163 | F a s c i c u l e 1 ANNALS of Faculty Engineering Hunedoara – International Journal of Engineering Tome XV [2017] – Fascicule 1 [February] ISSN: 1584-2665 [print; online] ISSN: 1584-2673 [CD-Rom; online] a free-access multidisciplinary publication of the Faculty of Engineering Hunedoara 1. D.O. ONWUKA, 2. O.M. IBEARUGBULEM, 3. A.C. ABAMARA, 4. U.G. EZIEFULA, 5. S.U. ONWUKA VIBRATION CHARACTERISTICS OF A FREELY VIBRATING SSSC RECTANGULAR THIN ORTHOTROPIC PLATE 1-2., 4. Department of Civil Engineering, Federal University of Technology, Owerri, NIGERIA 3. Federal Ministry of Transport, Abuja, NIGERIA 5. Department of Project Management, Federal University of Technology, Owerri, NIGERIA Abstract: In this article, a truncated Taylor–Maclaurin series was used in Rayleigh–Ritz method to analyze the free vibration of a rectangular thin orthotropic plate bounded by three simply supported edges and one clamped edge (i.e. SSSC plate). The total potential energy functional (which is a function of the strain energy and kinetic energy of a free vibrating plate), was derived from the theory of elasticity. Taylor–Maclaurin series truncated at the fourth term was used to obtain a shape function which satisfied all the boundary conditions of an SSSC plate under free vibration. The shape function was substituted into the total potential energy functional, and the resulting equation was eventually minimized. The equation for the fundamental frequency was then derived from the minimized equation, and fundamental frequencies computed for different aspect ratios, p (varying from 0.1 to 2.0 in steps of 0.1) and different flexural rigidity ratios, φ. The results show that the average percentage differences in the values of the fundamental frequency for flexural rigidity ratios, φ 1 , φ 2 , and φ 3 , are −3.404%, −2.029%, and −2.456%. Hence, the displacement function obtained for the SSSC plate is a very good approximation of the exact shape function for the plate. Keywords: Orthotropic Plate, Rayleigh-Ritz Method, Rectangular Plate, Taylor-Maclaurin Series, Free Vibration INTRODUCTION Thin rectangular plate elements used in engineering structures are often subject to free vibration. Thus, it is important to determine the vibration characteristics of thin rectangular plates undergoing free vibration. Many researchers have carried out investigations on vibration of thin orthotropic plates. Hearmon [3] proposed an approximate general solution based on Rayleigh method for the free vibrations of orthotropic plates. Leissa [6] presented the accurate analytical results for free vibrations of orthotropic plates for cases having two opposite sides simply supported and others with possible combinations of clamped, simply supported, and free edge conditions. According to Meirovitch [7], the Rayleigh–Ritz method is one of the most popular methods used for obtaining approximate solutions for the fundamental frequencies of an orthotropic rectangular plate due to its high versatility and simplicity. Wu et al. [9] proposed a novel Bessel function method for deriving exact solutions to free vibration problems of rectangular thin plates. Chakraverty [2] gave higher modes of vibrations for plates of various shapes and boundary conditions. Xing and Liu [10] used separation of variables for obtaining exact solutions for the free vibration of thin orthotropic rectangular plates, with all combinations of simply supported and clamped boundary conditions. Although a lot of researches have been done on plates, none of the researchers used Taylor’s series function in Rayleigh–Ritz method to obtain the fundamental frequencies of thin orthotropic rectangular SSSC plate subjected to free vibration. This work used Taylor’s series function in Rayleigh–Ritz method in formulating the deflection function, which in turn was used to obtain total potential energy function. Then, the total potential energy was used to obtain the fundamental frequency of rectangular orthotropic thin plate bounded by three simply supported edges and one clamped edge (i.e. SSSC plate) under free vibration.