Thermoelastic damping properties in hemi-ellipsoidal shells with variable thickness

IF 4.4 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Applied Mathematical Modelling Pub Date : 2024-09-22 DOI:10.1016/j.apm.2024.115720
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Abstract

Thermoelastic damping (TED) is a fundamental dissipation mechanism that inevitably exists in shell resonators with high quality factors. Based on the thermal energy method, this paper demonstrates an effective method for the TED characterization of the hemi-ellipsoidal shells with variable thickness which manifest lower TED compared with the hemispherical shells. The equation of motion of the hemi-ellipsoidal shell under clamped-free boundary conditions is established by Hamilton's principle and the assumed mode method, and the natural frequencies and mode shape functions of the hemi-ellipsoidal shell with variable thickness are obtained by solving the eigenvalue problem. The temperature field is acquired by solving the heat conduction equation along the radial direction, and an analytical model for the TED of the hemi-ellipsoidal shell with variable thickness is presented by calculating the maximum elastic potential energy and the work lost per cycle of vibration due to irreversible heat conduction. Analysis on TED at the vibration patterns of meridional wave number m = 1 and the circumferential wave number n = 2 or 3 where the shell resonators typically operate is carried out. The analytically calculated TED results are compared with those of the finite element method (FEM) to verify the feasibility and correctness of the present method. The influences of the geometrical parameters on the TED characteristics of the hemi-ellipsoidal shells with variable thickness are analyzed in detail. A meaningful discovery is that compared with the hemispherical shell, the hemi-ellipsoidal shell with variable thickness has a smaller TED when its semiminor axis is shorter than the semimajor axis, which is particularly significant for optimizing the design of the shell resonators with high quality factors.
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厚度可变半椭圆形壳体的热弹性阻尼特性
热弹性阻尼(TED)是一种基本的耗散机制,不可避免地存在于具有高品质因数的壳谐振器中。与半球形壳体相比,厚度可变的半椭圆形壳体表现出更低的 TED,本文基于热能法,展示了一种有效的 TED 表征方法。通过汉密尔顿原理和假定模态法建立了无夹紧边界条件下半椭圆形壳的运动方程,并通过求解特征值问题得到了厚度可变的半椭圆形壳的固有频率和模态振型函数。通过求解沿径向的热传导方程获得温度场,并通过计算不可逆热传导导致的最大弹性势能和每个振动周期的功损失,提出了厚度可变的半椭圆形壳体的 TED 分析模型。在壳体谐振器通常工作的经向波数 m = 1 和周向波数 n = 2 或 3 的振动模式下,对 TED 进行了分析。分析计算的 TED 结果与有限元法(FEM)的结果进行了比较,以验证本方法的可行性和正确性。详细分析了几何参数对厚度可变的半椭圆形壳的 TED 特性的影响。一个有意义的发现是,与半球形壳相比,厚度可变的半椭圆形壳的半主轴短于半长轴时,其 TED 更小,这对于优化设计具有高品质因数的壳谐振器尤为重要。
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来源期刊
Applied Mathematical Modelling
Applied Mathematical Modelling 数学-工程:综合
CiteScore
9.80
自引率
8.00%
发文量
508
审稿时长
43 days
期刊介绍: Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.
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