Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades

2008 ◽  
Vol 4 (1) ◽  
Author(s):  
Akira Saito ◽  
Matthew P. Castanier ◽  
Christophe Pierre ◽  
Olivier Poudou
Keyword(s):  
Finite Element ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Vibration Response ◽  
New Method ◽  
Beam Model ◽  
Element Analysis

The efficient nonlinear vibration analysis of a rotating elastic structure with a crack is examined. In particular, the solution of the forced vibration response of a cracked turbine engine blade is investigated. Starting with a finite element model of the cracked system, the Craig–Bampton method of component mode synthesis is used to generate a reduced-order model that retains the nodes of the crack surfaces as physical degrees of freedom. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, is modeled with a piecewise linear term in the equations of motion. Then, the efficient solution procedure for solving the resulting nonlinear equations of motion is presented. The approach employed in this study is a multiharmonic hybrid frequency∕time-domain technique, which is an extension of the traditional harmonic balance method. First, a simple beam model is used to perform a numerical validation by comparing the results of the new method to those from transient finite element analysis (FEA) with contact elements. It is found that the new method retains good accuracy relative to FEA while reducing the computational costs by several orders of magnitude. Second, a representative blade model is used to examine the effects of crack length and rotation speed on the resonant frequency response. Several issues related to the rotation are investigated, including geometry changes of the crack, shifts in resonant frequencies, and the existence of multiple solutions. For the cases considered, it is found that the nonlinear vibration response exhibits the jump phenomenon only when rotation is included in the model.

Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades

2006 ◽  
Author(s):  
Akira Saito ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Finite Element ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Piecewise Linear ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
New Method ◽  
Beam Model ◽  
Element Analysis

The efficient nonlinear vibration analysis of a rotating elastic structure with a crack is examined. In particular, the solution of the forced vibration response of a cracked turbine engine blade is investigated. Starting with a finite element model of the cracked system, the Craig-Bampton method of component mode synthesis is used to generate a reduced-order model that retains the nodes of the crack surfaces as physical DOF. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, is modeled with a piecewise linear term in the equations of motion. Then, the efficient solution procedure for solving the resulting nonlinear equations of motion is presented. The approach employed in this study is a multi-harmonic, hybrid frequency/time-domain (HFT) technique, which is an extension of the traditional harmonic balance method. First, a simple beam model is used to perform a numerical validation by comparing the results of the new method to those from transient finite element analysis (FEA) with contact elements. It is found that the new method retains good accuracy relative to FEA while reducing the computational costs by several orders of magnitude. Second, a representative blade model is used to examine the effects of crack length and rotation speed on the resonant frequency response. Several issues related to the rotation are investigated, including geometry changes of the crack and the existence of multiple solutions.

Nonlinear Vibration Analysis of Gas Turbine Bladings With Shroud Coupling

2008 ◽  
Author(s):  
Andreas Hohl ◽  
Christian Siewert ◽  
Lars Panning ◽  
Andreas Kayser
Keyword(s):  
Finite Element ◽  
Nonlinear Vibration ◽  
Gas Turbine ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Forced Response ◽  
Vibrational Amplitude ◽  
Friction Forces ◽  
Mapping Procedure

Rotating blades are subjected to vibrations caused by excitation forces due to a non-homogeneous pressure field of the fluid. Therefore, damping devices like tip shrouds are implemented which reduce the vibrational amplitude and apply additional stiffness and damping to the structure. To predict the resulting vibration response and stresses, a three dimensional contact model has been developed to determine the friction forces. The resulting equations of motion are solved in the frequency domain. The developed method has been implemented in a nonlinear forced response code called DATAR designed for the gas turbine division of Siemens Energy. In this paper, the transfer of common Finite Element models of bladings with shrouds or underplatform dampers to the DATAR code is presented. A mapping procedure based on Finite Element shape functions is used to couple the model with the regular contact grid used in the nonlinear vibration analysis performed with the DATAR code. As a practical example, the vibration behavior of a gas turbine blading with interlocked shrouds is investigated with the developed method.

Nonlinear Vibration Analysis of Turbine Bladed Disks With Mid-Span Dampers

2020 ◽  
Author(s):  
Erhan Ferhatoglu ◽  
Stefano Zucca ◽  
Daniele Botto ◽  
Jury Auciello ◽  
Lorenzo Arcangeli
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Normal Load ◽  
Harmonic Balance Method ◽  
Response Prediction ◽  
Forced Response ◽  
Algebraic Equations ◽  
Friction Contact ◽  
Bladed Disks ◽  
Cyclic Symmetric

Abstract Friction dampers are one of the most common structures used to alleviate excessive vibration amplitudes in turbomachinery applications. There are very well-known types of contact elements exploited efficiently, such as underplatform dampers. However, different design approach is sometimes needed to maximize the effectiveness further. In this paper, computational forced response prediction of bladed disks with a configuration of the secondary structure commonly used by Baker Hughes design, the so-called mid-span dampers, is presented. Mid-span dampers are metal devices positioned at the middle section of the airfoil span and come into contact with the blade by the centrifugal force acting during rotation. Proposed damping mechanism is applied to a realistic steam turbine bladed disk under cyclic symmetric boundary conditions. Friction contact is modeled through a large number of contact nodes between the blade and the damper by using a 2D friction contact element with variable normal load. Harmonic Balance Method and Alternating Frequency/Time approach are utilized to obtain nonlinear algebraic equations in frequency domain and nonlinear forced response is computed by using Newton-Raphson method. The results obtained by numerical simulations show that mid-span dampers are an efficient configuration type of a damping mechanism to be used in the design of the bladed disks for nonlinear vibration analysis.

Application of ESPI in the Vibration Analysis of Turbine Blading

1995 ◽  
Author(s):  
Robert X. Wang ◽  
Graham M. Chapman
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Vibration Analysis ◽  
Speckle Pattern ◽  
Vibration Measurement ◽  
Simplified Model ◽  
Electronic Speckle Pattern Interferometry ◽  
Coupled Modes ◽  
Element Analysis ◽  
Turbine Blading

Abstract This paper reports on the application of Electronic Speckle Pattern Interferometry (ESPI) technique in vibration measurement of turbine blading. Using the time-averaged mode of ESPI, the first six modes of a turbocharger blade with airfoil profile were identified. The effect of the complicated profile of the blade was established by studying simplified model blades. Coupled modes were identified and successfully separated. Experimental results are compared with those obtained using finite element analysis.

Investigation of stiffness of small wind turbine blade based on vibration analysis technique

2019 ◽  
Vol 44 (1) ◽  
pp. 49-59
Author(s):  
Nilesh Chandgude ◽  
Nitin Gadhave ◽  
Ganesh Taware ◽  
Nitin Patil
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Element Analysis ◽  
Finite Element Software ◽  
Small Wind Turbine

In this article, three small wind turbine blades of different materials were manufactured. Finite element analysis was carried out using finite element software ANSYS 14.5 on modeled blades of National Advisory Committee for Aeronautics 4412 airfoil profile. From finite element analysis, first, two flap-wise natural frequencies and mode shapes of three different blades are obtained. Experimental vibration analysis of manufactured blades was carried out using fast Fourier transform analyzer to find the first two flap-wise natural frequencies. Finally, the results obtained from the finite element analysis and experimental test of three blades are compared. Based on vibration analysis, we found that the natural frequency of glass fiber reinforced plastic blade reinforced with aluminum sheet metal (small) strips increases compared with the remaining blades. An increase in the natural frequency indicates an increase in the stiffness of blade.

scholarly journals Nonlinear Vibration Analysis of Damaged Microplate considering Size Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jihai Yuan ◽  
Xiangmin Zhang ◽  
Changping Chen
Keyword(s):  
Size Effect ◽  
Frequency Response ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Couple Stress Theory ◽  
Harmonic Balance Method ◽  
Damage Effect ◽  
Physical Parameters ◽  
Response Curves ◽  
Electrically Actuated

Since microplates are extensively used in MEMS devices such as microbumps, micromirrors, and microphones, this work aims to study nonlinear vibration of an electrically actuated microplate whose four edges are clamped. Based on the modified couple stress theory (MCST) and strain equivalent assumption, size effect and damage are taken into consideration in the present model. The dynamic governing partial differential equations of the microplate system were obtained using Hamilton’s principle and solved using the harmonic balance method after they are transformed into ordinary differential equation with regard to time. Size effect and damage effect on nonlinear free vibration of the microplate under DC voltage are discussed using frequency-response curve. In the forced vibration analysis, the frequency-response curves were also employed for the purpose of highlighting the influence of different physical parameters such as external excitation, damping coefficient, material length scale parameter, and damage variable when the system is under AC voltage. The results presented in this study may be helpful and useful for the dynamic stability of a electrically actuated microplate system.

scholarly journals Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method

1996 ◽  
Vol 3 (4) ◽  
pp. 259-268 ◽  
Author(s):  
M.S. Yao
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Finite Amplitude ◽  
Basis Vector ◽  
Reduced Basis ◽  
Ritz Vector ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Nonlinear Equations Of Motion

The large number of unknown variables in a finite element idealization for dynamic structural analysis is represented by a very small number of generalized variables, each associating with a generalized Ritz vector known as a basis vector. The large system of equations of motion is thereby reduced to a very small set by this transformation and computational cost of the analysis can be greatly reduced. In this article nonlinear equations of motion and their transformation are formulated in detail. A convenient way of selection of the generalized basis vector and its limitations are described. Some illustrative examples are given to demonstrate the speed and validity of the method. The method, within its limitations, may be applied to dynamic problems where the response is global in nature with finite amplitude.

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