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 Advances in Nano Research   Volume 15, Number 3, September 2023 , pages 215-224 DOI: https://doi.org/10.12989/anr.2023.15.3.215 Investigation of nonlinear vibration behavior of the stepped nanobeam Mustafa Oguz Nalbant, Süleyman Murat Bağdatli and Ayla Tekin Abstract Nonlinearity plays an important role in control systems and the application of design. For this reason, in addition to linear vibrations, nonlinear vibrations of the stepped nanobeam are also discussed in this manuscript. This study investigated the vibrations of stepped nanobeams according to Eringen's nonlocal elasticity theory. Eringen's nonlocal elasticity theory was used to capture the nanoscale effect. The nanoscale stepped Euler Bernoulli beam is considered. The equations of motion representing the motion of the beam are found by Hamilton's principle. The equations were subjected to nondimensionalization to make them independent of the dimensions and physical structure of the material. The equations of motion were found using the multi-time scale method, which is one of the approximate solution methods, perturbation methods. The first section of the series obtained from the perturbation solution represents a linear problem. The linear problem's natural frequencies are found for the simple-simple boundary condition. The second-order part of the perturbation solution is the nonlinear terms and is used as corrections to the linear problem. The system's amplitude and phase modulation equations are found in the results part of the problem. Nonlinear frequency-amplitude, and external frequency-amplitude relationships are discussed. The location of the step, the radius ratios of the steps, and the changes of the small-scale parameter of the theory were investigated and their effects on nonlinear vibrations under simple-simple boundary conditions were observed by making comparisons. The results are presented via tables and graphs. The current beam model can assist in designing and fabricating integrated such as nano-sensors and nano-actuators. Key Words analytical modelling; nonlocal elasticity; stepped nanobeams; vibration Address Mustafa Oguz Nalbant:Department of Electronic and Automation, Soma Vocational School, Manisa Celal Bayar University, 45500 Soma, Manisa, Turkey Süleyman Murat Bağdatli: Department of Mechanical Engineering, Manisa Celal Bayar University, Yunusemre, 45140 Manisa, Turkey Ayla Tekin: Department of Machinery and Metal Technologies, Soma Vocational School, Manisa Celal Bayar University, 45500 Soma, Manisa, Turkey

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