Saeidreza Mohebpour

Based on the modified strain gradient theory (MSGT) in conjunction with the Timoshenko beam theory, the vibrational behavior under thermal environment of variable section functionally graded (FG) microbeams carrying microparticles is studied. The eigenfrequency equations are derived using the Chebyshev–Ritz method. The effects of temperature dependence of material properties and the initial thermal stresses are considered. After validating the method, the influences of the width taper ratio, the position and values of the microparticle masses, temperature rise, length scale parameters and material gradient index on the free vibration behavior of microbeams are studied. In addition, comparisons between the results of the MSGT, the modified couple stress theory (MCST), and the classical theory (CT) are performed. It is found that in addition to the microparticle masses and locations, their influences on the natural frequencies depend on the vibration mode number and the edge restraints of microbeams. Also, it is shown that the temperature rise, length scale parameters and material gradient index have considerable effects on the natural frequencies of microbeams. Moreover, the results demonstrate that the MSGT and the CT provide the largest and the smallest natural frequencies, respectively.