Vibration Analysis Of Circular Plates Structures With Complex Boundary Conditions

Circular thin plates structures with complex boundary conditions are widely applied in various engineering fields such as mechanical engineering,aeronautics and astronautics,and ocean engineering.It is of great importance both in practice and theory to investigate the structural vibration characteristics of circular plates structures.As an important parameter affecting the vibration characteristics of the structure,boundary conditions have an important role in the active control of structural vibration.However,at present the research on the vibration characteristics of the circular plate structures,mainly focused on the classical boundary conditions of vibration modeling,and less involved with elastic boundary conditions.Therefore this paper will propose an improved Fourier-Bessel series method which is based on the traditional Fourier-Bessel series method to study the vibration of circular plate structure under the elastic boundary conditions.The specific research work is as follows:A unified free vibration analysis model of isotropic circular plate structure with complex boundary conditions is built.The improved method of Fourier-Bessel series of structural vibration displacement function will be described as a standard form of Fourier-Bessel series and ancillary items.At the same time using a linear displacement boundary uniformly distributed spring and torsion springs constraints to simulate complex boundary conditions,so that we can set a different spring rates to get a different complex boundary.Based on energy principles Rayleigh-Ritz method we will establish the matrix equation of the free vibration of isotropic circular plate structure with complex boundary conditions.The numerical results and the comparisons with those reported in the literature are presented to validate the correct of the method.Research and construct a forced vibration model of isotropic circular plate structure with complex boundary conditions.Isotropic circular plate structures are discussed in detail in the frequency domain and time domain harmonic dynamics and transient response characteristics.In the structure of harmonic response analysis,we introduce the complex Young's modulus to solve the structural frequency response characteristics of the Fourier-Bessel series based on improved methods and Rayleigh-Ritz method.In the transient dynamic analysis,we introduce Ritz damping theory to obtain structural response characteristics in the time domain based on the implicit Newmark algorithm iterative format.Promote the improved method of Fourier-Bessel series method,and establish vibration analysis model of orthotropic circular plate structure with complex boundary conditions.The improved method of Fourier-Bessel series of structural vibration displacement function will be described,according to the Rayleigh-Ritz method for free vibration characteristics of orthotropic circular plate structure,harmonic and transient response characteristics of the dynamic characteristics of the solution.Finally we compare with the literature and finite element numerical results to verify the correctness of the model in this paper.At last,experimental setups of circular plates with free and clamped boundary conditions are designed and respectively.The natural frequencies and mode shapes for experimental setups are obtained.By comparing the results with these theoretical results,the correctness of the method proposed in this dissertation is verified from the perspective of the experiment.