Free vibration of rubber matrix cord-reinforced combined shells of revolution under hydrostatic pressure

2021 ◽  
pp. 1-21
Author(s):  
Gao Hua ◽  
Shuai Changgeng ◽  
Ma Jianguo ◽  
Xu Guomin
Keyword(s):  
Hydrostatic Pressure ◽  
Free Vibration ◽  
Spherical Shell ◽  
Transfer Matrix ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Rubber Matrix ◽  
Shells Of Revolution ◽  
Related Field ◽  
Relationship Of

Abstract In this paper, the free vibration of rubber matrix cord-reinforced combined shells of revolution under hydrostatic pressure is investigated by the precise transfer matrix method. Under hydrostatic pressure, deformation and stress is generated in the rubber matrix composite shell. Based on the deformation characteristics of the rope structure, the deformation of the shell under hydrostatic pressure is analyzed. The stress of shell under hydrostatic pressure is included in the shell differential equation of motion in the form of pre-stress. Then considering the fluid-solid coupling boundary condition, the field transfer matrix of fluid-filled spherical shell is obtained. By the continuous condition of the state vector of the shell and the transformation relationship of the coordinate system, the transfer matrices at the position of the ring-stiffener and the connection position of the cylindrical shell and spherical shell are derived, and then the whole free vibration equation of the fluid-filled combined shells of revolution is assembled, and the natural frequencies are obtained by the boundary conditions. Eventually, the accuracy and reliability of the proposed method are verified by the results of literature and simulation results. Effects of the structural parameters of the spherical shell, the distribution of the ring-stiffeners, and the hydrostatic pressure on the natural frequencies of the fluid-filled combined shells of revolution are also discussed. Results of this paper can provide reference data for future studies in related field.

scholarly journals Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping

2012 ◽  
Vol 19 (6) ◽  
pp. 1167-1180 ◽  
Author(s):  
A.M. Yu ◽  
Y. Hao
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Axial Deformation ◽  
Cross Sectional ◽  
Helical Springs

Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45) in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical helical springs than that of cylindrical helical springs, which should be taken into consideration in the free vibration analysis of such springs.

A Method for the Calculation of Natural Frequencies of Orthotropic Axisymmetrically Loaded Shells of Revolution

1994 ◽  
Vol 116 (1) ◽  
pp. 16-25 ◽  
Author(s):  
A. Kayran ◽  
J. R. Vinson ◽  
E. Selcuk Ardic
Keyword(s):  
Numerical Integration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Shell Of Revolution ◽  
Initial Stresses ◽  
Integration Technique ◽  
Shells Of Revolution ◽  
Axisymmetric Loading

A methodology is presented for the calculation of the natural frequencies of orthotropic axisymmetrically loaded shells of revolution including the effect of transverse shear deformation. The fundamental system of equations governing the free vibration of the stress-free shells of revolution are modified such that the initial stresses due to the axisymmetric loading are incorporated into the analysis. The linear equations on the vibration about the deformed state are solved by using the transfer matrix method which makes use of the multisegment numerical integration technique. This method is commonly known as frequency trial method. The solution for the initial stresses due to axisymmetric loading is omitted; since the application of the transfer matrix method, making use of multisegment numerical integration technique for both linear and nonlinear equations are available in the literature. The method is verified by applying it to the solution of the natural frequencies of spinning disks, for which exact solutions exist in the literature, and a deep paraboloid for which approximate solutions exist. The governing equations for a shell of revolution are used to approximate circular disks by decreasing the curvature of the shell of revolution to very low values, and good agreement is seen between the results of the present method and the exact solution for spinning disks and the approximate solution for a deep paraboloid.

Research on Vibration and Instability of the Double-Span Beam Base on Transfer Matrix

2009 ◽  
Vol 16-19 ◽  
pp. 160-163 ◽  
Author(s):  
Ting Liu ◽  
Fei Feng ◽  
Ya Zhe Chen ◽  
Bang Chun Wen
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Axial Compression ◽  
Axial Force ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Euler Beam ◽  
Intermediate Support ◽  
Critical Axial Force

The vibration and instability of a beam which is Double-span Euler Beam with axial force is studied by transfer matrix method. The transfer matrix of transverse free vibration and axial compression of the beam is derived. Then based on the assembled transferring matrix, the effect of the position of intermediate support on the natural frequencies and Euler critical axial force of the beam is discussed, which offered a useful method to start research of vibration of complicated framework.

Effect of Semi-Geodesic Winding on the Vibration Characteristics of Filament Wound Shells of Revolution

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
Altan Kayran ◽  
Can Serkan İbrahimoğlu
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Vibration Modes ◽  
Integration Technique ◽  
Shells Of Revolution ◽  
Spherical Shells ◽  
Filament Wound ◽  
Winding Angle ◽  
Dominant Parameter

The effect of semigeodesic winding on the free vibration characteristics of filament wound shells of revolution is studied. For this purpose multisegment numerical integration technique is extended to the solution of the free vibration problem of composite shells of revolution which are wound along the semigeodesic fiber paths counting on the preset friction used during the winding process. Sample results are obtained for truncated conical and spherical shells of revolution and the effect of preset friction on the vibration characteristics of filament wound shells of revolution is particularly analyzed. Results show that when the preset friction is increased natural frequencies of higher circumferential vibration modes also increase irrespective of the initial winding angle, and the circumferential bending stiffness stands out as the dominant parameter governing the natural frequencies of higher circumferential vibration modes.

scholarly journals The free vibration characteristics of isotropic coupled conical-cylindrical shells based on the precise integration transfer matrix method

2017 ◽  
Vol 4 (1) ◽  
pp. 272-287
Author(s):  
Fuzhen Pang ◽  
Chuang Wu ◽  
Hongbao Song ◽  
Haichao Li
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Shell Thickness ◽  
Natural Frequencies ◽  
Integration Method ◽  
Vibration Characteristics ◽  
Precise Integration

Abstract Based on the transfer matrix theory and precise integration method, the precise integration transfer matrix method (PITMM) is implemented to investigate the free vibration characteristics of isotropic coupled conicalcylindrical shells. The influence on the boundary conditions, the shell thickness and the semi-vertex conical angle on the vibration characteristics are discussed. Based on the Flügge thin shell theory and the transfer matrix method, the field transfer matrix of cylindrical and conical shells is obtained. Taking continuity conditions at the junction of the coupled conical-cylindrical shell into consideration, the field transfer matrix of the coupled shell is constructed. According to the boundary conditions at the ends of the coupled shell, the natural frequencies of the coupled shell are solved by the precise integration method. An approach for studying the free vibration characteristics of isotropic coupled conical-cylindrical shells is obtained. Comparison of the natural frequencies obtained using the present method with those from literature confirms the validity of the proposed approach. The effects of the boundary conditions, the shell thickness and the semivertex conical angle on vibration characteristics are presented.

Free Vibration of a Point-Supported Spherical Shell

1985 ◽  
Vol 52 (4) ◽  
pp. 890-896 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
Y. Muramoto
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Lagrangian Multiplier ◽  
Legendre Functions ◽  
Associated Legendre Functions ◽  
Lagrangian Multiplier Method

An analysis is presented for the free vibration of an elastically or a rigidly point-supported spherical shell. For this purpose, the deflection displacements of the shell are written in a series of the products of the associated Legendre functions and the trigonometric functions. The dynamical energies of the shell are evaluated, and the frequency equation is derived by the Ritz method. For a rigidly point-supported shell, the Lagrangian multiplier method is conveniently employed. The method is applied to a closed spherical shell supported at equispaced four points located along a parallel of latitude; the natural frequencies and the mode shapes are calculated numerically, and the effects of the point supports on the vibration are studied.

scholarly journals Similitude Analysis on Mechanical Parameters of Thin Walled Shells

2011 ◽  
Vol 2-3 ◽  
pp. 936-941 ◽  
Author(s):  
Gao Ming Qin ◽  
Hai Yang Duan ◽  
Zhong Luo ◽  
Qing Kai Han
Keyword(s):  
Free Vibration ◽  
Scaling Laws ◽  
Natural Frequencies ◽  
Numerical Data ◽  
Fundamental Parameters ◽  
Thin Walled ◽  
Relationship Of ◽  
The Relationship ◽  
Finite Method ◽  
Walled Cylinder

The relationship of the kinetic fundamental parameters for both the prototype and model are derived by employing the finite method. Based on the relations, the scaling laws of the thin walled cylinder for the free vibration are found by applying the similitude transformation to the governing equation. In the absence of the experimental data, the validity of the scaling laws is testified by numerical data. This is done by calculating theoretically the natural frequencies for free vibration of the cylinders. By substituting the model frequencies in the scaling laws, the frequencies of the prototype are obtained. Consequently, the frequencies of the model and prototype are compared. Examples that one end of the thin walled shell is clamped and the other is simply supported show exact agreement.

scholarly journals Loading Performance of a Novel Shearer Drum Applied to Thin Coal Seams

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 358
Author(s):  
Kuidong Gao ◽  
Xiaodi Zhang ◽  
Liqing Sun ◽  
Qingliang Zeng ◽  
Zhihai Liu
Keyword(s):  
Rotational Speed ◽  
Production Efficiency ◽  
Loading Rate ◽  
Positive Impact ◽  
Structural Parameters ◽  
Helix Angle ◽  
Structure Design ◽  
Coal Seams ◽  
Coal Particles ◽  
Relationship Of

The poor loading performance of shearer drums restricts the development and production efficiency of coal in thin coal seams. Changing operation and structural parameters can improve the drum’s loading performance to some extent, but the effect is not obvious. A two-segment differential rotational speed drum (TDRSD) was proposed after analyzing the drum’s influence mechanism on coal particles. To further reveal the drum’s coal loading principle, the velocity, particles distribution, and loading rate were analyzed. The effect of the matching relationship of the rotational speed and helix angle between the front and rear drum are also discussed. The results show that a lower front drum rotational speed had a positive impact on improving the loading performance, and the loading rate first increases and then decreases with the increase in rear drum rotational speed. The optimal loading performance was obtained in the range 60–67.5 rpm. The front drum’s helix angle had no evident effect on loading performance, and the loading rate increase with the increase in the rear drum’s helix angle. The results provide a reference and guidance for operation parameters selection, structure design, and drum optimization.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

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