On the Nonlinear Dynamics of a Vibro-Impacting Cantilever With End Mass

2012 ◽  
Author(s):  
Prasanna Gandhi ◽  
Ajinkya Badkas
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Analysis ◽  
Frequency Response ◽  
Experimental Results ◽  
Response Curves ◽  
Close Match ◽  
Nonlinear Hysteresis ◽  
Fixed End ◽  
Stop Position ◽  
Harmonic Displacement

A theoretical and experimental dynamic analysis of a vibro-impacting cantilever with end mass is presented in this paper. The cantilever is excited by transverse harmonic displacement given at its fixed end with the help of a shaker. Nonlinearity in dynamics due to impact of cantilever on a motion limiting stop only on one side is considered. Experiments revealed quite interesting nonlinear hysteresis, jump, and drop phenomena in this case. Phenomena are experimentally characterized by varying the position and the gap between the stop and cantilever on a custom-built setup. Vibrating cantilever is modeled using assumed modes method while spring damper model for impacting stop is considered. Simulation and experimental results show close match for the same parameters under various cases of stop position and gap. Results are presented in terms of frequency response curves for range of parameters in non-dimensional form to enable their use in similar other cases.

scholarly journals Nonlinear Dynamics of a Planar Hinged-Supported Beam with One End Lumped Mass and Longitudinal Elastic Support

2018 ◽  
Vol 241 ◽  
pp. 01016 ◽  
Author(s):  
Lukasz Kloda ◽  
Stefano Lenci ◽  
Jerzy Warminski
Keyword(s):  
Nonlinear Dynamics ◽  
Finite Element Method ◽  
Frequency Response ◽  
Spring Stiffness ◽  
Lumped Mass ◽  
Response Curves ◽  
Simply Supported ◽  
Softening Behaviour ◽  
Damped Oscillations ◽  
Linear Spring

Nonlinear forced-damped oscillations of a non-slender hinged simply supported beam with mass and spring attached to one end are investigated by mean of a finite element method. The frequency response curves are constructed numerically and the variability of hardening/softening behaviour of frequency response curves due to the lumped mass and axial linear spring stiffness is investigated. Resonant and sub resonant motion of beam midpoint as well as jumps between solution branches are highlighted.

Self-Locking Satellite Boom With Flexure-Mode Joints

1997 ◽  
Vol 50 (11S) ◽  
pp. S225-S231 ◽  
Author(s):  
W. Szyszkowski ◽  
K. Fielden ◽  
D. W. Johnson
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Large Deflection ◽  
Cylindrical Shells ◽  
Experimental Results ◽  
Large Deflections ◽  
Large Rotations

Dynamic analysis, numerical simulation, and experimental results of the deployment of a self-locking lightweight satellite boom are presented. The joints that connect the two segments of the boom are made of flexible semi-cylindrical shells. During the deployment, the shells undergo large deflections and large rotations, up to π radians. The boom is to be launched in the folded configuration and then deployed from a rotating satellite. In the straight configuration, after locking the joints, the boom should be stiff enough to precisely position a heavy sensor in a required location. Several models of the boom are considered for analysis. In order to optimize the sensor trajectory and the locking sequence, a model that includes stiffness of the joints but neglects flexibility of the links is developed. The joints, which are prone to instabilities and snap-through behavior, are analyzed using large deflection quasistatic approach. Finally, nonlinear dynamics FEA is performed to simulate the deployment of the complete boom. The simulation is compared with experimental results obtained from the preliminary tests.

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

Study of plate vibrating in fluids having part-through crack at random angles and locations

2021 ◽  
pp. 095440622110127
Author(s):  
Ruqia Ikram ◽  
Asif Israr
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Peak Amplitude ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Crack Location ◽  
Cracked Plate ◽  
Nonlinear Frequency Response ◽  
Angle Crack ◽  
Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

Vibration Characteristics of Rotating Thin Disks—Part I: Experimental Results

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Linear Theory ◽  
Lateral Force ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Rotating Disks ◽  
Critical Speeds ◽  
Applied Forces ◽  
Thin Disks

Analysis of the linear vibration characteristics of unconstrained rotating isotropic thin disks leads to the important concept of “critical speeds.” These critical rotational speeds are of interest because they correspond to the situation where a natural frequency of the rotating disk, as measured by a stationary observer, is zero. Such speeds correspond physically to the speeds at which a traveling circumferential wave, of shape corresponding to the mode shape of the natural frequency being considered, travel around the disk in the absence of applied forces. At such speeds, according to linear theory, the blade may respond as a space fixed stationary wave and an applied space fixed dc force may induce a resonant condition in the disk response. Thus, in general, linear theory predicts that for rotating disks, with low levels of damping, large responses may be encountered in the region of the critical speeds due to the application of constant space fixed forces. However, large response invalidates the predictions of linear theory which has neglected the nonlinear stiffness produced by the effect of in-plane forces induced by large displacements. In the present paper, experimental studies were conducted in order to measure the frequency response characteristics of rotating disks both in an idling mode as well as when subjected to a space fixed lateral force. The applied lateral force (produced by an air jet) was such as to produce displacements large enough that non linear geometric effects were important in determining the disk frequencies. Experiments were conducted on thin annular disks of different thickness with the inner radius clamped to the driving arbor and the outer radius free. The results of these experiments are presented with an emphasis on recording the effects of geometric nonlinearities on lateral frequency response. In a companion paper (Khorasany and Hutton, 2010, “Vibration Characteristics of Rotating Thin Disks—Part II: Analytical Predictions,” ASME J. Mech., 79(4), p. 041007), analytical predictions of such disk behavior are presented and compared with the experimental results obtained in this study. The experimental results show that in the case where significant disk displacements are induced by a lateral force, the frequency characteristics are significantly influenced by the magnitude of forced displacements.

Dynamic Analysis of Planetary Gear Reducer

2018 ◽  
Vol 880 ◽  
pp. 87-92
Author(s):  
Daniela Vintilă ◽  
Laura Diana Grigorie ◽  
Alina Elena Romanescu
Keyword(s):  
Finite Elements ◽  
Differential Equations ◽  
Dynamic Analysis ◽  
Frequency Response ◽  
Planetary Gear ◽  
Resonance Phenomenon ◽  
Superposition Method ◽  
Planetary Gears ◽  
Tower Crane ◽  
Systems Of Differential Equations

This paper presents dynamic analysis of a three stage planetary gear reducer for operate a tower crane. Ordinary and planetary gears have been designed respecting the coaxial, neighboring and mounting conditions. Harmonic analysis has been processed to identify frequency response for displacements, strains and deformations. The aim of the study was to determine critical frequencies to avoid mechanical resonance phenomenon. The obtained results are based on the superposition method for solving the systems of differential equations resulting from the analysis with finite elements.

Magnification curves of electromagnetic seismographs

1964 ◽  
Vol 54 (5A) ◽  
pp. 1459-1471
Author(s):  
S. K. Chakrabarty ◽  
G. C. Choudhury ◽  
S. N. Roy Choudhury
Keyword(s):  
General Solution ◽  
Frequency Response ◽  
Experimental Method ◽  
Phase Shifts ◽  
Response Curves ◽  
Operating Condition ◽  
Coil Inductance ◽  
The World ◽  
Electromagnetic Seismograph ◽  
Proper Design

Abstract The general solution of the equations connecting the motion of the two coupled components in an electromagnetic seismograph has been obtained in another paper and it shows that the magnification of a seismograph depend on seven instrumental constants. Using these results, equations and curves have been derived in the present paper from which the Magnification as well as Phase shifts in the response of a seismograph and their variations with damping and coil inductance can be easily obtained. Based on these curves a number of magnification curves for different combinations, which are in operation at the different seismological stations of the world, have been derived. Suitable equations and curves have also been obtained which can be used for estimating the absolute Magnification of a Seismograph. An experimental method of obtaining the frequency response curves of seismographs in their operating condition has been described and the results obtained by this method has been given. It has been indicated how the results incorporated in the present paper can be used in the proper design of seismographs required for the different purposes.

Dynamic Analysis of a Floating Offshore Wind Turbine Under Extreme Environmental Conditions

2012 ◽  
Author(s):  
Tomoaki Utsunomiya ◽  
Shigeo Yoshida ◽  
Hiroshi Ookubo ◽  
Iku Sato ◽  
Shigesuke Ishida
Keyword(s):  
Dynamic Analysis ◽  
Wind Turbine ◽  
Environmental Conditions ◽  
Aerodynamic Force ◽  
Experimental Results ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Analysis Tool ◽  
Simulation Code ◽  
Floating Offshore Wind Turbine

This paper is concerned with the development of a Floating Offshore Wind Turbine (FOWT) utilizing spar-type floating foundation. In order to design such a structure, it is essential to evaluate the dynamic response under extreme environmental conditions. In this study, therefore, a dynamic analysis tool has been developed. The dynamic analysis tool consists of a multi-body dynamics solver (MSC.Adams), aerodynamic force evaluation library (NREL/AeroDyn), hydrodynamic force evaluation library (In-house program named SparDyn), and mooring force evaluation library (In-house program named Moorsys). In this paper, some details of the developed dynamic analysis tool are given. In order to validate the program, comparison with the experimental results, where the wind, current and wave are applied simultaneously, has been made. The comparison shows that satisfactory agreements between the simulation and the experimental results are obtained. However, when VIM (Vortex Induced Motion) occurs, the current loads and cross flow responses (sway and roll) are underestimated by the simulation since the simulation code does not account for the effect of VIM.

A transient technique for seismograph calibration

1962 ◽  
Vol 52 (4) ◽  
pp. 767-779
Author(s):  
A. F. Espinosa ◽  
G. H. Sutton ◽  
H. J. Miller
Keyword(s):  
Fourier Transform ◽  
Steady State ◽  
Input Pulse ◽  
Electrical Signal ◽  
Experimental Results ◽  
Response Curves ◽  
Amplitude Response ◽  
Transient Technique ◽  
Absolute Amplitude ◽  
The Fourier Transform

abstract A transient technique for seismograph calibration was developed and tested by a variety of methods. In the application of this technique a known transient in the form of an electrical signal is injected, through (a) a Willmore-type calibration bridge or (b) an independent coil, into the seismometer and the corresponding output transient of the system is recorded. The ratio of the Fourier transform of this transient to that of the input pulse yields phase and relative amplitude response of the seismograph as a function of period. Absolute amplitude response may be calculated if two easily determined constants of the seismometer are known. This technique makes practical the daily calibration of continuously-recording seismographs without disturbing the instruments more than a very few minutes. The transient technique was tested and proven satisfactory with results of more conventional steady-state methods, using both digital and analog analyses of the output transients. A variety of output transients corresponding to various theoretical response curves has been calculated for two standard input transients. By comparison of the calculated output transients with experimental results it is possible to obtain the response of the instrument with considerable precision quickly and without computation.

Nonlinear Dynamics of a Dielectric Elastomer Membrane Under Compressive Loading

2020 ◽  
Author(s):  
Robert L. Lowe ◽  
Christopher G. Cooley
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Frequency Response ◽  
Compressive Loading ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Dielectric Elastomer ◽  
Large Strains ◽  
Membrane Stretch ◽  
Wide Range

Abstract This paper investigates the nonlinear dynamics of square dielectric elastomer membranes under time-dependent, through-thickness compressive loading. The dielectric elastomer is modeled as an isotropic ideal dielectric, with mechanical stiffening at large strains captured using the Gent hyperelastic constitutive model. The equation of motion for the in-plane membrane stretch is derived using Hamilton’s principle. The static response of the membrane is first investigated, with equilibrium stretches calculated numerically for a wide range of compressive pre-loads and applied voltages. Snap-through instabilities are observed, with the critical snap-through voltage decreasing with increasing compressive pre-load. The dynamic response of the membrane is then investigated under forced harmonic excitation. Frequency response plots characterizing the steady-state vibration reveal primary, subharmonic, and superharmonic resonances. Near these resonances, two stable vibration states are possible, corresponding to upper and lower branches in the frequency response. Significant and practically meaningful differences in the dynamic response are observed when the system vibrates at a fixed frequency about the upper and lower branches, a feature not discussed in previous research.

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