Free Flexural Vibration of Composite Beam by Spectral Element Method

Abstract

The composite beam may be of the forms of uniform, non-uniform or tapered. Free vibration of uniform composite beam has been studied by researchers with different boundary conditions using various methods of analysis such as First Order Shear Deformation Theory(FSDT), Wittrick Williams algorithm, Trigonometric Shear Deformation Technique, Runge Kutta Nystran Method, Higher Order Beam Theory, Dynamic Finite Element Method(DFEM), Lagrange Multiplier Method etc., besides the conventional analytical methods and finite element methods. Rarely any literature is available on free vibration on composite stepped beam. The one employed by Lam and Sathiyamoorthy is based on Runge-Kutta-Nystran Method. They studied the behaviour of uniform composite beam and validated the result by Runge-Kutta-Nystran Method and extended it to the stepped composite beam. For the free vibration of composite tapered beam only few papers are available where methods like FSDT, higher order finite element method, complementary function method have been used. In this present work the Spectral Element Method (SEM) has been used for the free vibrations of composite uniform, stepped and tapered Timoshenko beam. The results obtained for all the above beams by Spectral Element Method (SEM) are more promising in accuracy compared to the other methods even for higher modes and with lesser degrees of freedom.