双稳振动能量收集器件的随机响应分析及结构优化设计

发布时间：2018-08-24 13:54

【摘要】：双稳振动能量收集器件有高的能量转化效率,并且对载荷及结构参数的变化具有鲁棒性,因此特别适于收集真实环境中的宽带能量。本文首先建立高斯白噪声激励下双稳振动能量收集器件随机响应的半解析分析技术,而后,在此基础上,完成浅球壳型和柱壳型双稳振动能量收集器件的结构优化设计,建立普适设计图线。在随机响应分析方面,发展了两步近似技术处理耦合的非线性随机微分方程组。收集电路对机械子系统的影响由修正的保守机制和耗散机制替换,通过引入广义谐和变换导出相应于原始耦合系统的修正机械系统。人为设定一个非线性随机系统族,其中任一系统均有解析的稳态概率密度；以与修正机械系统均方差最小为准则,在非线性随机系统族中,确立修正机械系统的等效非线性系统。从而,由等效非线性系统的各统计量近似原始耦合系统的响应统计。在结构优化设计方面,分别研究了浅球壳型及柱壳型两类典型结构形式的双稳振动能量收集器件。首先,应用假设模态法和拉格朗日方程法,导出结构的非线性随机微分方程。采用稳态期望穿阈率描述壳体结构的跳变频率,并分别选取浅球壳处于底圆位置和柱壳顶端处于由两固定直线边界所确定的平面位置时的应变能为参考应变能,衡量每次跳变相应的可收集能量。以稳态期望穿阈率与参考应变能的乘积构造可收集功率概念,以可收集功率最大为目标,导出最优的无量纲几何参数和相应的可收集功率。
[Abstract]:Bistable vibrational energy collection devices have high energy conversion efficiency and are robust to changes in load and structural parameters, so they are especially suitable for collecting broadband energy in real environment. In this paper, the semi-analytical analysis technique of random response of bistable vibration energy collection device excited by Gao Si white noise is established, and then, the structure optimization design of shallow spherical shell and cylindrical shell bistable vibration energy collection device is completed. Set up universal design drawing line. In the aspect of stochastic response analysis, a two-step approximation technique is developed to deal with coupled nonlinear stochastic differential equations. The influence of the collection circuit on the mechanical subsystem is replaced by the modified conservative mechanism and dissipative mechanism, and the modified mechanical system corresponding to the original coupling system is derived by introducing the generalized harmonic transformation. A family of nonlinear stochastic systems is artificially set, in which each system has an analytic steady-state probability density, and the minimum mean square error of the modified mechanical system is taken as the criterion in the family of nonlinear stochastic systems. The equivalent nonlinear system of modified mechanical system is established. Thus, each statistic of the equivalent nonlinear system approximates the response statistics of the original coupled system. In the aspect of structural optimization, bistable vibration energy collection devices with shallow spherical shell and cylindrical shell are studied. Firstly, the nonlinear stochastic differential equations of structures are derived by using the assumed mode method and Lagrange equation method. The steady-state expected threshold rate is used to describe the hopping frequency of shell structure, and the strain energy of shallow spherical shell in the bottom circle position and the cylindrical shell top in the plane position determined by two fixed linear boundaries is selected as the reference strain energy, respectively. Measure the amount of energy that can be collected for each jump. The concept of collectable power is constructed based on the product of steady-state expected threshold rate and reference strain energy. The optimal dimensionless geometric parameters and the corresponding collectable power are derived with the maximum collectable power as the target.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TM619

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