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Acoustic cavity modes in lens-shaped structures

The Journal of the Acoustical Society of America, 2003
A method for solving exactly the Helmholtz equation in parabolic rotational coordinates is presented using separability of the eigenfunctions and the Frobenius power series expansion technique. Two examples of interest in acoustics are considered and analyzed quasianalytically: The acoustic pressure in a cavity defined by two paraboloids (forming a ...
Willatzen, Morten, Lew Yan Voon, L.C.
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A neural mode shape identifier

Proceedings of 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society, 2002
A first stage for a fuzzy neural active controller is developed. Neural network technology is utilized in the real time identification of the mode of vibration of any structural system under seismic loading. The parallel processing nature of neural networks fit the nature of multi degree of freedom systems.
M.H.M. Hassan, B.M. Ayyub
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The mode shape reversal

Computers & Structures, 1989
Abstract Given an arbitrary modal matrix describing the vibrational displacements of a discrete, linear, undamped shear building, a theoretical solution is presented to find the mass and stiffness coefficients of the system; thereby reversing the usual vibration problem.
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ON THE MODE SHAPES OF THE HELMHOLTZ EQUATION

Journal of Sound and Vibration, 1995
Abstract The differential equation governing the free, transverse vibration of a thin membrane, the Helmholtz equation, is also the governing equation for problems of microwave propagation, stress waves and acoustics. Simple analytical solutions may be found in elliptic and parabolic co-ordinates.
G.M.L. Gladwell, N.B. Willms
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Mode shape identification and orthogonalization

AIAA Journal, 1988
An identification procedure to improve the mass-weighted orthogonality of measured mode shapes is introduced. The procedure takes into account the degree of mode isolation present during measurement. This is accomplished by establishing a set of new mode shapes, from the measured vectors, that satisfy cross-orthogonality constraints and are a minimum ...
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Frequency-shaped sliding modes: analysis and experiments

IEEE Transactions on Control Systems Technology, 1997
A recent improvement over a motion control algorithm, sliding mode control with perturbation estimation, is considered in this paper. It enforces the nonlinear system to follow a desired trajectory despite the presence of modeling uncertainties and disturbances.
Jairo Terra Moura   +2 more
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SENSITIVITY-BASED OPERATIONAL MODE SHAPE NORMALISATION

Mechanical Systems and Signal Processing, 2002
In the past few years, in-operation modal analysis has become a valid alternative for structures where classic forced vibration tests would be difficult, if not impossible, to conduct. A disadvantage of this method is that the excitation forces are unknown. Therefore, not all modal parameters can still be estimated.
Parloo, Eli   +3 more
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Surface vibrational modes in disk-shaped resonators

Ultrasonics, 2014
The natural frequencies and distributions of displacement components for the surface vibrational modes in thin isotropic elastic disks are calculated. In particular, the research is focused on even solutions for low-lying resonant vibrations with large angular wave numbers.
A V, Dmitriev   +2 more
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On mode shapes of a stability problem

Journal of Sound and Vibration, 1976
Abstract This paper presents data of mode shapes of some stable and unstable modes of a free-free beam under direction controlled thrusts. These mode shapes are pertinent in understanding this basic problem and hitherto were not available in the literature. It has been found that the node number of the mode shape corresponding to the first divergence
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Shaped Input Control of a System With Multiple Modes

Journal of Dynamic Systems, Measurement, and Control, 1993
This paper describes a method for limiting vibration in flexible systems that have more than one characteristic frequency and mode. It is only necessary to have knowledge of the component mode frequencies and damping ratios in order to be able to calculate the timing and magnitudes of the impulse sequence used in the shaping.
Singh, T., Heppler, G. R.
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