A Stability Criterion for Hill's Equation

1962 ◽  
Vol 13 (4) ◽  
pp. 601
Author(s):  
Harry Hochstadt
Keyword(s):  
Stability Criterion ◽  
Hill’S Equation ◽  
Hill's Equation

scholarly journals Variations on Lyapunov's stability criterion and periodic prey-predator systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Rafael Ortega
Keyword(s):  
Linear Systems ◽  
Stability Criterion ◽  
Two Dimensional ◽  
Mechanical Vibrations ◽  
Hill’S Equation ◽  
Classical Stability ◽  
Hill's Equation

<p style='text-indent:20px;'>A classical stability criterion for Hill's equation is extended to more general families of periodic two-dimensional linear systems. The results are motivated by the study of mechanical vibrations with friction and periodic prey-predator systems.</p>

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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