Numerical investigation of the stability of forced nonlinear vibrations of a shallow cylindrical shell

1989 ◽  
Vol 21 (4) ◽  
pp. 507-511
Author(s):  
G. V. Isakhanov ◽  
E. S. Dekhtyaryuk ◽  
E. D. Lumel'skii
Keyword(s):  
Cylindrical Shell ◽  
Numerical Investigation ◽  
Nonlinear Vibrations ◽  
Shallow Cylindrical Shell ◽  
The Stability

Strongly Nonlinear Vibrations of a Hyperelastic Thin-walled Cylindrical Shell Based on the Modified Lindstedt–Poincaré Method

2019 ◽  
Vol 19 (12) ◽  
pp. 1950160 ◽  
Author(s):  
Jing Zhang ◽  
Jie Xu ◽  
Xuegang Yuan ◽  
Wenzheng Zhang ◽  
Datian Niu
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear System ◽  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Harmonic Excitation ◽  
System Of Differential Equations ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Hardening Behavior ◽  
Thin Walled

Some significant behaviors on strongly nonlinear vibrations are examined for a thin-walled cylindrical shell composed of the classical incompressible Mooney–Rivlin material and subjected to a single radial harmonic excitation at the inner surface. First, with the aid of Donnell’s nonlinear shallow-shell theory, Lagrange’s equations and the assumption of small strains, a nonlinear system of differential equations for the large deflection vibration of a thin-walled shell is obtained. Second, based on the condensation method, the nonlinear system of differential equations is reduced to a strongly nonlinear Duffing equation with a large parameter. Finally, by the appropriate parameter transformation and modified Lindstedt–Poincar[Formula: see text] method, the response curves for the amplitude-frequency and phase-frequency relations are presented. Numerical results demonstrate that the geometrically nonlinear characteristic of the shell undergoing large vibrations shows a hardening behavior, while the nonlinearity of the hyperelastic material should weak the hardening behavior to some extent.

Numerical Investigation of the Solidity Effect on Linear Compressor Cascades

2014 ◽  
Author(s):  
J. Sans ◽  
M. Resmini ◽  
J.-F. Brouckaert ◽  
S. Hiernaux
Keyword(s):  
Numerical Investigation ◽  
State Of The Art ◽  
Leading Edge ◽  
Operating Conditions ◽  
Compressor Cascade ◽  
Minimum Loss ◽  
Low Speed ◽  
High Mach ◽  
The Stability ◽  
The Impact

Solidity in compressors is defined as the ratio of the aerodynamic chord over the peripheral distance between two adjacent blades, the pitch. This parameter is simply the inverse of the pitch-to-chord ratio generally used in turbines. Solidity must be selected at the earliest design phase, i.e. at the level of the meridional design and represents a crucial step in the whole design process. Most of the existing studies on this topic rely on low-speed compressor cascade correlations from Carter or Lieblein. The aim of this work is to update those correlations for state-of-the-art controlled diffusion blades, and extend their application to high Mach number flow regimes more typical of modern compressors. Another objective is also to improve the physical understanding of the solidity effect on compressor performance and stability. A numerical investigation has been performed using the commercial software FINE/Turbo. Two different blade profiles were selected and investigated in the compressible flow regime as an extension to the low-speed data on which the correlations are based. The first cascade uses a standard double circular arc profile, extensively referenced in the literature, while the second configuration uses a state-of-the-art CDB, representative of low pressure compressor stator mid-span profile. Both profiles have been designed with the same inlet and outlet metal angles and the same maximum thickness but the camber and thickness distributions, the stagger angle and the leading edge geometry of the CDB have been optimized. The determination of minimum loss, optimum incidence and deviation is addressed and compared with existing correlations for both configurations and various Mach numbers that have been selected in order to match typical booster stall and choke operating conditions. The emphasis is set on the minimum loss performance at mid-span. The impact of the solidity on the operating range and the stability of the cascade are also studied.

scholarly journals NONLINEAR VIBRATIONS OF A CURRENT-CARRYING ANISOTROPIC CYLINDRICAL SHELL IN A MAGNETIC FIELD.

2020 ◽  
Vol 81 (01) ◽  
pp. 205-211
Author(s):  
Ravshan Indiaminov ◽  
◽  
Sobir Mamaraupovich Kholjigitov ◽  
Akram Sidikovich Narkulov ◽  
◽  
...  
Keyword(s):  
Magnetic Field ◽  
Cylindrical Shell ◽  
Nonlinear Vibrations ◽  
A Current ◽  
Anisotropic Cylindrical Shell
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