Free Vibration Analysis Of Cylinder With Grooves

Cylinders are common structures in engineering applications and daily life.In recent years,there have been some studies on the three-dimensional vibrations of cylinders.In the study of some approximate methods,researchers have adopted Chebyshev polynomials as the admissible functions to study the 3-D vibrations of circular and annular plates and solid and hollow circular cylinders,respectively.The advantage of Chebyshev polynomials is the numerical stability,in particular as shown in the calculation of the higher-order vibration modes.Now,with a groove in the cylinder and changes of the original boundary conditions,makes it difficult to calculate as a whole,the Chebyshev polynomials will be used for the vibration analysis.Because of the change of the structure with open slits in a cylinder,the boundary conditions of the cylinder are also change.Since such changes make it difficult for the structure to use a particular displacement function to represent the overall displacement like in an ordinary cylinder,it is planned to divide the cylinder into several parts with each part is represented by a separate displacement function,and the stiffness and mass matrices are calculated by Rayleigh method.The grooved cylinder can be divided into upper and lower parts.The displacement in the contact surface is equal,and the two parts can be calculated together.By solving the characteristic equation,the characteristic frequency value of the grooved cylinder can be obtainedThe characteristic frequencies obtained from this study are in good agreement with those calculated by finite element method.The Chebyshev polynomials can not only calculate the characteristic frequency of cylinder vibration,but also calculate the characteristic frequency of cylinder vibration with the grooves by proper processing.Grooving the cylinder will have a greater impact on the vibrations of the cylinder,and the thicker the cylinder,the greater the impact of the grooves on it.