Effect of memory dependent derivative on forced transverse vibrations in transversely isotropic thermoelastic cantilever nano-Beam with two temperature |
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| Institution: | 1. Department of Basic and Applied Sciences, Punjabi University, Patiala, Punjab, India;2. Kurukshetra University Kurukshetra, India;1. Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China;2. Qiushi Honors College, Tianjin University, Tian jin 300350, China;3. McGill Metals Processing Centre, McGill University, Montreal, Quebec H3A 2B2 Canada;1. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 200016, China;2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;1. Department of Mathematics, Faculty of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia;2. Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt;3. Department of Mathematics, College of Science and Humanities at Howtat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia;4. Department of Mathematics, Faculty of Science, University of Tabuk, P.O.Box 741, Tabuk 71491, Saudi Arabia;5. Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, Porto 4249-015, Portugal;1. School of Reliability and Systems Engineering, Beihang University, Beijing 100083, China;2. Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100083, China;1. Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, India;2. Government P.G. College, Mushafirkhana, Uttar Pradesh, India |
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| Abstract: | The present research deals with the study of forced vibrations in transversely isotropic thermoelastic (TIT) nanoscale beam with two temperature (2T). Memory dependent derivative theory of thermoelasticity for clamped-free/cantilever nano-beam has been considered. The mathematical model is prepared for the nanoscale beam in a closed form with the application of Euler Bernoulli beam theory. Laplace transform method is employed to solve the problem. Forced vibrations due to exponential decaying time varying load acting vertically downward along the thickness direction of the nano-beam, Uniform load, Time harmonic load have been considered. Dynamic analysis for these forced vibrations and Static analysis has been carried out in this research. The dimensionless expressions for lateral deflection, thermal moment, temperature change, and axial stress are solved for these three forced vibrations. Response ratio has also been calculated. The analytical results have been numerically analysed using programming in MATLAB. The effect of kernel function has been depicted graphically on the lateral deflection, thermal moment, temperature change, axial stress and response ratio for all the three types of forced vibrations. Some particular cases have also been discussed. |
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