不同质量块布局双端固支梁的等效弹簧系数的热效应

摘要

Thermal effect on the equivalent spring constants of double-clamped beams (bridges) with two kinds of mass arrangements including central mass and side mass were studied by theoretical analysis and finite element simulation. An equation to describe the change of the equivalent spring constants of beams due to temperature variation was derived and the equivalent spring constants from simulation results of the fundamental vibration frequency and the displacement under a static loadwere obtained respectively by the finite element analysis. Results show that the temperature variation has an important effect on the equivalent spring constants.For the fundamental vibration frequency,there are a good agreement between the derived equation and the vibration simulation results for the both structures. For the displacement under a static load, the asymmetry in mass arrangement results in the bending of the beam when temperature shifts,and the bending causes a displacement of the mass to the side. As a result, the asymmetric arrangement of mass changes the initial displacement of mass when temperature varies, which would cause the changes of output signals for Micro Electro Mechanic System (MEMS) sensors or actuators.%通过理论研究和有限元仿真分析了热效应对两种不同质量块布局的双端固支梁的等效弹簧系数的影响,两种质量块分别布局为质量块与梁对称布置和质量块位于梁平面一侧布置. 推导了双端固支梁等效弹簧系数随温度的变化公式,仿真分析了双端固支梁-质量块系统的一阶固有频率以及质量块在静载荷作用下的位移.通过固有频率及载荷-位移两种方式,分别得到了两种布局下的质量系统在不同温度下的等效弹簧系数.对于质量块对称布置和单侧布置,根据一阶固有频率得到的等效弹簧系数随温度的变化与理论分析都吻合;而利用载荷-位移得到的等效弹簧系数随温度的变化,需要对位移进行修正.计算结果表明,对于质量块位于梁一侧的系统,温度变化对其等效弹簧系数有重要影响,质量块的不对称会在温度变化时产生对梁的弯矩作用,从而使质量块产生位移,造成微机电传感器和执行器输出信号的改变.