Mode localization and veering of natural frequency loci in two circular plates coupled with a fluid

2006 ◽  
Vol 22 (6) ◽  
pp. 719-739 ◽  
Author(s):  
Kyeong-Hoon Jeong
Keyword(s):  
Natural Frequency ◽  
Circular Plates ◽  
Mode Localization

scholarly journals INVESTIGATION OF THE DYNAMIC BEHAVIOUR OF NON-UNIFORM THICKNESS CIRCULAR PLATES RESTING ON WINKLER AND PASTERNAK FOUNDATIONS

2020 ◽  
Vol 60 (2) ◽  
pp. 127-144
Author(s):  
Saheed Salawu ◽  
Gbeminiyi Sobamowo ◽  
Obanishola Sadiq
Keyword(s):  
Natural Frequency ◽  
Circular Plate ◽  
Analytical Solutions ◽  
Dynamic Behaviour ◽  
Circumferential Stress ◽  
Thickness Variation ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Weighted Residuals ◽  
Elastic Foundations

The study of the dynamic behaviour of non-uniform thickness circular plate resting on elastic foundations is very imperative in designing structural systems. This present research investigates the free vibration analysis of varying density and non-uniform thickness isotropic circular plates resting on Winkler and Pasternak foundations. The governing differential equation is analysed using the Galerkin method of weighted residuals. Linear and nonlinear case is considered, the surface radial and circumferential stresses are also determined. Thereafter, the accuracy and consistency of the analytical solutions obtained are ascertained by comparing the existing results available in pieces of literature and confirmed to be in a good harmony. Also, it is observed that very accurate results can be obtained with few computations. Issues relating to the singularity of circular plate governing equations are handled with ease. The analytical solutions obtained are used to determine the influence of elastic foundations, homogeneity and thickness variation on the dynamic behaviour of the circular plate, the effect of vibration on a free surface of the foundation as well as the influence of radial and circumferential stress on mode shapes of the circular plate considered. From the results, it is observed that a maximum of 8.1% percentage difference is obtained with the solutions obtained from other analytical methods. Furthermore, increasing the elastic foundation parameter increases the natural frequency. Extrema modal displacement occurs due to radial and circumferential stress. Natural frequency increases as the thickness of the circular plate increases, Conversely, a decrease in natural frequency is observed as the density varies. It is envisioned that; the present study will contribute to the existing knowledge of the classical theory of vibration.

Study on Modal Change Dual Planetary Composite Transmission System

2014 ◽  
Vol 620 ◽  
pp. 388-394
Author(s):  
Xue Zeng Zhao ◽  
Xi Gui Wang ◽  
Yong Mei Wang
Keyword(s):  
Natural Frequency ◽  
Dynamic Performance ◽  
Transmission System ◽  
Frequency Curve ◽  
Modal System ◽  
Mode Change ◽  
Mode Localization ◽  
Modal Change ◽  
System Mode ◽  
Influence Degree

In the study of the dynamic characteristics of the system, should pay attention to the influence on the dynamic performance of the system mode change. Mode change is closely related with mutation phenomena of mode localization process, in the natural frequency with the change of parameters, with a large curvature are quickly turned to separate the two natural frequency curve in the close position. Mode change will lead to the drastic changes in the natural frequency and modal energy, the variation of system parameters is also the location of the influence degree mutation position. Based on the modal characteristics of unique two stage power branch double wide helical planetary composite transmission system, studied the mode change phenomena, reveal the modal system changes.

Mode Localization in Coupled Circular Plates

1994 ◽  
Vol 116 (3) ◽  
pp. 286-294 ◽  
Author(s):  
C. O. Orgun ◽  
B. H. Tongue
Keyword(s):  
Periodic Structures ◽  
Qualitative Change ◽  
Disk Drive ◽  
Circular Plates ◽  
Mode Localization ◽  
Infinite Dimensional ◽  
Write Heads ◽  
The Individual ◽  
Support Motion ◽  
Computer Disk

When analyzing structures that are comprised of many similar pieces (periodic structures), it is common practice to assume perfect periodicity. Such an assumption will lead to the existence of eigenmodes that are global in character, i.e., the structural deflections will occur throughout the system. However, research in structural mechanics has shown that, when only weak coupling is present between the individual pieces of the system, small amounts of disorder can produce a qualitative change in the character of the eigenmodes. A typical eigenmode of such a system will support motion only over a limited extend of the structure. Often only one or two of the smaller pieces that make up the structure show any motion, the rest remain quiescent. This phenomenon is known as “mode localization”, since the modes become localized at particular locations on the overall structure. This paper will examine the behavior of several circular plates that are coupled together through springs, a system that models a multiple disk computer disk drive. These drives typically consist of several disks mounted on a single spindle, coupled by read/write heads, which act as weak springs, thus leading one to suspect the possibility of localization. Since such an effect would impact accurate read/write operations at small fly heights, the problem deserves attention. Although computer disk drives contain space fixed read/write heads, this paper will consider springs that are fixed to the plates in order to understand the effect of localization on a set of infinite dimensional structures (the circular plates). Later work will extend the model to the case of space fixed springs and the wave behavior and destabilizing effects that such a configuration will induce.

Primary Resonance of MEMS/NEMS Circular Plate Biosensors

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Natural Frequency ◽  
Circular Plate ◽  
Dna Detection ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Van Der Waals Forces ◽  
Electrostatic Actuation ◽  
Circular Plates ◽  
Saddle Node Bifurcation ◽  
Saddle Node

This investigation deals with M/NEMS circular plates under electrostatic actuation. Such structures can be used as resonator sensors for medicine and biology applications such as virus, bacteria or DNA detection. The system consists of a clamped circular plate over a ground. The actuation of the plate is done through an AC voltage whose frequency is near half natural frequency of the plate. This produces a primary resonance to be used afterwards for sensing purposes. It is showed that a saddle-node bifurcation occurs. The effects of damping, voltage, Casimir, and van der Waals forces are predicted.

On Localization in Coupled, Spinning, Circular Plates

1994 ◽  
Vol 116 (4) ◽  
pp. 555-561 ◽  
Author(s):  
C. O. Orgun ◽  
B. H. Tongue
Keyword(s):  
Analytical Model ◽  
Rotation Speed ◽  
Response Mode ◽  
Circular Plates ◽  
Mode Localization ◽  
Central Spindle ◽  
Vibrational Response ◽  
Modal Response ◽  
Weakly Coupled ◽  
All Speeds

The vibrational response of multiple rotating circular plates, stacked together on a central spindle and coupled through stationary springs, is investigated. An analytical model is derived and a Rayleigh-Ritz approach employed in order to obtain the system’s modal response. Mode localization is shown to occur at all speeds of rotation for weakly coupled subcomponents and the degree to which the system exhibits localized behavior is shown to increase with rotation speed.

Natural frequency veering and mode localization caused by straight through–cracks in rectangular plates with elastic boundary conditions

2018 ◽  
Vol 229 (10) ◽  
pp. 4017-4031 ◽  
Author(s):  
Tianming Huang ◽  
Huancai Lu ◽  
D. Michael McFarland ◽  
Wen L. Li ◽  
Chin An Tan ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Rectangular Plates ◽  
Mode Localization ◽  
Elastic Boundary ◽  
Elastic Boundary Conditions

Parametric Resonance of MEMS Circular Plate Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Circular Plate ◽  
Parametric Resonance ◽  
Elastic Plate ◽  
Electrostatic Force ◽  
Circular Plates ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Ground Plate

This paper investigates parametric resonance of electrostatically actuated MEMS circular plates for resonator sensing applications. The system consists of a clamped circular elastic plate over a ground plate. Soft AC voltage of frequency near natural frequency of the plate gives the electrostatic force that leads the elastic plate into vibration, more specifically into parametric resonance which can be used afterwards for biosensing purposes. Frequency response and corresponding bifurcations are reported. The effects of damping and voltage are predicted.

Natural Frequency Veering Patterns of Planetary Gears Under Design Parameter Variation

2000 ◽  
Author(s):  
Jian Lin ◽  
Robert G. Parker
Keyword(s):  
Natural Frequency ◽  
Dynamic Models ◽  
Natural Frequencies ◽  
Turbine Blades ◽  
Planetary Gear ◽  
Design Parameters ◽  
Vibration Modes ◽  
Frequency Spectra ◽  
Strongly Coupled ◽  
Mode Localization

Abstract Noise and vibration reduction is a critical concern in planetary gear applications. During the design process, system parameters are varied to evaluate alternative design choices, avoid resonances, optimize load distribution, and reduce weight. It is important to characterize the effects of parameter variations on the natural frequencies and vibration modes for effective vibration tuning. In planetary gear dynamic models (Figure 1), the key design parameters include the mesh stiffness, support/bearing stiffness, component mass, and moment of inertia. Some plots of natural frequencies versus planetary gear parameters are presented by Cunliffe et al. (1974), Botman (1976), Kahraman (1994), and Saada and Velex (1995). Lin and Parker (1999a) analytically characterized the unique, highly-structured properties of planetary gear natural frequency spectra and vibration modes. They also derived simple, closed-form expressions for the sensitivities of natural frequencies and vibration modes to these parameters (Lin and Parker, 1999b). The natural frequency plots in the above literature show natural frequency veering phenomena where two eigenvalue loci approach each other as a parameter is varied but then abruptly veer away like two similar charges repelling (Figure 2a). The phenomenon has been extensively studied (Leissa, 1974; Perkins and Mote, 1986; Pierre, 1988; Chen and Ginsberg, 1992; Happawana et al., 1998). The vibration modes of the veering eigenvalues are strongly coupled and undergo dramatic changes in the veering neighborhood. Eigenvalue veering is also related to mode localization that can occur when disorder is introduced into nominally symmetric systems like turbine blades, space antennae, multi-span beams and other structures (Pierre, 1988). In the case of especially sharp veering, it is sometimes difficult to distinguish between intersection and veering just by observing eigenvalue plots. Curve veering/crossing complexity obstructs the tracing of eigenvalue loci under parameter changes. Also, when multiple curves veer or intersect close together (Figure 3), strong modal coupling (and associated operating condition response changes) occurs that is not identifiable from frequency loci plots. The objective of this work is to analytically characterize the rules of eigenvalue veering in planetary gear vibration. The special veering patterns derived here help to trace natural frequencies and examine impacts of design parameters on vibration. These veering patterns, combined with the unique modal properties (Lin and Parker, 1999a) and the eigensensitivies analysis (Lin and Parker, 1999b), provide designers considerable insight into planetary gear free vibration.

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