Modification of Stiffness for Shifting Natural Frequencies of Damped Mechanical Systems

1991 ◽  
Author(s):  
Eric K. L. Yee ◽  
Y. G. Tsuei
Keyword(s):  
System Dynamics ◽  
Mechanical System ◽  
Natural Frequency ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Original System ◽  
Force Response ◽  
Modal Coupling ◽  
Response Equation ◽  
Final Equation

Abstract A method for shifting the natural frequency of a damped mechanical system to a desired value is discussed. The solution is derived from the force response equation of the original system. The final equation contains only the degrees of freedom connected to the modifying parameter. Iterations are required but the solution converges rapidly. Modal coupling effects and sensitivity for shifting a frequency are also derived. Modification of stiffness is used as an example for shifting the natural frequency. Numerical results indicate that the method is effective for system dynamics modification.

The Optimization of Thermocouple Galvanometer System Dynamics When Measuring Temperature Transients

1973 ◽  
Vol 6 (9) ◽  
pp. 384-388
Author(s):  
W. H. McKenzie ◽  
A. H. Richards
Keyword(s):  
System Dynamics ◽  
Natural Frequency ◽  
Time Constant ◽  
Exponential Type ◽  
Natural Frequencies ◽  
Low Voltage ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Ultra Violet ◽  
Dimensional Parameter

When using thermocouples directly connected to ultra-violet galvanometers for recording temperature transients, the low-voltage outputs necessitate the use of galvanometers with low natural frequencies. This puts a limitation on the overall dynamic performance. In a particular application, the user has to select the damping resistor for the galvanometer and the work describes how this is done so that the system is optimised for minimum integrated errors during a transient. The transient considered was of an exponential type which occurs frequently in practice and it is shown that the correct damping ratio and hence damping resistor for the galvanometer depends upon the non-dimensional parameter defined by the product of the natural frequency of the galvanometer and the time constant of the exponential. The results show that the usual value of damping ratio of 0·64 based on minimum sinusoidal distortion has to be modified for best dynamic performance. However, if the non-dimensional parameter is sufficiently large, higher values of damping can be used, which produce a large trace with acceptably small errors.

DYNAMIC PROPERTIES OF AIRCRAFT COMPONENTS AT REAL CONSTRAINTS

Aviation ◽  
2008 ◽  
Vol 12 (4) ◽  
pp. 113-117
Author(s):  
Igor Pavelko ◽  
Vitalijs Pavelko
Keyword(s):  
System Dynamics ◽  
Mechanical System ◽  
Convenient Method ◽  
Discrete System ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Internal Constraints ◽  
Variable Parameters ◽  
Basic Purpose ◽  
Definition Of

The basic purpose of this article is consideration of the problems connected with the application of a method of concentrated weights in the tasks of mechanical system dynamics with non‐classic internal and external constraints. The method of concentrated weights is a convenient method to analyse the dynamic properties of elastic mechanical systems. It has relative simplicity of definition of the parameters of the equivalent discrete system and clearness of computing algorithms and provides comprehensible accuracy of definition of the lowest natural frequencies. A doubtless advantage of the method is its convenience of modelling non‐classic constraints of fastening and internal constraints between elements of complex systems. Such problems arise when making decisions about the practice tasks of the analysis of the dynamics of real systems. The method is used for the analysis of vibrations of a beam with variable parameters at the presence of elastic supporting of the beam and attached additional concentrated weight. Santrauka Pagrindinis straipsnio tikslas – analizuoti atskiras problemas, susijusias su koncentruotų masių metodu mechaninių sistemų dinamikos uždaviniuose su neklasikiniais vidiniais ir išoriniais ryšiais. Koncentruotų masių metodu yra patogu analizuoti tamprių mechaninių sistemų dinamines savybes. Šio metodo savybės yra tokios: ekvivalentinės diskrečios sistemos parametrų paprastas nustatymas; aiškus skaičiavimo algoritmas; pakankamai tikslus laisvųjų virpesių žemo dažnio nustatymas. Modeliuojant neklasikinius vidinius ir išorinius elementų ryšius sudėtingoje mechaninėje sistemoje išryškėja neabejotini metodo privalumai. Tokios problemos iškyla analizuojant realias dinamines sistemas. Šių tyrimų metu metodas buvo panaudotas analizuoti sraigtasparnio sijos virpesius, kai kinta tampraus įtvirtinimo ir tampriai pritvirtintos koncentruotos masės parametrai.

scholarly journals ANALYTICAL MODELING OF PLANETARY GEAR AND SENSITIVITY OF NATURAL FREQUENCIES

2013 ◽  
pp. 35-40
Author(s):  
MAJID MEHRABI ◽  
DR. V.P. SINGH
Keyword(s):  
Natural Frequency ◽  
Degrees Of Freedom ◽  
Analytical Modeling ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Planetary Gears ◽  
System Parameters ◽  
Inertia Parameters

This work develops an analytical model of planetary gears and uses it to investigate their natural frequencies and vibration modes. The model admits three planar degrees of freedom for each of the sun, ring, carrier and planets. Vibration modes are classified into rotational, translational and planet modes. The natural frequency sensitivities to system parameters are investigated for tuned (cyclically symmetric) planetary gears. Parameters under consideration include support and mesh stiffnesses, component masses, and moments of inertia. Using the well-defined vibration mode properties of tuned planetary gears, the eigen sensitivities are calculated and expressed in simple exact formulae. These formulae connect natural frequency sensitivity with the modal strain or kinetic energy and provide efficient means to determine the sensitivity to all stiffness and inertia parameters by inspection of the modal energy distribution.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

scholarly journals A Vibration-Based Structural Health Monitoring System for Transmission Line Towers

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 515 ◽  
Author(s):  
Long Zhao ◽  
Xinbo Huang ◽  
Ye Zhang ◽  
Yi Tian ◽  
Yu Zhao
Keyword(s):  
Structural Health Monitoring ◽  
Transmission Line ◽  
Natural Frequency ◽  
Health Monitoring ◽  
Structural Changes ◽  
Natural Frequencies ◽  
Transmission Tower ◽  
Health Monitoring System ◽  
Wind Speeds ◽  
Before And After

In this paper, we present a vibration-based transmission tower structural health monitoring system consisting of two parts that identifies structural changes in towers. An accelerometer group realizes vibration response acquisition at different positions and reduces the risk of data loss by data compression technology. A solar cell provides the power supply. An analyser receives the data from the acceleration sensor group and calculates the transmission tower natural frequencies, and the change in the structure is determined based on natural frequencies. Then, the data are sent to the monitoring center. Furthermore, analysis of the vibration signal and the calculation method of natural frequencies are proposed. The response and natural frequencies of vibration at different wind speeds are analysed by time-domain signal, power spectral density (PSD), root mean square (RMS) and short-time Fouier transform (STFT). The natural frequency identification of the overall structure by the stochastic subspace identification (SSI) method reveals that the number of natural frequencies that can be calculated at different wind speeds is different, but the 2nd, 3rd and 4th natural frequencies can be excited. Finally, the system was tested on a 110 kV experimental transmission line. After 18 h of experimentation, the natural frequency of the overall structure of the transmission tower was determined before and after the tower leg was lifted. The results show that before and after the tower leg is lifted, the natural frequencies of each order exhibit obvious changes, and the differences in the average values can be used as the basis for judging the structural changes of the tower.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

Modeling of nonlinear torsional vibration of the automotive powertrain

2016 ◽  
Vol 24 (9) ◽  
pp. 1774-1786 ◽  
Author(s):  
Sérgio J Idehara ◽  
Fernando L Flach ◽  
Douglas Lemes
Keyword(s):  
Natural Frequency ◽  
Torsional Vibration ◽  
Degrees Of Freedom ◽  
Front Wheel ◽  
Torsional Stiffness ◽  
Bench Test ◽  
Passenger Car ◽  
Engine Torque ◽  
Friction Moment ◽  
Wheel Drive

A vibration model of the powertrain can be used to predict its dynamic behavior when excited by fluctuations in the engine torque and speed. The torsional vibration resulting from torque and speed fluctuations increases the rattle noise in the gearbox and it should be controlled or minimized in order to gain acceptance by clients and manufactures. The fact that the proprieties of the torsional damper integrated into the clutch disc alter the dynamic characteristic of the system is important in the automotive industry for design purposes. In this study, bench test results for the characteristics of a torsional damper for a clutch system (torsional stiffness and friction moment) and powertrain torsional vibration measurements taken in a passenger car were used to verify and calibrate the model. The adjusted model estimates the driveline natural frequency and the time response vibration. The analysis uses order tracking signal processing to isolate the response from the engine excitation (second-order). It is shown that a decrease in the stiffness of the clutch disc torsional damper lowers the natural frequency and an increase in the friction moment reduces the peak amplitude of the gearbox torsional vibration. The formulation and model adjustment showed that a nonlinear model with three degrees of freedom can represent satisfactorily the powertrain dynamics of a front-wheel drive passenger car.

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