Application of nonlocal continuum theory to the primary resonance analysis of an axially loaded nano beam under time delay control |
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| Institution: | 1. Institute for Infrastructure and Environment, Heriot–Watt University, Edinburgh EH14 4AS, United Kingdom;2. Creative Engineering and Management Services, Deans Centre Peshawar, Pakistan;3. Department of Mechanical and Industrial Engineering, College of Engineering, Sultan Qaboos University, Oman;4. Maxwell Institute for Mathematical Sciences and Department of Mathematics, Heriot–Watt University, Edinburgh, EH14 4AS, United Kingdom;1. Department of Mathematics, Sarala Birla University, Ranchi-835103, India;2. Department of Mathematics, Birla Institute of Technology, Mesra-835215, India;1. Barcelona Supercomputing Center, 08034 Barcelona, Spain;2. Laboratory of Hydraulic Engineering, Department of Civil Engineering, University of Patras, 26500, Patras, Greece;1. Departamento de Ingeniería de Proyectos, Universidad de Guadalajara, José Guadalupe Zuno No. 48, Zapopan, C.P. 45150, Jalisco, México;2. Departamento de Ingeniería en Redes y Telecomunicaciones, Universidad Politécnica de Juventino Rosas, Hidalgo No. 102, Santa Cruz de Juventino Rosas, Gto., Comunidad de Valencia, C.P. 38253, México;3. School of Biosciences, University of Nottingham, Sutton Bonington Campus, Loughborough, Leicestershire, LE12 5RD, UK;4. GSC & CEIGRAM, ETSIAAB, Universidad Politécnica de Madrid (UPM). Ciudad Universitaria, C.P. 28040, Madrid, España |
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| Abstract: | The paper is concerned with the nonlinear primary resonance of nano beams with axial load under the velocity time delay control. In order to have a deep insight into the system, the amplitude frequency response curve of the system is firstly obtained using the multiple scales method. The effects of the control gains and time delays on the system stability are then investigated. The analyses illustrated that both delay feedback gain coefficient and velocity time delay control can mitigate the system vibrations properties (e.g. hardening nonlinearity, resonance amplitude and the corresponding width) to an excellent level. The nonlinear primary resonance of nano beam is also discussed with the influences of small scale effect, axial initial load, wave number, Winkler foundation modulus and the ratio of the length to the diameter. This paper establishes the relationship between the time delay controller and vibration properties of a nano beam system which provides the guidance for applying time delayed active control for different types of nano devices in engineering practices. |
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