The receptance method applied to the free vibration of continuous rectangular plates

Free Vibration of Line Supported Rectangular Plates Using a Set of Static Beam Functions

“…The ®rst six eigenfrequency values obtained are listed in Table 1 for the plate with various boundary conditions. The ®rst four mode shapes for the plate with clamped edges at x 0 and x a are shown in Figure 3, which are very close to the exact mode shapes presented in the literature [7]. It can be seen from Table 1 that in all the numerical methods listed, the present results are closest to the exact values given by Azimi et al [7], while the computational cost is the lowest as can be seen by the considerably smaller number of eigenfrequency equations used.…”

“…Early research mainly focused on rectangular plates simply supported at two opposite edges and continuous over line supports perpendicular to those edges. Veletsos and Newmark [1] used the Holzer's method, Ungar [2] used a semi-graphical approach, Bolotin [3] and Moskalenko and Chien [4] used the dynamic edge-effect method, Lin et al [5] used the transfer matrix method, Elishakoff and Sternberg [6] used the modi®ed Bolotin's method, and Azimi et al [7] used the receptance method for such plates. Furthermore, Cheung and Cheung [8] used the single-span vibrating beam functions in the ®nite strip method and Mizusawa and Kajita [9] used the B-spline functions in the Rayleigh± Ritz method to analyze the free vibration of one-direction continuous plates with arbitrary boundary conditions.…”

Semi-analytical determination of natural frequencies and mode shapes of multi-span bridge decks

“…The modified Bolotin method, developed by Vijayakumar [7] and Elishakoff [8], was applied by Elishakoff and Sternberg [9] to determine eigenfrequencies of rectangular plates, with continuous over line supports with an arbitrary number of equal spans in one direction. More recently, the receptance method was exploited by Azimit et al [10] in a similar application. Gorman and Garibaldi [11] applied the superposition method and the span-by-span approach to obtain an accurate analytical solution for free vibration of multispan bridge decks.…”

Plate vibration under irregular internal supports

“…Elishakoff and Sternberg (1979) treated similar multi-span plates in one direction, by using a modified Bolotin method. Using the receptance method, Azimi et al (1984) obtained closed form solutions for the vibration of simply supported multi-span rectangular plates. Mizusawa and Kajita (1984) utilized the B-spline functions in association with the Rayleigh-Ritz method to analyze free vibration of one-direction continuous plates with arbitrary boundary conditions.…”