An investigation to identify the thrust in flapping and undulatory motion of smart Timoshenko beam
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ORIGINAL ARTICLE
An investigation to identify the thrust in flapping and undulatory motion of smart Timoshenko beam Ganesh Govindarajan1 Received: 13 December 2018 / Accepted: 11 September 2019 © The Japan Society of Naval Architects and Ocean Engineers (JASNAOE) 2019
Abstract In this paper, a computational approach to investigate the feasibility of using Smart Timoshenko beam (STB) for underwater locomotion is presented. The main objective of the current study is to understand different thrust producing mechanisms, namely flapping and undulatory modes of locomotion and to identify the critical parameters, such as body length, flexural stiffness and tail beat frequency affecting the locomotion. The thrust for different modes of locomotion with a variation in Young’s modulus and moment of inertia for the STB has been calculated. The results will help improve the understanding of thrust generation in both flapping and undulatory modes which are essential in the design and development of the bioinspired robotic systems for underwater locomotion. Keywords Timoshenko beam (TB) · Non-uniform cross-section · Bio-inspired robotic system · Propulsive velocity · Wave velocity · Smart Timoshenko beam (STB)
1 Introduction Bio-inspired locomotion opens up a new area of research due to its extensive application in various fields like drug delivery, underwater robotics, etc. For instance, robotic fish prototypes are used in civil and defence research to understand and develop underwater vehicles. At present, most of the underwater locomotive systems use servomotor technology and complex mechanical systems. Their maintenance is quite expensive and challenging. To surpass the challenges posed by the above-mentioned techniques, researchers used an alternative way to design underwater locomotive systems [1]. In this regard, smart materials are found to be a potential candidate for designing actuator for underwater propulsion system due to their lightweight nature and minimum design complexity. The smart beam swimming system draws inspiration from the tail motion of thunniform fish, which are efficient swimmers that produce forward momentum by rapidly undulating their tail. In the present work, the method is adopted from the previous work on modelling fish as a non-uniform Timoshenko beam with varying * Ganesh Govindarajan [email protected]; [email protected] 1
Young’s modulus and the moment of inertia along its length from head to tail [2]. The non-uniform Timoshenko beam is assumed to be a cantilever with the fixed end at the head and the free end at the tail and the corresponding mode shapes are determined. Based on the mode shapes, the thrust is calculated with respect to the input parameters such as wave velocity, propulsive velocity and wavelength. The increase in propulsive velocity results in a reduction in the calculated thrust, especially in the higher modes. The velocity with a lower frequency and higher amplitude always generate a significant thrust as compared to that with higher frequency and low
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