Vibrations of Shells and Plates

Soedel, W.

doi:10.4324/9780203026304

Cited by 540 publications

(227 citation statements)

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“…Resonant speeds of a rotating ring are defined as the speeds at which resonances of the ring subjected to a stationary load occur. They are the speeds which satisfy the conditionω = 0 [3,5], namely the natural frequency in the space-fixed coordinate becomes zero at these speeds. By substitutingω = 0 into the characteristic equation 16, one can solve for resonant speeds for each circumferential wavenumber.…”

Section: Critical Speeds Of Rotating Rings 31 Resonant Speedsmentioning

confidence: 99%

In-plane vibration of rotating rings using a high order theory

2018

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In-plane dynamics of rotating rings on elastic foundation is a topic of continuous research, especially in the field of tire dynamics. When the inner surface of a ring is connected to a stiff foundation, the through-thickness variation of radial and shear stress needs to be accounted for. This effect is often overlooked in the ring models proposed in the literature. In this paper, a new high order theory is developed for the in-plane vibration of rotating rings whose inner surface is connected to an immovable hub by distributed springs while the outer surface is stress-free. The high-order terms are chosen such that the boundary conditions at the inner and outer surfaces are satisfied at all times. Instability, which is usually overlooked in the literature, is predicted using the present model. Resonant speeds are investigated, at which modes appear as a stationary displacement pattern to a space-fixed observer. The exact satisfaction of boundary conditions at the inner and outer ring surfaces together with the through-thickness variation of the radial and shear stresses are shown to be of significant importance when the ring rotates at high speeds or is supported by relatively stiff foundation.

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Section: Critical Speeds Of Rotating Rings 31 Resonant Speedsmentioning

confidence: 99%

In-plane vibration of rotating rings using a high order theory

2018

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“…The arc length d of curved surfaces can be denoted as [25] The internal forces of the infinitesimal surface can be expressed as…”

Section: Governing Equationmentioning

confidence: 99%

The Dynamic Similitude Design Method of Thin Walled Structures and Experimental Validation

Zhang

Wang

Zhu

et al. 2016

Shock and Vibration

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For the applicability of dynamic similitude models of thin walled structures, such as engine blades, turbine discs, and cylindrical shells, the dynamic similitude design of typical thin walled structures is investigated. The governing equation of typical thin walled structures is firstly unified, which guides to establishing dynamic scaling laws of typical thin walled structures. Based on the governing equation, geometrically complete scaling law of the typical thin walled structure is derived. In order to determine accurate distorted scaling laws of typical thin walled structures, three principles are proposed and theoretically proved by combining the sensitivity analysis and governing equation. Taking the thin walled annular plate as an example, geometrically complete and distorted scaling laws can be obtained based on the principles of determining dynamic scaling laws. Furthermore, the previous five orders’ accurate distorted scaling laws of thin walled annular plates are presented and numerically validated. Finally, the effectiveness of the similitude design method is validated by experimental annular plates.

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“…To determine the parameters of the glass plate that control its vibrational response, the analytical model of the vibration of generally curved glass shells is developed in this section. Using the fundamental equations presented in basic textbooks [29][30][31], i.e., equations expressing 1) equilibrium of forces and moments acting on an infinitesimal shell element, 2)…”

Section: Analytical Estimation Of the Acoustic Impedance Of A Cumentioning

confidence: 99%

Application of piezoelectric macro-fiber-composite actuators for the suppression of noise transmission through curved glass plates

Nováková

Mokrý

2011

2011 International Symposium on Applications of Ferroelectrics (ISAF/PFM) and 2011 International Symposium on Piezoresponse For

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An investigation on the application of the piezoelectric Macro-Fiber-Composite (MFC) actuators for the suppression of the noise transmission through the curved glass plates is presented. It is known that when the incident sound wave in the air hits the glass plate or curved plate or shell, part of the acoustic wave is reflected, which makes the plate vibrate, and part of the wave is transmitted. It is easy to understand that the higher the flexural rigidity of the glass plate the bigger part of the acoustic sound wave is reflected than transmitted. This simple physical phenomenon can be profitably used for the suppression of the noise transmission through glass plates. The noise suppression effect is achieved using the MFC actuator, which is attached to the vibrating glass plate. When the piezoelectric MFC actuator is shunted by the active electronic circuit, which has a negative capacitance, it is possible to greatly suppress the vibration of the glass plate and also the noise transmission through the glass plate. The sound shielding efficiency of the glass plate is measured by the acoustic transmission loss (TL), which is expresed in decibel scale. If the amplitude of the window vibrations decreases, the value of TL increases. The effect of the glass plate geometry, and the electrical properties of the active shunt circuit on the enhancement of TL is analyzed using Finite Element Method numerical simulations. The comparison of the results of numerical simulations with acoustic measurements is presented. The possibility of the use of this method for the suppression of the noise transmission through the glass window plates is discussed.

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Vibrations of Shells and Plates

Cited by 540 publications

References 0 publications

In-plane vibration of rotating rings using a high order theory

In-plane vibration of rotating rings using a high order theory

The Dynamic Similitude Design Method of Thin Walled Structures and Experimental Validation

Application of piezoelectric macro-fiber-composite actuators for the suppression of noise transmission through curved glass plates

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