Nonlinear oscillations of cracked large-amplitude vibrating plates subjected to harmonic loads

2021 ◽  
Author(s):  
Dayang Li ◽  
Maosen Cao ◽  
Emil Manoach ◽  
Minvydas Ragulskis
Keyword(s):  
Large Amplitude ◽  
Nonlinear Oscillations ◽  
Vibrating Plates

Nonlinear oscillations of viscous liquid drops

1992 ◽  
Vol 241 ◽  
pp. 169-198 ◽  
Author(s):  
Osman A. Basaran
Keyword(s):  
Viscous Liquid ◽  
Large Amplitude ◽  
Liquid Drop ◽  
Nonlinear Oscillations ◽  
Resonant Mode ◽  
Drop Deformation ◽  
Algebraic Equations ◽  
Initial Amplitude ◽  
Viscous Drops ◽  
Initial Drop

A fundamental understanding of nonlinear oscillations of a viscous liquid drop is needed in diverse areas of science and technology. In this paper, the moderate- to large-amplitude axisymmetric oscillations of a viscous liquid drop, which is immersed in dynamically inactive surroundings, are analysed by solving the free boundary problem comprised of the Navier–Stokes system and appropriate interfacial conditions at the drop–ambient fluid interface. The means are the Galerkin/finite-element technique, an implicit predictor-corrector method, and Newton's method for solving the resulting system of nonlinear algebraic equations. Attention is focused here on oscillations of drops that are released from an initial static deformation. Two dimensionless groups govern such nonlinear oscillations: a Reynolds number, Re, and some measure of the initial drop deformation. Accuracy is attested by demonstrating that (i) the drop volume remains virtually constant, (ii) dynamic response to small-and moderate-amplitude disturbances agrees with linear and perturbation theories, and (iii) large-amplitude oscillations compare well with the few published predictions made with the marker-and-cell method and experiments. The new results show that viscous drops that are released from an initially two-lobed configuration spend less time in prolate form than inviscid drops, in agreement with experiments. Moreover, the frequency of oscillation of viscous drops released from such initially two-lobed configurations decreases with the square of the initial amplitude of deformation as Re gets large for moderate-amplitude oscillations, but the change becomes less dramatic as Re falls and/or the initial amplitude of deformation rises. The rate at which these oscillations are damped during the first period rises as initial drop deformation increases; thereafter the damping rate is lower but remains virtually time-independent regardless of Re or the initial amplitude of deformation. The new results also show that finite viscosity has a much bigger effect on mode coupling phenomena and, in particular, on resonant mode interactions than might be anticipated based on results of computations incorporating only an infinitesimal amount of viscosity.

Large Amplitude Vibrations of Clamped Circular Plate of Variable Thickness

1984 ◽  
Vol 51 (1) ◽  
pp. 207-210 ◽  
Author(s):  
S. K. Chaudhuri
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Large Amplitude ◽  
Nonlinear Oscillations ◽  
Numerical Results ◽  
Varying Thickness ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Plate Of Variable Thickness ◽  
Large Amplitude Vibrations

In this paper nonlinear oscillations of a clamped circular plate of linearly varying thickness have been investigated using von Karman equations expressed in terms of displacement components. Numerical results obtained have been compared and discussed.

Modal interactions and energy transfers in large-amplitude vibrations of functionally graded microcantilevers

2017 ◽  
Vol 24 (17) ◽  
pp. 3882-3893 ◽  
Author(s):  
Hamed Farokhi ◽  
Mergen H Ghayesh ◽  
Alireza Gholipour ◽  
Shahid Hussain
Keyword(s):  
Large Amplitude ◽  
Nonlinear Oscillations ◽  
Couple Stress Theory ◽  
Continuation Method ◽  
Continuous Model ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Modal Interactions ◽  
Energy Transfers ◽  
Highly Nonlinear

Modal interactions and internal energy transfers are investigated in the large-amplitude oscillations of a functionally graded microcantilever with an intermediate spring-support. Based on the Mori–Tanaka homogenization technique and the modified couple stress theory, the energy terms of the functionally graded microsystem (kinetic and size-dependent potential energies) are developed and dynamically balanced. Large-amplitude deformations, due to having one end free, are modeled taking into account curvature-related nonlinearities and assuming an inextensibility condition. The continuous model of the functionally graded microsystem is reduced, by means of the Galerkin method, yielding an inertial- and stiffness-wise nonlinear model. Numerical simulations on this highly nonlinear reduced-order model of the functionally graded microcantilever are performed using a continuation method; a possible case of modal interactions is determined by obtaining the natural frequencies of the microsystem. The nonlinear oscillations of the microcantilever are examined, and it is shown how the energy fed to the functionally graded microsystem (from the base excitation) is transferred between different modes of oscillation.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

Information and estimation in image processing

1987 ◽  
Vol 45 ◽  
pp. 14-17
Author(s):  
B. Roy Frieden
Keyword(s):  
Image Processing ◽  
Optical System ◽  
Large Amplitude ◽  
Communication Theory ◽  
Image Data ◽  
Direct Approach ◽  
Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

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