Research on Analytic Solution Strategies for 3-DOF Modal Analysis
A solution strategy based on analytical methods was studied for the fast solution of 3-DOF modal analysis problem of complex structures.On the basis of analyzing the difficulties in solving modal problems,an analytical solution approach for 3-DOF modal analysis was proposed.At the same time,the analytical solution methods for polynomial and trigonometric trans-formations of cubic equations were systematically reviewed,and their respective applicability was discussed.Through the anal-ysis of typical calculation examples,it can be seen that polynomial substitution and trigonometric substitution have the same solution results for three different real solutions,and the result form of trigonometric substitution is more concise.In addition,for fourth and fifth degree equations,polynomial substitution and factorization methods can be used to solve.For the modal analysis of the counterweight mechanism of an ultrasonic machining machine tool,an analytical solution can be obtained based on the triangular substitution method,and a maximum error is 1.5％compared to the binary numerical solution.The analytical solution method provides a method for the digital twinning of modal analysis while ensuring computational accuracy.
万方数据
维普
