LARGE AMPLITUDE FREE VIBRATION OF MICRO/NANO BEAMS BASED ON NONLOCAL THERMAL ELASTICITY THEORY

Abstract

THIS PAPER IS CONCERNED WITH THE NONLINEAR FREE VIBRATION OF A HEATED MICRO/NANO BEAM MODELED AFTER THE NONLOCAL CONTINUUM ELASTICITY THEORY AND EULER-BERNOULLI BEAM THEORY. THE GOVERNING PARTIAL DIFFERENTIAL EQUATIONS ARE DERIVED FROM THE HAMILTON VARIATIONAL PRINCIPLE AND VON KáRMáN GEOMETRIC NONLINEARITY, IN WHICH THE EFFECTS OF THE NONLOCALITY AND AMBIENT TEMPERATURE ARE INCLUSIVE. THESE EQUATIONS ARE CONVERTED INTO ORDINARY FORMS BY EMPLOYING THE KANTOROVICH METHOD. THE SOLUTIONS OF NONLINEAR FREE VIBRATION ARE THEN SOUGHT THROUGH THE USE OF SHOOTING METHOD IN SPATIAL DOMAIN. NUMERICAL RESULTS SHOW THAT THE PROPOSED TREATMENT PROVIDES EXCELLENT ACCURACY AND CONVERGENCE CHARACTERISTICS. THE INFLUENCES OF THE ASPECT RATIO, NONLOCAL PARAMETER AND TEMPERATURE RISE PARAMETER ON THE DIMENSIONLESS RADIAN FREQUENCY ARE CAREFULLY INVESTIGATED. IT IS CONCLUDED THAT THE NONLOCAL AND TEMPERATURE RISE PARAMETERS LEAD TO REDUCTIONS OF THE NONLINEAR VIBRATION FREQUENCY, WHILE THE INFLUENCE OF THE NONLOCAL EFFECT DECREASES WITH AN INCREASE IN THE ASPECT RATIO.