On the asymptotic amplitude of vibrating plates

1973 ◽  
Vol 111 (1) ◽  
pp. 2236-2240
Author(s):  
K. Gopalsamy
Keyword(s):  
Vibrating Plates

Rayleigh-Ritz Analysis of Vibrating Plates Based on a Class of Eigenfunctions

2009 ◽  
Author(s):  
Giuseppe Catania ◽  
Silvio Sorrentino
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Linear Combination ◽  
Equation Of Motion ◽  
Extensive Literature ◽  
Shape Functions ◽  
Element Analysis ◽  
Vibrating Plates ◽  
General Basis

In the Rayleigh-Ritz condensation method the solution of the equation of motion is approximated by a linear combination of shape-functions selected among appropriate sets. Extensive literature dealing with the choice of appropriate basis of shape functions exists, the selection depending on the particular boundary conditions of the structure considered. This paper is aimed at investigating the possibility of adopting a set of eigenfunctions evaluated from a simple stucture as a general basis for the analysis of arbitrary-shaped plates. The results are compared to those available in the literature and using standard finite element analysis.

Visualization of nodes and antinodes in vibrating plates

1968 ◽  
Vol 8 (5) ◽  
pp. 225-231 ◽  
Author(s):  
C. R. Hazell ◽  
R. D. Niven
Keyword(s):  
Vibrating Plates

scholarly journals Secondary states of vibrating plates

1981 ◽  
Vol 69 (6) ◽  
pp. 1682-1687 ◽  
Author(s):  
Leonard J. Putnick ◽  
Bernard J. Matkowsky ◽  
Edward L. Reiss
Keyword(s):  
Vibrating Plates

Identification of Forces in Vibrating Plates by Pointwise and Line Observations: Uniqueness and Stability

1995 ◽  
Author(s):  
Masahiro Yamamoto
Keyword(s):  
Finite Time ◽  
Large Time ◽  
Single Point ◽  
Time Interval ◽  
Finite Time Interval ◽  
Line Parallel ◽  
Vibrating Plates ◽  
External Forces ◽  
Spatially Varying

Abstract We consider determination of spatially varying external forces in a rectangle vibrating plate from displacement observed along a line parallel to a side of the plate over a finite time interval. For a suitable choice of the line and a sufficient large time interval, we prove the uniqueness of external forces and estimate them by appropriate norm of displacement. Moreover we discuss determination of external forces from displacement observed at a single point over a time interval.

Modal coupling in vibrating plates

1982 ◽  
Vol 72 (S1) ◽  
pp. S83-S83
Author(s):  
Graham Caldersmith ◽  
Thomas D. Rossing
Keyword(s):  
Modal Coupling ◽  
Vibrating Plates

Spatial mapping of modal damping in vibrating plates.

2009 ◽  
Vol 126 (4) ◽  
pp. 2244 ◽  
Author(s):  
Hande Öztürk ◽  
J. Gregory McDaniel
Keyword(s):  
Spatial Mapping ◽  
Modal Damping ◽  
Vibrating Plates

Frequencies in vibrating wood – Does cell organization matter?

IAWA Journal ◽  
2019 ◽  
Vol 40 (1) ◽  
pp. 124-142
Author(s):  
Oliver Dünisch
Keyword(s):  
Spatial Organization ◽  
Ring Width ◽  
Spatial Arrangement ◽  
Cell Types ◽  
Dominant Frequency ◽  
Fast Fourier Transformation ◽  
Frequency Spectra ◽  
Laser Sensors ◽  
Vibrating Plates ◽  
Dominant Frequencies

ABSTRACT The relationship between the spatial organization of different cell types, of the xylem rays, and of the tree rings and the frequencies in vibrating softwoods and hardwoods was studied under controlled conditions. In total, the frequencies in 1007 standardized vibrating plates from 16 softwoods and 74 hardwoods were analysed using high resolution laser sensors (accuracy ± 0.02 μm, sampling frequency 30 kHz) for vibration measurements. Overlapping frequencies within the frequency spectra were identified by means of Fast Fourier Transformation analysis. With regard to the number of distinct frequencies within the spectra, four different vibration types were identified: type 1–one dominant frequency within the frequency spectra; type 2-two dominant frequencies within the frequency spectra; type 3-three dominant frequencies within the frequency spectra; type 4-no dominant frequencies within the frequency spectra. The presence of distinct frequencies was correlated with a highly organized spatial arrangement of tracheids in softwoods, with a storied arrangement of the xylem rays in hardwoods, and with low variation in tree-ring width in both softwoods and hardwoods. The grid size for repetition in these xylem structures influenced the frequencies of the vibrating wood in absolute numbers. The results indicate that the analysis of the anatomical structure of the wood can contribute to the grading of timber for its vibration characteristics, which is of special interest for the selection of resonance wood for musical instruments.

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