Large amplitude axisymmetric vibration of a circular plate having a circumferential crack

Bose, Tanmoy; Mohanty, A.R.

doi:10.1016/j.ijmecsci.2017.01.015

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…Since the silicon and ZnO layers are thicker than the other layers and are likely to play a significant role in the system’s dynamics, we have considered only these two layers in our model (see Supporting Information Section S4). By assuming large displacement amplitude (that is, incorporating the in-plane forces), imposing the condition of axial symmetry, , and assuming the initial static displacement in the system, we obtain the following equation of motion for PMUT: .25ex2ex D a 0 4 ∇ 4 w 0 ( r ) + D a 0 4 ∇ 4 w 1 ( r ) + c ∂ ∂ t w 1 ( r , t ) + ρ s ∂ 2 ∂ t 2 w 1 ( r , t ) − N a 0 4 ( ∫ 0 a 0 r true( true( ∂ w 1 ( r , t ) ∂ r true) 2 + 2 ∂ w 0 ( r ) ∂ r ∂ w 1 ( r ) ∂ r true) …”

Section: Resultsmentioning

confidence: 99%

Mixed Nonlinear Response and Transition of Nonlinearity in a Piezoelectric Membrane

Arora,

Singh,

Kumar

et al. 2024

ACS Appl. Electron. Mater.

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Nonlinearities play a critical role in the dynamics of mechanical resonators, enhancing sensitivity and enabling signal manipulation. Understanding the parameters affecting nonlinearities is crucial for developing strategies to counteract their effects or manipulate them for improved device performance. This study investigates the impact of fabrication-induced curvature on the dynamics of zinc-oxide-based piezoelectric micromachined ultrasonic transducers (PMUTs). Our experiments reveal that these devices exhibit hardening, softening, and mixed nonlinear responses with varying initial static displacements. Notably, PMUTs with an almost flat initial static displacement exhibit hardening nonlinearity, while those with a curved initial static displacement show softening nonlinearity. An exotic mixed nonlinear response is observed for intermediate static displacement. We attribute the observed nonlinear response to the interplay between static displacement induced quadratic nonlinearity and midplanestretching induced cubic nonlinearity. We provide a theoretical formulation for the dynamics of the devices, which explains the experimental results and highlights the nonlinear responses and their dependence on the initial static displacement. Our findings underscore the significance of nonlinearities in the dynamics of mechanical resonators and suggest ways to optimize the device performance.

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Section: Resultsmentioning

confidence: 99%

Mixed Nonlinear Response and Transition of Nonlinearity in a Piezoelectric Membrane

Arora,

Singh,

Kumar

et al. 2024

ACS Appl. Electron. Mater.

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“…Bahaloo et al [20] researched the transverse vibration and stability of rotating annular disk with a circumferential crack and found the phenomenon that the disk critical speed will decrease with the crack depth increasing and the crack radius decreasing. Bose and Mohanty [21] studied the large amplitude axisymmetric vibration of circular disk with circumferential crack and the natural frequency variations of axisymmetric modes through combining the Berger's approximation, Galerkin's method, and multiple scales method. Furthermore, some researchers have systematically studied the vibration characteristics of flexible annular disks; Yuan [22,23] deduced the analytical formula of the natural frequency of flexible cracked disk and gave the natural frequency parameters for the free vibration of annular, circular, and sectorial plates.…”

Section: Introductionmentioning

confidence: 99%

A Study on Mode Shape and Natural Frequency of Rotating Flexible Cracked Annular Thin Disk

Zhao

Zhang

Jiang

2021

Shock and Vibration

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As an important rotating component, the flexible annular thin disk is widely used in mechanical engineering. Cracks may occur in some weak disk parts, which will greatly shorten the equipment service life and even cause equipment failure. Due to the centrosymmetric structure of the flexible annular disk, two typical cracks are studied in this paper; one is radial crack parallel to diameter, including radial closed crack (RC-crack) and radial opening crack (RO-crack); the other one is vertical crack perpendicular to diameter, including circumferential crack (CF-crack) and tangential crack (TG-crack). The effect of crack parameters, such as crack length, direction, and position, on disk vibration characteristics are studied through theoretical simulation and experimental verification. The research shows that the effect of cracks on vibration characteristic gets more obvious with cracks extending in most cases, RO-crack decreases the natural frequency obviously, and vertical cracks would affect mode shapes. In addition, the bigger the nodal diameter is, the more obvious the effect gets. Meanwhile, the most obvious effect appears in the mode of a nodal diameter locating on the crack. The research possesses some guiding significance in industrial production; by comparing with the vibration characteristics of the flawless disk, the integrity of the rotating flexible disk can be judged to prevent possible equipment damage.

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X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks

Benedetti

Gulizzi

Milazzo

2019

Aerotec. Missili Spaz.

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Large amplitude axisymmetric vibration of a circular plate having a circumferential crack

Cited by 5 publications

References 20 publications

Mixed Nonlinear Response and Transition of Nonlinearity in a Piezoelectric Membrane

Mixed Nonlinear Response and Transition of Nonlinearity in a Piezoelectric Membrane

A Study on Mode Shape and Natural Frequency of Rotating Flexible Cracked Annular Thin Disk

X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks

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