质量块-悬挂梁热弹性阻尼的L-R理论适用性

Applicability of L-R Theory for Thermoelastic Damping of Mass Suspension Beam Structure

摘要:

热弹性阻尼是谐振器中的一种基本能量耗散机制,决定了高Q谐振器的性能极限。检测质量块-悬挂支撑梁结构由于截面的变化,难以进行解析求解。已有研究表明,质量块刚性假设后,经典的L-R理论可以适用于该结构,然而该假设相对于实际器件所造成的计算误差却没有结论。针对这一问题,采用L-R理论计算与ANSYS有限元计算的对比分析方法,比较了在支撑梁和质量块尺度分别变化时的一阶固有频率和该频率下热弹性阻尼系数的计算误差,结果表明,L-R理论的计算误差较大,并不适用于质量块-悬挂支撑梁结构热弹性阻尼系数的精确计算,但可有效估计尺度变化后热弹性阻尼的变化趋势。

Abstract:

Thermoelastic damping is a basic energy dissipation mechanism in the resonator, which determines the performance limit of high Qresonator. Testing the mass suspension support beam is difficult to solve analytically due to the variation of the cross section. Studies have shown that the classical L-R theory can be applied to the structure after the mass rigidity assumptions, yet the assumptions with respect to calculation error caused by the actual device is inconclusive. To solve this problem, a comparative analysis between the L-R calculation and ANSYS finite element analysis method was used to compare the first-order intrinsic frequency and the calculated error of thermoelastic damping coefficients at this frequency when the scales of the support beam and mass block were varied respectively. The results show that the calculation error of L-R theory is too large to calculate thermoelastic damping coefficient of mass suspension beam structure accurately, but it can estimate the change trend of thermoelastic damping effectively when the scale changes.