Journal of Sound and Vibration (1975) 38(2), 271

FUNDAMENTAL FREQUENCY OF A SQUARE PANEL WITH MULTIPLE POINT SUPPORTS ON EDGES

It is necessary to study the vibration and stability characteristics of panels which are parts of a complex structure like an aircraft wing. Generally the panels are riveted at discrete points, but it is customary to idealize the panel boundary conditions as either simply supported or clamped. The actual boundary conditions are more complex, perhaps somewhere in between simply supported and clamped. In the work reported in this note, the discrete rivets were idealized as point supports and an attempt was made to determine the number of point supports required to effectively attain a simply supported boundary condition, for the particular case of the vibrations of a square panel with a number of point supports on its edges. The calculations were carried out only for the fundamental frequency; a similar study for higher modes would be useful to establish if the boundary conditions similarly would be idealized for them as well. The calculations were carried out by the finite element method, the high precision triangular plate bending element of Cowper et al. [1 ] being used.

TABLE 1

Fundamental frequency ). of a square panel with multiple point supports on edges

Number of equally spaced point supports on an edge 2

3 331.0667 5 385.6528 7 388.6574 9 389.2520

Simply supported panel---exactvalue 389.6364

Table I gives the fundamental frequency parameter, 2 (defined as 2 = ptoJZL4/D, where p is the mass density, t is the thickness of the plate, o9 is the circular frequency, L is the length of the plate and D is the plate flexural rigidity), of a square panel, for several different numbers of point supports on its edges. It can be seen from this table that five equally spaced point supports on an edge is a good approximation for a simply supported idealization with the error being about 1 ~o for obtaining the fundamental frequency.

Structural Enghleering Division, O. VENKATESWARA RAO Space Science attd Technology Centre, Trivandrum, India (Received 30 August 1974)

REFERENCE

1. G. R. COWPER, E. KOSKO, G. M. LINDBERG and M. D. OLSON 1968 National Research Cotlncil of Canada, ,4eronautical Report LR-514. A high precision triangular plate bending element.

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