Methods of numerical investigation of nonlinear vibrations of flexible plates and shells

1985 ◽  
Vol 17 (11) ◽  
pp. 1570-1575
Author(s):  
G. V. Isakhanov ◽  
E. S. Dekhtyaryuk ◽  
E. D. Lumel'skii
Keyword(s):  
Numerical Investigation ◽  
Nonlinear Vibrations ◽  
Flexible Plates ◽  
Plates And Shells

Turbulent Phenomena in Flexible Plates and Shells

2014 ◽  
pp. 49-76
Author(s):  
J. Awrejcewicz ◽  
A. V. Krysko ◽  
V. A. Krysko ◽  
E. Yu. Krylova ◽  
S. A. Mitskievich ◽  
...  
Keyword(s):  
Flexible Plates ◽  
Plates And Shells

Stability and bifurcations of the steady-state modes in nonlinear vibrations of plates and shells

1989 ◽  
Vol 21 (12) ◽  
pp. 1740-1747 ◽  
Author(s):  
G. V. Isakhanov ◽  
E. S. Dekhtyaryuk ◽  
V. B. Kovtunov ◽  
E. D. Lumel'skii
Keyword(s):  
Steady State ◽  
Nonlinear Vibrations ◽  
Plates And Shells ◽  
Stability And Bifurcations

Analysis of almost equally strong flexible plates and shells

1978 ◽  
Vol 14 (10) ◽  
pp. 1048-1052
Author(s):  
M. A. Aleksandrov ◽  
M. S. Kornishin ◽  
N. N. Stolyarov
Keyword(s):  
Flexible Plates ◽  
Plates And Shells

Application of Variational Equation of Motion to the Nonlinear Vibration Analysis of Homogeneous and Layered Plates and Shells

1963 ◽  
Vol 30 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Nonlinear Vibration ◽  
Nonlinear Vibrations ◽  
Variational Equation ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Free Vibrations ◽  
Layered Plates ◽  
Variational Approximations ◽  
Elastic Systems ◽  
Plates And Shells

An integrated procedure is presented for applying the variational equation of motion to the approximate analysis of nonlinear vibrations of homogeneous and layered plates and shells involving large deflections. The procedure consists of a sequence of variational approximations. The first of these involves an approximation in the thickness direction and yields a system of equations of motion and boundary conditions for the plate or shell. Subsequent variational approximations with respect to the remaining space coordinates and time, wherever needed, lead to a solution to the nonlinear vibration problem. The procedure is illustrated by a study of the nonlinear free vibrations of homogeneous and sandwich cylindrical shells, and it appears to be applicable to still many other homogeneous and composite elastic systems.

Numerical study of nonlinear vibrations of plates and shells with two-frequency excitation

1991 ◽  
Vol 27 (8) ◽  
pp. 793-798
Author(s):  
V. A. Bazhenov ◽  
E. S. Dekhtyaryuk ◽  
Yu. S. Petrina ◽  
K. O. �neremadu
Keyword(s):  
Nonlinear Vibrations ◽  
Numerical Study ◽  
Plates And Shells ◽  
Frequency Excitation

Asymptotic solution of the Cauchy problem for the first-order equation with perturbed Fredholm operator

2020 ◽  
pp. 48-56
Author(s):  
Vladimir I. Uskov
Keyword(s):  
Cauchy Problem ◽  
Small Parameter ◽  
Fredholm Operator ◽  
Gas Flow ◽  
First Order ◽  
Flexible Plates ◽  
The Cauchy Problem ◽  
Plates And Shells ◽  
Step Transition ◽  
The Right

We consider the Cauchy problem for a first-order differentialequation in a Banach space. The equation contains a small parameter in the highest derivative and a Fredholm operator perturbed by an operator addition on the right-hand side. Systems with small parameter in the highest derivative describe the motion of a viscous flow, the behavior of thin and flexible plates and shells, the process of a supersonic viscous gas flow around a blunt body, etc. The presence of a boundary layer phenomenon is revealed; in this case, even a small additive has a strong influence on the behavior of the solution. Asymptotic expansion of the solution in powers of small parameter is constructed by means of the Vasil’yeva- Vishik-Lyusternik method. Asymptotic property of the expansion is proved. To construct the regular part of the expansion, the equation decomposition method is used. It is consisted in a step-by-step transition to similar problems of decreasing dimensions.

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