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.

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 Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method

2017 ◽  
Vol 39 (3) ◽  
pp. 215-228 ◽  
Author(s):  
Tran Van Lien ◽  
Ngo Trong Duc ◽  
Nguyen Tien Khiem
Keyword(s):  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Theoretical Development ◽  
Mode Shapes ◽  
Functionally Graded Beam ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Fgm Beam

Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.

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 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.

Dynamic Analysis of Rotating Beams with Nonuniform Cross Sections Using the Dynamic Stiffness Method

2001 ◽  
Vol 123 (4) ◽  
pp. 536-539 ◽  
Author(s):  
K. J. Huang ◽  
T. S. Liu
Keyword(s):  
Dynamic Analysis ◽  
Cross Sections ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Equation Of Motion ◽  
The Finite Element Method ◽  
Rotating Beam ◽  
Rotating Beams ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

This study develops dynamic analysis based on the dynamic stiffness method for a rotating beam of nonuniform cross-section. To deal with nonuniform beams, coefficients related to material and geometric properties in the equation of motion are expressed in a polynomial form. A dynamic stiffness matrix is accordingly formulated in terms of power series. The dynamic response of the rotating beam is calculated by performing modal analysis. It is demonstrated that the present method provides an alternative to the finite element method in dealing with nonuniform rotating beams.

scholarly journals Dynamic Analysis for an Internally Coupled Fluid/Riser System

2010 ◽  
Author(s):  
Yongming Cheng ◽  
J. Kim Vandiver
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Vibration Absorber ◽  
Theoretical Formulation ◽  
System A ◽  
Concentric Cylinders ◽  
Effective Dynamic ◽  
Fluid Coupling

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. A top-tensioned riser generally consists of outer casing, inner casing and tubing. The pipes are coupled either through fluids in the annuli or through intermediate guides (centralizers) or through both. This paper investigates the dynamic analysis for such an internally coupled fluid/ riser system. This paper first presents a theoretical formulation for a general riser system coupled with fluids in the annuli and centralizers between pipes. Hydrodynamic forces associated with the viscous fluid in between concentric cylinders are considered. An effective dynamic stiffness matrix method is then developed to evaluate the added mass and damping influence of the fluid on the natural frequencies and the dynamic response of the coupled riser system. A riser example is used to illustrate the fluid coupling impact on the system’s dynamic performance. The coupling through the fluid and centralizers can be optimally designed such that an inner pipe acts as a vibration absorber to the outer casing.

The Dynamic Stiffness Method for Linear Rotor-Bearing Systems

1996 ◽  
Vol 118 (3) ◽  
pp. 332-339 ◽  
Author(s):  
F. A. Raffa ◽  
F. Vatta
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Matrix Analysis ◽  
Theoretical Formulation ◽  
Dynamic Stiffness Matrix ◽  
Rotor Systems ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Rotor Bearing

The behavior of linear rotor-bearing systems is investigated by using the exact approach of the dynamic stiffness method, which entails the use of continuous rather than lumped models. In particular, the theoretical formulation for rotor systems with anisotropic bearings is developed by utilizing the complex representation of all the involved variables. The proposed formulation eventually leads to the 8 × 8 complex dynamic stiffness matrix of the rotating Timoshenko beam; this matrix proves to be related, by a simple rule, to the 4 × 4 dynamic stiffness matrix, which describes rotor systems with isotropic bearings. The method is first applied to the critical speeds evaluation of a simple rotor system with rigid supports; for this case, the exact results of the dynamic stiffness approach are compared to the usual convergence procedure of the finite element method. Successively, the steady-state unbalance response of two rotor systems with anisotropic supports is analyzed; for these examples, the dynamic stiffness results compare favorably with the results of the finite element and the transfer matrix analysis performed by other authors.

Dynamic Analysis for a Pipe-in-Pipe Riser System

2012 ◽  
Author(s):  
Yongming Cheng ◽  
Tao Qi ◽  
Xiaoxian Chen
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Element Model ◽  
Theoretical Formulation ◽  
Concentric Cylinders ◽  
Effective Dynamic ◽  
Steel Catenary Risers ◽  
Offshore Industry ◽  
Model Approach

A Pipe-In-Pipe (PIP) riser system is widely used in the offshore industry. A typical top tensioned riser system consists of an outer casing, inner casing and tubing. A PIP thermal insulation technology is often used to satisfy stringent insulation requirements and to maintain an acceptable global performance for pipe-in-pipe steel catenary risers. This paper investigates dynamic analysis for a PIP riser system. This paper first presents a theoretical formulation for a PIP riser system coupled with fluids in the annuli and centralizers between pipes. Hydrodynamic forces associated with the viscous fluid in between concentric cylinders are considered. An effective dynamic stiffness matrix method is then developed to evaluate the added mass and damping influence of the fluid on the natural frequencies and the dynamic response of the coupled riser system. The composite model approach is commonly used for modeling concentric PIP riser systems. In reality, however, the riser pipes may contact with the outer pipe at the connectors and centralizers under dynamic loading. This paper then discusses a detailed PIP finite element model to capture the coupling effects of centralizers with gaps. Examples are used to illustrate the dynamic behavior of a PIP riser system. The first example shows the frequency response of a PIP riser coupled through the fluid in the annulus and centralizers distributed longitudinally. The second one represents a PIP riser system coupled through centralizers with gaps. The analysis was performed by using the FEA program ABAQUS.

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