The Vibration of Rectangular Plates

In this paper are considered the free transverse vibrations of rectangular plates with all possible boundary conditions obtained by combining free, freely-supported, and fixed edges. The Rayleigh method, assuming waveforms similar to those of beams, is used to derive a simple approximate frequency expression for all modes of vibration. The terms in this expression depend on the nodal pattern and the boundary conditions; they are tabulated for fifteen boundary conditions—all four edges free, freely-supported, or fixed and the twelve cases in which some of the edges have one condition and the rest another. The expression can also be used to obtain frequencies for a plate which has a combination of all three boundary conditions. The effect on frequency of an edge being supported and partially restrained is discussed.For some boundary conditions it is possible to compare derived frequencies with those obtained by various methods of accurate analysis and by experiment; except for a few cases, the results from ...

[1]  B. Grinsted.  Nodal Pattern Analysis , 1952 .

[2]  H. Eschler.  Zur Ermittlung der Eigenschwingungszahlen der in ihrer Mittelebene belasteten Rechteckplatte , 1950 .

[3]  R N Arnold,et al.  Flexural vibrations of the walls of thin cylindrical shells having freely supported ends , 1949, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  Mary D Waller,et al.  Vibrations of Free Rectangular Plates , 1949 .

[5]  M. Waller.  Vibrations of free square plates: part I. Normal vibrating modes , 1939 .

[6]  S. Iguchi.  Die Knickung der rechteckigen Platte durch Schubkräfte , 1938 .

[7]  S. Iguchi,et al.  Die Biegungsschwingungen der vierseitig eingespannten rechteckigen Platte , 1937 .

[8]  S. Tomotika D.Sc.,et al.  LX. The transverse vibration of a square plate clamped at four edges , 1936 .

[9]  Bohuslav Pavlik.  Beitrag zur theoretischen und experimentellen Untersuchung der Biegungsschwingungen bei rechteckigen Platten mit freien Rändern , 1936 .

[10]  K. Sezawa.  On the Lateral Vibration of a Rectangular Plate Clamped at Four Edges , 1931 .

[11]  Alice Lemke.  Experimentelle Untersuchungen zur W. Ritzschen Theorie der Transversalschwingungen quadratischer Platten , 1928 .

[12]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[13]  W. Ritz,et al.  Theorie der Transversalschwingungen einer quadratischen Platte mit freien Rändern , 1909 .

[14]  C. Zeissig.  Ein einfacher Fall der transversalen Schwingung einer rechteckigen elastischen Platte , 1898 .

[15]  W. Voigt.  Bemerkung zu dem Problem der transversalen Schwingungen rechteckiger Platten , 1893 .