摘要
为提高印刷电路板(Printed Circuit Board,简称PCB)的避振性能,对具有两阶频率约束的某电路板设计方法及解的存在性进行了研究。基于APDL语言建立该问题的有限元模型,采用Block Lanczos方法求解固有频率,选用双变量切比雪夫多项式拟合了前两阶固有频率的响应面。通过分析约束频率的边界曲线得到了可行解的存在性判据,并据此将原含有振动微分方程的优化问题转为等式约束极值问题,在保证精度的同时提高了求解效率。给出的算例表明,该方法合理有效,可作为工程中求解类似具有频率约束问题的参考。
In order to avoid vibration failure,an optimization design method with frequency constraints of printed circuit board is studied as well as its solution existence.Firstly,a dynamic FEM model of the printed circuit board is established based on APDL language in ANSYS and its natural frequencies are calculated by using the Block Lanczos method.Then,the response surfaces are fitted by the Chebyshev series X/Y bivariate polynomials equations within 5% relative error.It is detected that the feasible solution region of the problem is besieged by two sets of projection curves of the boundary frequencies.Finally,in order to cut down the time consumption of computing,the original problem with complex differential equation of vibration is translated into a simple form.The computing method is validated by an example at last.The method studied in this paper may be used for reference for solving the similar engineering optimization problem which has frequency constraints.
出处
《振动．测试与诊断》
EI
CSCD
2008年第1期31-34,共4页
Journal of Vibration,Measurement & Diagnosis
基金
国防预研基金资助项目(编号:51421060505DZ0155)
陕西省自然科学基金资助项目(编号:2005A009)
关键词
频率约束
优化设计
响应面方法
切比雪夫多项式
frequency constraints optimum design response surface method Chebyshev polynomial
