Effect of thermal environment on free vibration of cracked rectangular plate: An analytical approach

• Free vibration of thin cracked rectangular plate in thermal environment is studied.
• A relation is devised for buckling temperature of thin cracked rectangular plate.
• The effect of crack location and length on buckling temperature is analyzed.
• Variation of buckling temperature with plate aspect ratio is established.
• The influence on crack length, location and temp. rise on frequency is studied.
• Natural frequency is least when the crack is internal and symmetric about mid plane.

An analytical model is proposed for free vibration and geometrically linear thermal buckling phenomenon of a thin rectangular isotropic plate containing a continuous line surface or internal crack located at the centre of the plate using classical plate theory. The crack terms are formulated using Line Spring Model. The in-plane forces are due to the uniform heating of the cracked plate. Applying the Galerkin׳s method, the equation is transformed into Duffing equation which shows the effect of uniform rise in temperature on natural frequencies. A classical relation for buckling temperature for a cracked plate is also determined.