumped parameter system can or cannot resonate is presented. The relations are derived based on criteria for resonance in the single degree of freedom case, and on the definiteness of certain combinations of coefficient matrices. An example follows that both numerically verifies the derivation and illustrates the simplicity of implementing the result as a design criterion.

Periodic Motions in a Single-Degree-of-Freedom System Under Both an Aerodynamic Force and a Harmonic Excitation

2019 ◽  
Author(s):  
Bo Yu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Aerodynamic Force ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Period

Abstract In this paper, a semi-analytical approach was used to predict periodic motions in a single-degree-of-freedom system under both aerodynamic force and harmonic excitation. Using the implicit mappings, the predictions of period-1 motions varying with excitation frequency are obtained. Stability of the period-1 motions are discussed, and the corresponding eigenvalues of period-1 motions are presented. Finally, numerical simulations of stable period-1 motions are illustrated.

The Estimation of Viscous and Coulomb Damping in Harmonically Excited Oscillators

1999 ◽  
Author(s):  
J.-W. Liang ◽  
B. F. Feeny
Keyword(s):  
Free Vibration ◽  
Numerical Simulations ◽  
Dry Friction ◽  
Mechanical Vibration ◽  
Degree Of Freedom ◽  
Identification Algorithm ◽  
Single Degree Of Freedom ◽  
Coulomb Damping ◽  
Single Degree

Abstract This paper proposes a simple identification algorithm for estimating both viscous and dry friction in harmonically forced single-degree-of-freedom mechanical vibration systems. The method is especially suitable for the identification of systems for which the traditional free-vibration scheme is difficult to implement. Numerical simulations are included to show the effectiveness of the proposed algorithm. A numerical perturbation study is also included for insight on the robustness of the algorithm.

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.

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.

Understanding Damping in Acoustic and Mechanical Systems

2014 ◽  
Author(s):  
Hugh Goyder
Keyword(s):  
Linear System ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Degree Of Freedom ◽  
Vibration Modes ◽  
Acoustic System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Modes Of Vibration ◽  
Straightforward Extension

A system with damping is much more difficult to model than an undamped system. In particular, the effect of damping on a multi-degree-of-freedom system is not a straightforward extension of the damping found in a single-degree-of-freedom system. The complications of a multi-degree-of-freedom system are first examined by investigating the acoustic modes of a pipe with energy leaking from the boundaries. This system can be modelled exactly and identifies the complexities that need to be understood. Although this is a linear system it is found that in contradistinction to an undamped system it cannot be separated into individual modes of vibration. Modes which bear some similarity to undamped modes can be found but these are always coupled by damping effects which, to add more complications, may involve some modes being active and supplying energy to other modes. The original acoustic system is simplified to systems of finite and eventually two-degrees-of-freedom in an effort to understand the effects of damping. It is found that when damping is added to a system some damping ratios may decrease moving the system into an unfavourable state. Overall some general properties of damping, for example, the constancy of average damping, are deduced.

Sign in / Sign up

Export Citation Format

Share Document