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Two-Dimensional Simulation of Generalized Thermoelastic Damping in Vibrations of Strain Gradient Beam Resonators

Wade GhribiDepartment of Computer Engineering, College of Computer Science, King Khalid University, Al-Faraa, KSAPinank PatelDepartment of Mechanical Engineering, Faculty of Engineering and Technology, Marwadi University, Rajkot 360003, Gujarat, IndiaM K RanganathaswamyDepartment of Mechanical Engineering, School of Engineering and Technology, JAIN (Deemed to be University), Bangalore, Karnataka, IndiaRohit SharmaDepartment of Mechanical Engineering, Arka Jain University, Jamshedpur, Jharkhand 831001, IndiaSabir WidatallaDepartment of Mathematics, Faculty of Science, University of Tabuk, Tabuk, 71491, Saudi ArabiaVikasdeep Singh MannPunjab Engineering CollegeMarwa AlhedraweCollege of Technical Engineering, The Islamic University of Al Diwaniyah, Al Diwaniyah, IraqAnkit KediaNIMS School of Mechanical and Aerospace Engineering, NIMS University Rajasthan, Jaipur, IndiaMukesh Kumar SharmaDepartment of Mathematics, Chaudhary Charan Singh University, Meerut, Uttar Pradesh, 250004, IndiaAbhinav KumarDepartment of Mechanical Engineering, Karpagam Academy of Higher Education, Coimbatore, 641021, India

2024en

ABI

Annotatsiya

The operation of micro/nanobeam resonators is greatly impacted by the thermoelastic damping (TED) phenomenon, highlighting the need for precise determination of its value. Given the confirmed size effects in both mechanical and thermal fields, along with the importance of utilizing the two-dimensional (2D) heat transfer model over the 1D model for more accurate simulation of the thermomechanical behavior of small-scale beams, this paper aims, for the first time, to present a 2D model for TED using the modified strain gradient theory (MSGT) and the nonlocal dual-phase-lag (NDPL) heat equation. To accomplish this, the 2D NDPL-based temperature distribution is calculated using the Galerkin method, while the MSGT is applied to determine the size-dependent constitutive equations. The obtained relations are then used in the energy dissipation (ED) method to derive a TED formula in the form of infinite series. To validate the model’s accuracy, a simplified version is employed for comparison. A detailed convergence study is also performed to determine the optimal number of terms needed for precise results. Finally, a thorough parametric analysis is undertaken to explore how key factors like 2D heat transfer and non-classical constants in the MSGT and NDPL model impact TED. The findings highlight the importance of using the MSGT and NDPL model in micro- and sub-micro dimensions, and the need for the 2D model in beams with low aspect ratios.

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Identifikatorlar

DOI: 10.1142/s0219455426500707

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