Int. J. Mech. Sci. Vol. 40, No. 11, pp. 1119— 1131, 1998  1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0020—7403/98 $19.00#0.00 PII : S0020 – 7403(98)00013 – 7 COMPARISONS OF EXPERIMENTAL AND THEORETICAL FREQUENCIES FOR RECTANGULAR PLATES WITH VARIOUS BOUNDARY CONDITIONS AND ADDED MASSES K. H. LOW*, G. B. CHAI*, T. M. LIM* and S. C. SUE *School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore; and Temasek Polytechnic, 21 Tampines Avenue 1, Singapore 529757, Singapore (Received 22 April 1997; and in revised form 16 December 1997) Abstract—This paper is concerned with a vibration analysis of rectangular plates with masses mounted on various locations. The edges of the plates may either be clamped or simply supported. The study is particularly useful in the understanding of the vibration of printed circuit boards used in the electronics industry. An energy method is developed to obtain analytical frequencies of the plates with various edge support conditions. The analytical procedure using the Rayleigh—Ritz approach is adopted in which each of single and multiple trigonometric series terms is used to represent the shape function. Two experimental methods, a spectrum analyser and a TV-holographic system, are used to study the behaviour of the plate vibrations. The holo- graphic image produced at the corresponding mode frequencies by using the TV-holography technique has been applied to verify the frequency spectra obtained from the spectrum analyser. The experimental results have been used to illustrate the validity of the analytical model. The comparisons show that the analytical model predicts natural frequencies reasonably well, in which the EM 100-term model is suggested for vibration plates with higher modes or heavier loads.  1998 Elsevier Science Ltd. All rights reserved Keywords: frequency analysis, mass-loaded plates, Rayleigh—Ritz approach, spectrum analyser, TV-holo- graphic. NOTATION a, b effective dimension of plate A  constant amplitude D flexural rigidity of plate ( "Et/[12(1!)]) E Young’s modulus of plate material f  nth-mode frequency of the loaded plate (Hz) f  nth-mode frequency of the unloaded plate (Hz) t plate thickness j number of concentrated masses on the plate surface k, h coordinates of mass placed on the plate surface K stiffness matrix m, n mode number M concentrated mass mounted on the plate surface M  concentrated mass mounted on the plate’s centre M  mass of the bare plate S mass matrix ¹  maximum kinetic energy º  strain energy of bending w transverse plate displacement function X, ½ transverse beam displacement functions  density of plate ( "t) (kg/m)  frequency ( "2f ) (rad/s)  density of plate (kg/m)  Poisson’s ratio of plate material 1. INTRODUCTION Considerable attention has been paid to the solution of the vibration problems of rectangular plates [1—8]. These studies are useful in respect to the vibration of printed circuit boards because most such boards can be approximated as flat rectangular plates with different edge conditions and various loading conditions [1, 7]. 1119