Bending Frequency of a Rotating Beam With an Elastically Restrained Root

1991 ◽  
Vol 58 (1) ◽  
pp. 209-214 ◽  
Author(s):  
Sen Yung Lee ◽  
Yee Hsiung Kuo
Keyword(s):  
Lower Bounds ◽  
Transfer Matrix Method ◽  
Rotational Speed ◽  
Matrix Method ◽  
Upper And Lower Bounds ◽  
Rotating Beam ◽  
Uniform Beam ◽  
Setting Angle ◽  
Divergence Instability ◽  
Elastically Restrained

Upper and lower bounds of the fundamental bending frequency of a rotating uniform beam with an elastically restrained root are obtained by the Rayleigh’s and minimum principles, respectively. It is shown that the fundamental bending frequency of the rotating uniform beam with rotational flexibility only is always higher than that of the nonrotating beam. If the setting angle is not equal to zero, the fundamental bending frequency of the rotating uniform beam with translational flexibility can be less than that of the nonrotating beam, and the phenomenon of divergence instability (tension buckling due to the centrifugal force) may occur. Finally, the influence of hub radius, setting angle, rotational speed, and elastic root restraints on the fundamental bending frequency of the beam is also investigated numerically by the transfer matrix method.

Effect of Hub Radius on the Vibrations of a Uniform Bar

1956 ◽  
Vol 23 (2) ◽  
pp. 287-290
Author(s):  
W. E. Boyce
Keyword(s):  
Lower Bounds ◽  
Constant Speed ◽  
Upper And Lower Bounds ◽  
Beam Length ◽  
Uniform Beam

Abstract Methods are discussed for obtaining upper and lower bounds on the frequencies of a uniform beam, rotating at a constant speed about an axis at one end, and vibrating transversely to the plane of rotation. Previous results are extended to include the case of a nonzero hub radius. Bounds on the first two frequencies are given for several ratios of hub radius to beam length. These show that the frequencies depend almost linearly on the hub radius for various rotational speeds.

VIBRATIONS OF A ROTOR SYSTEM WITH MULTIPLE COUPLER OFFSETS

2011 ◽  
Vol 35 (1) ◽  
pp. 81-100
Author(s):  
Chao-Yang Tsai ◽  
Shyh-Chin Huang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Rotational Speed ◽  
Matrix Method ◽  
Rotor System ◽  
Response Amplitude ◽  
External Excitation ◽  
Phase Offset ◽  
Major Response ◽  
Before And After

In this paper, a transfer matrix method (TMM) for rotors with multiple coupler offsets was derived. The studies showed the coupler’s stiffness altered the rotor’s critical speeds but offset caused additional external excitation. The cases of two offsets in- and anti-phase in a typical rotor were given as examples. In the in-phase case, significantly increased response amplitude occurred at lower rotational speed and the increase was linearly proportional to the offset value. As to the anti-phase case, the increased response was insignificant, implying an opposite offset would cancel out a major response of the previous offset. The whirling orbits before and after the offset couplers were also illustrated. The results, as expected, showed the in-phase offset displayed much larger radii than the anti-phase’s. The rotor’s orbits changed the whirling direction once the rotation fell within a certain range and this feature seemed to be unaffected by coupler offsets.

scholarly journals Counting Polyominoes on Twisted Cylinders

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Gill Barequet ◽  
Micha Moffie ◽  
Ares Ribó ◽  
Günter Rote
Keyword(s):  
Growth Rate ◽  
Transfer Matrix ◽  
Lower Bounds ◽  
Exponential Growth ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Compact Representation ◽  
Exponential Growth Rate ◽  
Successive Iteration ◽  
International Audience

International audience We improve the lower bounds on Klarner's constant, which describes the exponential growth rate of the number of polyominoes (connected subsets of grid squares) with a given number of squares. We achieve this by analyzing polyominoes on a different surface, a so-called $\textit{twisted cylinder}$ by the transfer matrix method. A bijective representation of the "states'' of partial solutions is crucial for allowing a compact representation of the successive iteration vectors for the transfer matrix method.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

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