{'fraction_non_alphanumeric': 0.01816911250873515, 'fraction_numerical': 0.0, 'mean_word_length': 5.119658119658119, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Control of the non-linear static deflection experienced by a fluid-carrying double-walled carbon nanotube using an external distributed load

In this work, an external distributed line load is used to control the postbuckled static deflection of a double-walled carbon nanotube within which a continuous non-viscous fluid flows at a constant velocity. The non-linear equation of motion and boundary conditions are derived using the non-local Timoshenko beam model for the double-walled carbon nanotube, incorporating Von Karman-type geometric non-linear behavior and taking account of the Van der Waals interaction between adjacent layers. First, in the absence of the control force, an analytical approach is used to determine the buckling fluid flow velocities and steady state non-linear static deflection at velocities greater than the buckling velocity for both the cases of a simple-simple and a simple-clamped end support. Then, the control force participates as an indeterminate parameter in the equations. The control force is obtained by resolving equations in which the postbuckled configuration is considered to be an exponential function of time with a negative exponential gain and initial value of the time that is equal to a steady configuration before the control force is applied. The influences of the non-local parameter, aspect ratio and the end supports on the maximum value of control force are investigated.