| Thin plates are widely used in various engineering structures.It is prone to vibration under the action of the excitation load,and cause adverse impact on the engineering structure.In ships,aerospace and other engineering fields,one or more instruments and equipment are often installed on the thin plate.When the equipments and instruments work,excessive vibration of the thin plate may be caused,which may affect its normal operation.In this paper,based on the modal theory,the large-scale nonlinear finite element analysis software Abaqus is used to study the periodic concentrated loads,periodic concentrated loads with additional mass,and the vibration characteristics and dynamic response of thin plates subjected to surface loads.The thickness,different length-width ratios,different natural frequencies,natural vibration modes,kinetic kinetic energy spectrum,displacement spectrum,etc.of the thin plate at different loading positions are analyzed and studied.The distribution characteristics of vibration characteristics and dynamic response,and various influencing factors are given.And the vibration design method for equipment and equipment layout is put forward,which provides theoretical basis and numerical verification for the design and installation of instrument equipment in the thin plate in the project.The research content of this article includes:(1)The free vibration control equations of thin rectangular plates,the natural frequency and natural mode equations of the simply supported thin plate and the forced vibration equation of the simply supported thin plate under cyclic loading are introduced.(2)Based on Abaqus software,the natural frequencies and natural mode shapes of the simply-supported rectangular thin plate are extracted.The dynamic responses in the frequency domain with different plate thicknesses、loading positions and structural damping under periodic concentrated loads are analyzed.The influence of surface load on vibration characteristics and dynamic response of thin plates with different operating areas is analyzed;the modal analysis method is used to explain the abrupt change of the kinetic energy of the thin plate during the increase of the load interaction area.According to the modal superposition theory,it is found that when multiple loads act on specific positions,the modes can be generated.The cancellation effect is proposed by controlling the loading phase of the periodic loading phase and load to achieve modal cancellation.A vibration reduction design method is proposed to protect the engineering structure from the influence of vibration hazards.Using the symmetry/anti-symmetry of each mode,a symmetric loading method and an improved symmetric loading method are proposed.By adjusting the phase,the thin plate vibration generated by periodic loads at different frequencies is controlled and designed.(3)For thin plates with larger mass points,the vibration characteristics of the natural frequencies and natural modes of thin plates with different additive masses,different plate thicknesses,and different positions are studied.The effect of additional mass,plate thickness and mass point position on the kinetic energy of thin plate in the frequency domain of periodic load is obtained.The vibration characteristics and dynamic response of the thin plate were studied when several devices on the thin plate were working at the same time.The result of the research shows that the thin plate vibration damping can be achieved by using the symmetrical loading method. |
