In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The ...In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The study of plate behavior is a very sensitive subject because it is part of the structural elements. The study of the dynamic behavior of free vibration structures is done by modal analysis in order to calculate natural frequencies and modal deformations. In this paper, we present the modal analysis of a thin rectangular plate simply supported. The analytical solution of the differential equation is obtained by applying the method of separating the variables. We are talking about the exact solution of the problem to the limit values. However, numerical methods such as the finite element method allow us to approximate these functions with greater accuracy. It is one of the most powerful computational methods for predicting dynamic response in a complex structure subject to arbitrary boundary conditions. The results obtained by MEF through Ansys 15.0 are then compared with those obtained by the analytical method.展开更多
The wavelet finite element methods （WFEMs） own higher calculation accuracy and efficiency for structure analysis. Unfortunately, the existing WFEMs are still limited in low-frequency domain when capturing dynamic ch...The wavelet finite element methods （WFEMs） own higher calculation accuracy and efficiency for structure analysis. Unfortunately, the existing WFEMs are still limited in low-frequency domain when capturing dynamic characteristics of thin plate. This paper proposes the wavelet multi-elements method based on C1 type B-spline Kirchhoff plate （CIBKP） element to break up this limitation. The validity, numerical stability and convergence respectively are investigated systematically in numerical study. The corresponding results show that the calculation accuracy and numerical stability are very excellent when predicting the high-order natural frequency. The maximum relative errors can be rapidly reduced to 0.4% within the first 1000 modes of thin plate under simply supported. Besides, the method is suitable for predicting the dynamic characteristics of thin plate under various boundary conditions.展开更多
文摘In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The study of plate behavior is a very sensitive subject because it is part of the structural elements. The study of the dynamic behavior of free vibration structures is done by modal analysis in order to calculate natural frequencies and modal deformations. In this paper, we present the modal analysis of a thin rectangular plate simply supported. The analytical solution of the differential equation is obtained by applying the method of separating the variables. We are talking about the exact solution of the problem to the limit values. However, numerical methods such as the finite element method allow us to approximate these functions with greater accuracy. It is one of the most powerful computational methods for predicting dynamic response in a complex structure subject to arbitrary boundary conditions. The results obtained by MEF through Ansys 15.0 are then compared with those obtained by the analytical method.
基金supported by the National Natural Science Foundation of China(Nos.51405370&51225501)the National Basic Research Program of China(Grant No.2015CB057400)the Project Funded by China Postdoctoral Science Foundation(Grant No.2016T90908)
文摘The wavelet finite element methods （WFEMs） own higher calculation accuracy and efficiency for structure analysis. Unfortunately, the existing WFEMs are still limited in low-frequency domain when capturing dynamic characteristics of thin plate. This paper proposes the wavelet multi-elements method based on C1 type B-spline Kirchhoff plate （CIBKP） element to break up this limitation. The validity, numerical stability and convergence respectively are investigated systematically in numerical study. The corresponding results show that the calculation accuracy and numerical stability are very excellent when predicting the high-order natural frequency. The maximum relative errors can be rapidly reduced to 0.4% within the first 1000 modes of thin plate under simply supported. Besides, the method is suitable for predicting the dynamic characteristics of thin plate under various boundary conditions.
