Nonlinear forced vibrations of curved microbeam resting on nonlinear foundation using the modified strain gradient theory

• Main Authors: Allahkarami, F., Nikkhah-bahrami, M.
• Format: Article
• Language: English
• Published: Інститут механіки ім. С.П. Тимошенка НАН України 2018
• Series: Прикладная механика
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/174264

The nonlinear forced vibrations of a curved micro- beam resting on the nonlinear foundation are examined. The equations of motion are derived using the Hamilton's principle and the modified strain gradient theory which is capable to examine the size effects in the microstructures. The nonlinear partial differential equations of motion are reduced to a time-dependent ordinary differential equation containing quadratic and cubic nonlinear terms. A frequency response of the curved microbeam for the primary resonance is determined using multiple time scales perturbation method. From the application point of view, the frequency response curves may be useful to select the optimum values of design parameters. The effects of geometry parameters and foundation moduli on the vibration behavior of the curved microbeam are illustrated.