Vibrational Analysis of micropipe under the influence of Velocity and Temperature fields using the Point interpolation Meshless method

Tubes with diameters in micro and nano dimensions with long length, while having a special manufacturing technology, have wide applications in the field of biosensors, atomic microscopes, actuators, tanks for fluid transfer in drug delivery, etc. The reason for the wide application of micropipes is their hollow geometry and very good mechanical properties. In this research, while comparing and using the classical theory of continuous medium mechanics and the non-classical theory of strain gradient based on the classical Euler-Bernoulli beam model and von-Carman nonlinear geometry, the mathematical equations are expressed in terms of three longitudinal parameters, then to investigate the vibrations of the micropipe under the influence Velocity and temperature fields are discussed. For this purpose, the frequencies and vibration amplitudes have been calculated by the integral solution of the governing differential equations using the point interpolation numerical meshless method of the displacement field, and the effect of temperature and diameter on the linear and non-linear behaviors in the micropipe has been studied. The findings of the research, while showing the effectiveness of the point interpolation numerical meshless method with base functions developed for the mentioned analysis, state that; by reducing the diameter of the micropipe, the natural frequency and critical speed increase and whit the temperature increases, resulting in a decrease in the basic frequency and an increase in the amplitude and becomes the nonlinear behavior of micropipe.