Restrained Edges Effect on the Dynamics of Thermoelastic Plates under Different End Conditions - Abdul-Majeed, Wael R.; Jweeg, Muhsin J; Jameel, Adnan N (Al-Khwarizmi Engineering Journal, 2012)
Frequency equations for rectangular plate model with and without the thermoelastic effect for the cases are: all edges are simply supported, all edges are clamped and two opposite edges are clamped others are simply supported.   These were obtained through direct method for simply supported ends using Hamilton’s principle with minimizing Ritz method to total energy (strain and kinetic) for the rest of the boundary conditions. The effect of restraining edges on the frequency and mode shape has been considered. Distributions temperatures have been considered as a uniform temperature the effect of developed thermal stresses due to restrictions of ends conditions on vibration characteristics   of a plate with different will be investigated. it is noticed that the thermal stress will increase with increasing the heatnig temperature and that will cause the natural frequency to be decreased for all types of end conditions and for all modes of frequency.