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

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

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

scholarly journals Steady-state stability and bifurcations of friction oscillators due to velocity-dependent friction characteristics

2007 ◽  
Vol 221 (3) ◽  
pp. 401-412 ◽  
Author(s):  
H Hetzler ◽  
D Schwarzer ◽  
W Seemann
Keyword(s):  
Steady State ◽  
Basin Of Attraction ◽  
Analytical Investigation ◽  
Friction Characteristic ◽  
Friction Characteristics ◽  
Friction Oscillator ◽  
Stability And Bifurcations ◽  
Bifurcation Behaviour ◽  
Steady State Stability ◽  
Friction Oscillators

This article presents an analytical investigation on stability and bifurcation behaviour due to an exponential and a generalized friction characteristics in the sliding domain of a simple friction oscillator, which is commonly referred to as ‘mass-on-a-belt’ oscillator. The friction is described by a friction coefficient which depends on the relative velocity between the two tribological partners. The standard way of examining the steady-state only gives very rough insight in the behaviour and is not able to provide further informations about the steady-state's basin of attraction or about limit-cycles. It is found that the system may undergo bifurcations of Hopf type. Hereby, the character of the bifurcations strongly depends on the parameters of the friction characteristic.

On an Non-Ideal Global and Local Energy Transfer, Using an Electro-Magneto and Magneto-Rheological Dampers

2009 ◽  
Author(s):  
Jose´ Manoel Balthazar ◽  
Jorge L. F. Palacios
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Nonlinear Vibrations ◽  
Resonance Condition ◽  
Mr Damper ◽  
Local Energy ◽  
Sommerfeld Effect ◽  
Large Amplitude Vibrations ◽  
Magneto Rheological ◽  
Global And Local

In this paper, we investigated the nonlinear vibrations of a Non-ideal (NIS) electromechanical absorber (NEVA), taking into account a modified mathematical model of (MR) Damper. We observed the presence of the Sommerfeld effect (it is the steady state frequencies of the DC motor, which it will usually increasing as more power (Voltage) is given to it, in a step-by-step fashion. When a resonance condition it is reached, the better part of this energy it is consumed to generate large amplitude vibrations of the foundation, without sensible change of the motor frequency). The obtained results, by using numerical and analytical simulations, were discussed, in details.

scholarly journals 3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions

2022 ◽  
Vol 12 (1) ◽  
pp. 512
Author(s):  
Salvatore Brischetto ◽  
Roberto Torre
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Stress Analysis ◽  
Numerical Models ◽  
Functionally Graded ◽  
Analytical Models ◽  
Direct Result ◽  
Equilibrium Equations ◽  
Plates And Shells ◽  
Moisture Conditions

This paper presents the steady-state stress analysis of single-layered and multilayered plates and shells embedding Functionally Graded Material (FGM) layers under moisture conditions. This solution relies on an exact layer-wise approach; the formulation is unique despite the geometry. It studies spherical and cylindrical shells, cylinders, and plates in an orthogonal mixed curvilinear coordinate system (α, β, z). The moisture conditions are defined at the external surfaces and evaluated in the thickness direction under steady-state conditions following three procedures. This solution handles the 3D Fick diffusion equation, the 1D Fick diffusion equation, and the a priori assumed linear profile. The paper discusses their assumptions and the different results they deliver. Once defined, the moisture content acts as an external load; this leads to a system of three non-homogeneous second-order differential equilibrium equations. The 3D problem is reduced to a system of partial differential equations in the thickness coordinate, solved via the exponential matrix method. It returns the displacements and their z-derivatives as a direct result. The paper validates the model by comparing the results with 3D analytical models proposed in the literature and numerical models. Then, new results are presented for one-layered and multilayered FGM plates, cylinders, and cylindrical and spherical shells, considering different moisture contents, thickness ratios, and material laws.

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