A limit law for the ground state of Hill's equation

1994 ◽  
Vol 74 (5-6) ◽  
pp. 1227-1232 ◽  
Author(s):  
H. P. McKean
Keyword(s):  
Ground State ◽  
Hill’S Equation ◽  
Hill's Equation

scholarly journals On the shape of the ground state eigenvalue density of a random Hill's equation

2006 ◽  
Vol 59 (7) ◽  
pp. 935-976 ◽  
Author(s):  
Santiago Cambronero ◽  
Brian Rider ◽  
José Ramírez
Keyword(s):  
Ground State ◽  
Hill’S Equation ◽  
Eigenvalue Density ◽  
Hill's Equation

Erratum: On the shape of the ground state eigenvalue density of a random Hill's equation

2006 ◽  
Vol 59 (9) ◽  
pp. 1377-1377
Author(s):  
Santiago Cambronero ◽  
Brian Rider ◽  
José Ramírez
Keyword(s):  
Ground State ◽  
Hill’S Equation ◽  
Eigenvalue Density ◽  
Hill's Equation

On the solution of Hill's equation using Milne's method

1991 ◽  
Vol 24 (9) ◽  
pp. 2069-2081 ◽  
Author(s):  
J A Nunez ◽  
F Bensch ◽  
H J Korsch
Keyword(s):  
Hill’S Equation ◽  
Hill's Equation

Vibration and Stability of an Elastic Beam Subjected to a Periodic Axial Load With Time-Dependent Displacement Excitation at Both Ends

1991 ◽  
Author(s):  
Xiao-Feng Wu ◽  
Adnan Akay
Keyword(s):  
Axial Load ◽  
Perturbation Technique ◽  
Harmonic Balance Method ◽  
Elastic Beam ◽  
Time Dependent ◽  
Transverse Load ◽  
Order Partial Differential Equation ◽  
Weighted Residual Method ◽  
Hill’S Equation ◽  
Hill's Equation

Abstract This paper concerns the transverse vibrations and stabilities of an elastic beam simultaneously subjected to a periodic axial load, a distributed transverse load, and time-dependent displacement excitations at both ends. The equation of motion derived from Bernoulli-Euler beam theory is a fourth-order partial differential equation with periodic coefficients. To obtain approximate solutions, the method of assumed-modes is used. The unknown time-dependent function in the assumed-modes method is determined by a generalized inhomogeneous Hill’s equation. The instability regions possessed by this generalized Hill’s equation are obtained by both the perturbation technique up to the second order and the harmonic balance method. The dynamic response and the corresponding spectrum of the transversely oscillating elastic beam are calculated by the weighted-residual method.

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