Abstract In this thesis, the dynamic behavior of ultrasonic micro / nano-probe is investigated based on the non-local strain gradient theory. The nano-probe is modeled as a single-bar with variable cross-section and has two parts, horn and piezoelectric. Horn cross section is eva‎luated by considering exponential, power of one half and power of one third functions. By applying a harmonic voltage to the piezoelectric part, the piezoelectric force is applied in an oscillating manner, which causes the vibration and its amplitude is amplified in the horn due to the reduction of the cross-sectional area. To achieve the governing equations, in terms of the displacement field, the nonlocal strain gradient theory is used and after extracting the kinetic and strain energies, the dynamic equations of the probe are obtained using the Hamilton’s principle. In the following, the vibration behavior of the system is eva‎luated in two modes of free and forced vibrations. The governing vibration equation is solved by two methods, analytical and finite element approaches. In the analytical solution method, the natural frequencies and the mode shapes are determined using the Rayleigh-Ritz methods and displacement of the end of the probe will be calculated using Galerkin’s approach. In numerical solution, a combination of methods of finite difference and finite element is utilized and natural frequencies and vibrational amplitudes are obtained. After convergence analysis in both methods, the results of numerical and analytical methods are compared with each other and the agreement between the results of two methods is observed. In the following, the results of classical, non-local theory and non-local strain gradient theories are compared with each other and the differences and errors resulting from the two non-local and classical theories are assessed. Finally, frequency response and sensitivity diagrams are eva‎luated.

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