A General Method to Study the Sound Radiation of a Finite Cylindrical Shell Based on Elastic Theory

A general method was proposed to study the sound and vibration of a finite cylindrical shell with elastic theory. This method was developed through comprehensive analysis of the uncoupled Helmholtz equation obtained by the decomposition of elastic equations and the structure of the solution of a finite cylindrical shell analyzed by thin shell theory. The proposed method is theoretically suitable for arbitrary thickness of the shell and any frequency. Also, the results obtained through the method can be used to determine the range of application of the thin shell theory. Furthermore, the proposed method can deal with the problems limited by the thin shell theory. Additionally, the method can be suitable for several types of complex cylindrical shell such as the ring-stiffened cylindrical shell, damped cylindrical shell, and double cylindrical shell.

Exact free vibration analysis of open circular cylindrical shells by the method of reverberation-ray matrix

This paper is concerned with the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitrary classical boundary conditions. Based on the Donnell-Mushtari-Vlasov thin shell theory, an analytical solution of the traveling wave form along the simply supported edges and the modal wave form along the remaining two edges is obtained. With such a unidirectional traveling wave form solution, the method of the reverberation-ray matrix is introduced to derive the equation of natural frequencies of the shell with different classical boundary conditions. The exact solutions for natural frequencies of the open circular cylindrical shell are obtained with the employment of a golden section search algorithm. The calculation results are compared with those obtained by the finite element method and the methods in the available literature. The influence of length, thickness, radius, included angle, and the boundary conditions of the open circular cylindrical shell on the natural frequencies is investigated. The exact calculation results can be used as benchmark values for researchers to check their numerical methods and for engineers to design structures with thin shell components.

Motion equations of hemispherical resonator and analysis of frequency split caused by slight mass non-uniformity

The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass non-uniformity and frequency split,which can provide a theoretical basis for mass balance of imperfect resonator.The starting point of error mechanism analysis for gyroscope is the motion equations of resonator.Firstly,based on the Kirchhoff-Love hypothesis in the elastic thin shell theory,the geometric deformation equations of resonator are deduced.Secondly,the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell.Thirdly,the kinetic energy equation of resonator is deduced by the Coriolis theorem.Finally,the motion equations of resonator are established by the Lagrange mechanics principle.The theoretical values of precession factor and natural frequency are calculated by the motion equations,which are substantially consistent with the ones by the finite element method and practical measurement,the errors are within a reasonable range.Simultaneously,the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis.The above conclusions prove the correctness and rationality of motion equations.Similarly,the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping,and the state equations with respect to the velocity and displacement of vibration system are derived,then twonatural frequencies are solved by the characteristic equation.It is concluded that one of reasons for frequency split is the 4 th harmonic of mass non-uniformity,and thus much attention should be paid to minimizing the 4 th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.

Standing wave drift of hemispherical resonator with quality factor non-uniformity under a ring electrode excitation

Hemispherical Resonator Gyroscope(HRG)is a classical high precision Coriolis Vibration Gyroscope(CVG),which performs attitude estimation of carrier by detecting the precession of standing wave of resonator,thus,the drift of standing wave of resonator has a great influence on the output accuracy of gyroscope,where the quality factor non-uniformity of resonator is one of main error sources.Ring electrode is a classical excitation structure of HRG because the standing wave can precess freely under its excitation,which makes the gyroscope have more accurate scale factor,larger measurement range and better dynamic characteristics.In this paper,the equations of motion of an ideal resonator excited by a ring electrode are derived by the elastic thin shell theory and Lagrange mechanical principle,then the corresponding equivalent mechanical model is established.According to the“average method”,it can be seen that the ideal resonator excited by the ring electrode works in integral mode,and any position in the circumferential direction of resonator can be a working point,which means that the quality factor non-uniformity has a great effect on the drift of standing wave.Therefore,the equations of motion of resonator with quality factor non-uniformity under the ring electrode excitation are deduced by the equivalent mechanical model,and the drift model of standing wave is established by the“average method”,it can be found that both the amplitude of quality factor non-uniformity and angle between the“inherent damping axis”and antinode axis of standing wave can affect the drift rate of standing wave.Moreover,the drift model indicates that if the input angular rate does not reach the threshold,the precession angular rate of standing wave will appear“self-locking”phenomenon,that is,the gyroscope will lose the integral effect.

Recent Development of Pressure Vessel Technology in China——Formulation of Chinese Design Code by Analysis

This paper is a summarized account of the Chinese professional stantard—JB4732 Steel Pressure Vessels—Design by Analysis. As compared with similar standards in other countries, there are some features in elastic plastic analysis of pressure vessels and their components in JB4732. Three of them are introduced in brief. It includes: flat head design method considering plastic carrying capactities of structures; a reinforcement design method based on limit analysis of spherical shells with nozzles and the calculation method of stress concentration factors of two intersecting cylindrical shells with d/D≤0 7 based on an analytical solution.