Nonlinear Vibration Reduction Analysis And Dynamic Optimization Of Plates Attached A Concentrated Mass

Plate structures are widely used in aeronautics and astronautics;ocean engineering;machinery and electronic engineering;vehicle engineering;building construction and so on.Compared with traditional mechanical structure,plate structures are lighter and smaller,which can save lots of material.However,the large amplitude vibration of thin plates are more easily aroused by the external excitation.In this dissertation,the dynamic model of plate with a concentrated mass was established to research vibration characteristic and the influence of concentrated masses on vibration reduction.Especially,the main content of the dissertation is generalized as follows:(1)Based on the classical thin plate theory and von Karman nonlinear theory,the dynamic partial differential equations of rectangular plates with simple-supported boundary and a lumped mass were presented by Hamilton principle.Then,the single-mode and double-mode truncation are carried out by Galerkin method to gain the nonlinear dynamic control equations.Finally,introducing the frequency coordinate parameters,the primary amplitude-frequency curves under single-mode and first-order,second-order amplitude-frequency curves under double-mode were drawn out through the method of multiple scale.(2)To research the influence of concentrated masses on vibration reduction,the process was divided into three steps:(a)for the single-mode truncation,the relationship between concentrated masses and primary amplitude-frequency curves were researched;(b)for the double-mode truncation,the condition of 1:3 internal resonance was found and the influence of deviation from 1:3 internal resonance on second-order amplitude-frequency curves caused by internal resonance were studied;and(c)considering the above two situations,the difference of the amplitude-frequency curve with and without internal resonance were compared.Finally,using the vibration synchronization and the features of extreme points on amplitude-frequency curves,the mechanism analysis for amplitude modification arising from mass was investigated,which provides a concrete method to control the vibration.(3)In order to verify the established model,the phenolic moulding plate with a mass was experimented including impulse text and basic incentive test.In the paper,due to the lack of laboratory instruments,the method of approximate analogy was used to verify experiment.Specifically,with the finite element software as link,the correct of the model could be verified in another way.