Natural oscillations of a rectangular plates with two adjacent edges clamped

Abstract

We study the natural oscillations of a rectangular plate, two adjacent edges of which are clamped, and the other two are free (CCFF-plate), as an element of many building structures. The deflection function is chosen as a sum of two hyperbolic trigonometric series. Both series obey the main equation of free vibration. Meeting all boundary conditions of a problem leads to an infinite system of homogeneous linear algebraic equations with respect to eight series coefficients. This system is transformed in two subsystems due to four basic coefficients, for which the iterative solution process is organized. Initial values of a pair of basic coefficient series are chosen randomly. Frequency values are chosen so that iterations coincide starting with a certain number. This provides non-trivial solutions of the reduced system. For the first eight obtained natural frequencies there have been presented relevant 3D mode shapes. The paper provides accuracy analysis and its comparison with other familiar results.

Keywords

• civil and structural engineering
• building and construction
• rectangular plate
• accurate natural frequency
• resonance
• fourier series