Significance of memory-dependent derivative approach for the analysis of thermoelastic damping in micromechanical resona
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Significance of memory-dependent derivative approach for the analysis of thermoelastic damping in micromechanical resonators Ravi Kumar1
· Rakhi Tiwari2
· Roushan Kumar1
Received: 30 May 2020 / Accepted: 31 October 2020 © Springer Nature B.V. 2020
Abstract Thermoelastic damping is becoming a leading factor for determining the quality of the micromechanical resonators in terms of their sensitivity. The present study is devoted to the analysis of thermoelastic damping of a micro-beam resonator by employing the concept of three-phase-lag (TPL) theory of thermoelasticity in the context of the memorydependent derivative (MDD). The memory-dependent derivative is characterized by its time delay and the kernel function that can be chosen freely with imposed restrictions. Analytical expressions of thermoelastic damping, attenuation as well as frequency shift have been derived. Computational results for the prominent parameters of micromechanical resonators such as thermoelastic damping, attenuation, and frequency shift are obtained. The influence of the constituents of memory-dependent derivative, i.e. time-delay and kernel functions, on the parameters of the micro-beam resonator has been analyzed through graphical results. Furthermore, numerical results are compared with the results obtained in the absence of a memory-dependent derivative through numerical simulations. The significant role of the memory-dependent derivative has been identified and it has been found that the insertion of the memory-dependent derivative is capable of providing accurate results as compared to the results obtained in its absence. Keywords Micromechanical resonators · Thermoelastic damping · Three-phase-lag heat equation · Memory-dependent derivative (MDD) · Quality factor
B R. Tiwari
[email protected] R. Kumar [email protected] R. Kumar [email protected]
1
Department of Mathematics, Central University of South Bihar, Gaya, 824236, India
2
Department of Mathematics, Nitishwar College, A Constituent unit of Babasaheb Bhimrao Ambedkar Bihar University, Muzaffarpur, 842002, India
Mech Time-Depend Mater
1 Introduction Due to the multifold applications of the micro-beam resonators such as bio and information technologies, bioengineering, aerospace, medicines, signal filtering, and energy harvesting, this topic has become very popular among the scientists and researchers. Due to their excellent characteristics including high fast response, low energy dissipation, favorable scaling property, and comparative ease of fabrication, micromechanical resonators are playing a crucial role in several applications in the field of sensing and actuation. However, it is a wellknown fact that modifications are always required in each field. The thermoelastic damping is defined as the prominent loss mechanism at room temperature in micro-beam resonators and the dissipation of energy is directly proportional to the thermoelastic damping. Due to this, there is always scope of improvement in the mechanical and producing methods a
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