| Modal analysis is a widely used technology in engineering and research.As a way to predict and control the structural noise,it is based on the theory of vibration mechanics and experimental measurements.With the promotion of new types of sandwich materials,acoustic metamaterials and partially-damped materials,a large amount of non-proportional damping exists on the structure,thereby stimulating complex modal phenomena.Different states of damping will cause different complex modals,therefore,numerous modal complexity parameters were created to describe the degree of ‘complex'.People are paying more and more attention to the acoustic comfort of structures.Laws and regulations relating to cabin noise,environmental noise,construction noise,etc.are also increasingly stringent to protect human and ecological safety and improve life quality.Therefore,the problem of structural sound radiation and parametric measurement under complex mode also deserves special attention.In this paper,the history of complex modal analysis is comprehensively and exhaustively reviewed and introduced,and the focus is placed on the parametric measurement of the modal complexity and structural acoustic radiation characteristics of flat plate structures.This paper introduces the Mindlin theory based on the finite element method giving the analytical formula to calculate the natural frequencies and natural modes.Results calculated by Fortran are compared with the analytical solutions to verify the correctness of coding..In this paper,the accuracy of conventional method by using the first two order control frequencies to determine the proportional coefficients in Rayleigh damping model is reconsidered and discussed.According to the basic properties of the damping ratio function,the trend of the damping ratio is predicted and ‘virtual standard' is proposed.All the possible pairs of control frequencies are calculated,and according to ‘virtual standard deviation',the control frequency combination with low dispersion degree and multiple calculation orders is selected.This paper focuses on the complexity parameters as well as solutions to complex modes.Three parameters,which are most widely used in modal analysis,are calculated to verify the complex modal characteristics of cantilever beam with highly non-proportional damping.From the point of acoustic radiation power,a new parameter ‘AMSC' is proposed to measure acoustic properties of structures with complex modes.Different damping are applied on rectangular steel plates.The modal complexity and acoustic radiation characteristics are investigated to verify the validity and reliability of the new parameters.In this paper,ANSYS and COMSOL are used in simulation.Both of their advantages and disadvantages,the accuracy of calculated results and the operation of building a nonproportional damping model are briefly introduced. |
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