scholarly journals Dynamic stiffness method for free vibrations analysis of partial fluid-filled orthotropic circular cylindrical shells

2015 ◽  
Vol 37 (1) ◽  
pp. 43-56
Author(s):  
Tran Ich Thinh ◽  
Nguyen Manh Cuong ◽  
Vu Quoc Hien
Keyword(s):  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Cylindrical Shells ◽  
Computational Cost ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Various Boundary Conditions ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Circular Cylindrical Shells

Free vibrations of partial fluid-filled orthotropic circular cylindrical shells are investigated using the Dynamic Stiffness Method (DSM) or Continuous Element Method (CEM) based on theFirst Order Shear Deformation Theory (FSDT) and non-viscous incompressible fluid equations. Numerical examples are given for analyzing natural frequencies and harmonic responses of cylindrical shells partially and completely filled with fluid under various boundary conditions. The vibration frequencies for different filling ratios of cylindrical shells are obtained and compared with existing experimental and theoretical results which indicate that the fluid filling can reduce significantly the natural frequencies of studiedcylindrical shells. Detailed parametric analysis is carried out to show the effects of some geometrical and material parameters on the natural frequencies of orthotropic cylindrical shells. The advantages of this current solution consist in fast convergence, low computational cost and high precision validating for all frequency ranges.

scholarly journals Comparison Study on the Exact Dynamic Stiffness Method for Free Vibration of Thin and Moderately Thick Circular Cylindrical Shells

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Xudong Chen ◽  
Kangsheng Ye
Keyword(s):  
Free Vibration ◽  
Dynamic Stiffness ◽  
Cylindrical Shells ◽  
High Accuracy ◽  
Radius Ratio ◽  
Comparison Study ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Circular Cylindrical Shells ◽  
Thick Shells

Comparison study on free vibration of circular cylindrical shells between thin and moderately thick shell theories when using the exact dynamic stiffness method (DSM) formulation is presented. Firstly, both the thin and moderately thick dynamic stiffness formulations are examined. Based on the strain and kinetic energy, the vibration governing equations are expressed in the Hamilton form for both thin and moderately thick circular cylindrical shells. The dynamic stiffness is assembled in a similar way as that in classic skeletal theory. With the employment of the Wittrick-Williams algorithm, natural frequencies of circular cylindrical shells can be obtained. A FORTRAN code is written and used to compute the modal characteristics. Numerical examples are presented, verifying the proposed computational framework. Since the DSM is an exact approach, the advantages of high accuracy, no-missing frequencies, and good adaptability to various geometries and boundary conditions are demonstrated. Comprehensive parametric studies on the thickness to radius ratio (h/r) and the length to radius ratio (L/r) are performed. Applicable ranges of h/r are found for both thin and moderately thick DSM formulations, and influences of L/r on frequencies are also investigated. The following conclusions are reached: frequencies of moderately thick shells can be considered as alternatives to those of thin shells with high accuracy where  h/r is small and L/r is large, without any observation of shear locking.

scholarly journals Dynamic Stiffness Analysis of Curved Thin-Walled Beams

1993 ◽  
Vol 1 (1) ◽  
pp. 77-88 ◽  
Author(s):  
A.Y.T. Leung ◽  
W.E. Zhou
Keyword(s):  
Present Method ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
High Accuracy ◽  
Stiffness Analysis ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Out Of Plane ◽  
Thin Walled

The natural vibration problem of curved thin-walled beams is solved by the dynamic stiffness method. The dynamic stiffness of a curved open thin-walled beam is given. The computed natural frequencies of the beam are compared with those obtained by a completely analytical method to show the high accuracy of the present method. The interaction of in-plane and out-of-plane modes is emphasized.

scholarly journals Free Vibration Analysis for Shells of Revolution Using an Exact Dynamic Stiffness Method

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Xudong Chen ◽  
Kangsheng Ye
Keyword(s):  
Free Vibration ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Fortran Program ◽  
Shells Of Revolution ◽  
Governing Equations ◽  
Arbitrary Boundary ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Circular Cylindrical Shells

An exact generalised formulation for the free vibration of shells of revolution with general shaped meridians and arbitrary boundary conditions is introduced. Starting from the basic shell theories, the vibration governing equations are obtained in the Hamilton form, from which dynamic stiffness is computed using the ordinary differential equations solver COLSYS. Natural frequencies and modes are determined by employing the Wittrick-Williams (W-W) algorithm in conjunction with the recursive Newton’s method, thus expanding the applications of the abovementioned techniques from one-dimensional skeletal structures to two-dimensional shells of revolution. A solution for solving the number of clamped-end frequenciesJ0in the W-W algorithm is presented for both uniform and nonuniform shell segment members. Based on these theories, a FORTRAN program is written. Numerical examples on circular cylindrical shells, hyperboloidal cooling tower shells, and spherical shells are given, and error analysis is performed. The convergence of the proposed method onJ0is verified, and comparisons with frequencies from existing literature show that the dynamic stiffness method is robust, reliable, and accurate.

EXACT VIBRATION FREQUENCIES AND MODES OF BEAMS WITH INTERNAL RELEASES

2002 ◽  
Vol 02 (01) ◽  
pp. 63-75 ◽  
Author(s):  
M. EISENBERGER
Keyword(s):  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Beam Element ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Dynamic Stiffness Matrix ◽  
Continuous Beams ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

The exact vibration frequencies of continuous beams with internal releases are found using the dynamic stiffness method. Two types of releases are considered: hinge and sliding discontinuities. First, the exact dynamic stiffness matrix for a beam element with a release is derived and then used in the assembly of the structure dynamic stiffness matrix. The natural frequencies are found as the values of frequency that make this matrix singular. Then the mode shapes are found exactly. Examples are given for continuous beams with different releases.

scholarly journals Riser Dynamic Analysis Using WKB-Based Dynamic Stiffness Method

2012 ◽  
Author(s):  
Yongming Cheng ◽  
J. Kim Vandiver
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Shape Function ◽  
Dynamic Stiffness ◽  
Mode Shapes ◽  
Marine Riser ◽  
Theoretical Formulation ◽  
Eigen Value ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

Risers are fluid conduits from subsea equipment to surface floating production platforms. The integrity of a riser system plays a very important role in deepwater developments. Riser dynamic analysis is an important part to the system design. This paper investigates riser dynamic analysis using the WKB-Based dynamic stiffness method. This paper first presents a theoretical formulation of the dynamic stiffness method. It then combines the dynamic stiffness method with the WKB theory, which assumes that the coefficients in the differential equation of motion are slowly varying. The WKB-based dynamic stiffness method is derived and a frequency dependent shape function is expressed implicitly. The Wittrick and Williams (W-W) algorithm is further extended to solve eigen value problem for a general non-uniform marine riser. Examples of non-uniform riser are analyzed and the results show the efficiency of this method. In addition, a pipe-in-pipe riser system is analyzed for natural frequencies and mode shapes using the WKB-based dynamic stiffness method with the W-W algorithm. The characteristic of the mode shapes is described for such a riser system.

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