Receptance Series for Systems Possessing “Rigid Body” Modes

1962 ◽  
Vol 66 (618) ◽  
pp. 394-397 ◽  
Author(s):  
G. M. L. Gladwell ◽  
R. E. D. Bishop ◽  
D. C. Johnson
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Series Representation ◽  
Forced Vibrations ◽  
Rigid Bodies ◽  
Points Of Interest ◽  
Elastic Systems ◽  
Rigid Body Modes ◽  
Simple Systems

SummaryCertain elastic systems may not only vibrate freely at proper (non-zero) natural frequencies, but may also move as rigid bodies. Such systems have “rigid body” modes which behave like principal modes corresponding to zero natural frequencies. These modes may be disregarded in the series representation of static distortions of such systems but must be taken into account in the representation of forced vibrations.This note is concerned with the series representation of receptances of certain simple systems of this type, namely strings, bars, shafts and beams. These systems were discussed in reference 1, but there the rigid body modes were omitted. As the matter appears to raise some points of interest, a discussion of it seems to be called for. A similar analysis to that presented here may be applied to other unsupported, or partially supported systems, such as an unsupported plate.

In-Plane Inertial Coupling in Tuned and Severely Mistuned Bladed Disks

1982 ◽  
Author(s):  
E. F. Crawley
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Analytic Model ◽  
Angular Rotation ◽  
Structural Coupling ◽  
Nodal Diameter ◽  
Rigid Disk ◽  
Compressor Rotor ◽  
Rigid Body Modes ◽  
Bending Modes

A model has been developed and verified for blade-disk-shaft coupling in rotors due to the in-plane rigid body modes of the disk. An analytic model has been developed which couples the in-plane rigid body modes of the disk on an elastic shaft with the blade bending modes. Bench resonance tests were carried out on the M.I.T. Compressor Rotor, typical of research rotors with flexible blades and a thick rigid disk. When the rotor was carefully tuned, the structural coupling of the blades by the disks was confined to zero and one nodal diameter modes, whose modal frequencies were greater than the blade cantilever frequency. In the case of the tuned rotor, and in two cases where severe mistuning was intentionally introduced, agreement between the predicted and observed natural frequencies is excellent. The analytic model was then extended to include the effects of constant angular rotation of the disk.

In-Plane Inertial Coupling in Tuned and Severely Mistuned Bladed Disks

1983 ◽  
Vol 105 (3) ◽  
pp. 585-590
Author(s):  
E. F. Crawley
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Analytic Model ◽  
Structural Coupling ◽  
Nodal Diameter ◽  
Rigid Disk ◽  
Inertial Coupling ◽  
Compressor Rotor ◽  
Rigid Body Modes ◽  
Bending Modes

A model has been developed and verified for blade-disk-shaft coupling in rotors due to the in-plane rigid body modes of the disk. An analytic model has been derived which couples the in-plane rigid body modes of the disk on an elastic shaft with the blade bending modes. Bench resonance tests were carried out on the MIT Compressor Rotor, typical of research rotors with flexible blades and a thick rigid disk. When the rotor was carefully tuned, the structural coupling of the blades by the disks was confined to zero and one nodal diameter modes, whose modal frequencies were greater than the blade cantilever frequency. In the case of the tuned rotor, and in two cases where severe mistuning was intentionally introduced, agreement between the predicted and observed natural frequencies is excellent.

Non-linearly Forced Vibrations of Elastic Systems Carrying Rigid Bodies

1994 ◽  
Vol 169 (1) ◽  
pp. 71-87
Author(s):  
R. Räty ◽  
J. von Boehm ◽  
M.A. Ranta
Keyword(s):  
Forced Vibrations ◽  
Rigid Bodies ◽  
Elastic Systems

scholarly journals Modelling of speleothems failure in the Hotton cave (Belgium). Is the failure earthquake induced?

2001 ◽  
Vol 80 (3-4) ◽  
pp. 315-321 ◽  
Author(s):  
J.F. Cadorin ◽  
D. Jongmans ◽  
A. Plumier ◽  
T. Camelbeeck ◽  
S. Delaby ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Quantitative Information ◽  
Rigid Bodies ◽  
Tensile Failure ◽  
Future Research ◽  
Geometrical Parameters ◽  
Laboratory Measurements ◽  
Ground Acceleration ◽  
Strong Ground

AbstractTo provide quantitative information on the ground acceleration necessary to break speleothems, laboratory measurements on samples of stalagmite have been performed to study their failure in bending. Due to their high natural frequencies, speleothems can be considered as rigid bodies to seismic strong ground motion. Using this simple hypothesis and the determined mechanical properties (a minimum value of 0.4 MPa for the tensile failure stress has been considered), modelling indicates that horizontal acceleration ranging from 0.3 m/s2 to 100 m/s2 (0.03 to 10g) are necessary to break 35 broken speleothems of the Hotton cave for which the geometrical parameters have been determined. Thus, at the present time, a strong discrepancy exists between the peak accelerations observed during earthquakes and most of the calculated values necessary to break speleothems. One of the future research efforts will be to understand the reasons of the defined behaviour. It appears fundamental to perform measurements on in situ speleothems.

scholarly journals ClusterSLAM: A SLAM backend for simultaneous rigid body clustering and motion estimation

2021 ◽  
Author(s):  
Jiahui Huang ◽  
Sheng Yang ◽  
Zishuo Zhao ◽  
Yu-Kun Lai ◽  
Shi-Min Hu
Keyword(s):  
Motion Estimation ◽  
Rigid Body ◽  
Iterative Scheme ◽  
Dynamic Environments ◽  
Rigid Bodies ◽  
Factor Graph ◽  
Agglomerative Clustering ◽  
Multiple Objects ◽  
Graph Optimization ◽  
Dynamic Objects

AbstractWe present a practical backend for stereo visual SLAM which can simultaneously discover individual rigid bodies and compute their motions in dynamic environments. While recent factor graph based state optimization algorithms have shown their ability to robustly solve SLAM problems by treating dynamic objects as outliers, their dynamic motions are rarely considered. In this paper, we exploit the consensus of 3D motions for landmarks extracted from the same rigid body for clustering, and to identify static and dynamic objects in a unified manner. Specifically, our algorithm builds a noise-aware motion affinity matrix from landmarks, and uses agglomerative clustering to distinguish rigid bodies. Using decoupled factor graph optimization to revise their shapes and trajectories, we obtain an iterative scheme to update both cluster assignments and motion estimation reciprocally. Evaluations on both synthetic scenes and KITTI demonstrate the capability of our approach, and further experiments considering online efficiency also show the effectiveness of our method for simultaneously tracking ego-motion and multiple objects.

Damping of Forced Vibrations in Systems of Connected Rigid Bodies

2003 ◽  
Vol 39 (3) ◽  
pp. 343-349 ◽  
Author(s):  
Aleksandr Mikhailovich Kovalev ◽  
I. A. Bolgrabskaya ◽  
D. A. Chebanov ◽  
V. F. Shcherbak
Keyword(s):  
Forced Vibrations ◽  
Rigid Bodies

The Use of Projective Geometry on the Mechanism System Motion and Stability of the Special Problems in Judgement

2012 ◽  
Vol 482-484 ◽  
pp. 1041-1044
Author(s):  
Xiao Zhuang Song ◽  
Ming Liang Lu ◽  
Tao Qin
Keyword(s):  
Rigid Body ◽  
Projective Geometry ◽  
Euclidean Geometry ◽  
Specific Problem ◽  
Zero Point ◽  
Rigid Bodies ◽  
Parallel Connection ◽  
Fixed Plane ◽  
Instantaneous Center ◽  
Proof Of Principle

In a principle of kinematics, when a rigid body is motion in a plane, and the fixed plane only the presence of a speed zero point -- the instantaneous center of velocity. In the mechanism of two rigid bodies be connected by two parallel connection links, why can the continuous relative translation? Where is the instantaneous center of velocity? ... ... The traditional Euclidean geometry theory can’t explain these phenomenon, must use projective geometry theory to solve. The actual motion of the mechanism is disproof in Euclidean geometry principle limitation. This paper introduces the required in projective geometry basic proof of principle, and applied to a specific problem.

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