Dynamic Response of Cracked Cylindrical Shells With Internal Pressure

2002 ◽  
Author(s):  
A. Vaziri ◽  
H. Nayeb-Hashemi ◽  
H. E. Estekanchi
Keyword(s):  
Dynamic Response ◽  
Internal Pressure ◽  
Nodal Point ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Resonant Frequencies ◽  
Crack Location ◽  
Theoretical Investigations ◽  
Axial Crack ◽  
Internal Pressures

Sub-surface cracks in pipelines with internal pressure may severely affect their dynamic response. The extreme cases of these cracks are when these cracks go through the thickness of the pipes. Dynamic responses of cracked and un-cracked pipes with fixed ends and under various internal pressures were evaluated experimentally and theoretically. In the experimental part, the effects of pipe internal pressure on the resonant frequencies and damping of the pipe were evaluated. In the theoretical part, finite element analyses were performed to find dynamic response of pipes with various crack length and orientation respect to the axis of the pipe. The experimental results showed resonant frequencies of the pipe are little sensitive to the pipe internal pressure. Similar results were obtained from the theoretical investigations. An axial crack had little effect on the pipe resonant frequencies. In contrast, cracks oriented at an angle to the axis of the pipe had a pronounced effect on some of the resonant frequencies of the pipe. This depended on the crack location in a particular mode shapes. For frequencies where the nodal point of the mode shape was located on the crack region, the frequencies were not significantly affected by the presence of the crack in the pipe. Furthermore, it was observed that the pipe internal pressure had little effect on the resonant frequencies of the cracked pipes.

Minimizing Dynamic Response of Counter-Rotating Engines Through Optimized Node Placement

2010 ◽  
Author(s):  
Peter D. Hylton
Keyword(s):  
Nodal Point ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Rotating System ◽  
Node Placement ◽  
Location Optimization ◽  
Bending Mode ◽  
Node Location ◽  
Rotor Balancing ◽  
Additional Reduction

It has been previously proposed that a low-speed rotor balancing procedure can be suitable for supercritical shafting (GT2008-50077). That paper documented the necessity of taking into account nodal locations in the bending mode shapes of a supercritical rotor when designing an optimum balance process for such a rotor. This is due to the fact that balance correction forces (or for that matter, any forces) have the least impact when applied near the nodes of a particular mode. This result led to consideration that node location optimization could help with another issue, i.e. the excitation of backward excited whirl modes in a counter-rotating system. When designing a two rotor gas turbine, there are distinct advantages to having the two rotors turn in opposite directions. Among these are the ability to shorten and lighten the engine by reducing the length of the engine since a row of static turning vanes can be eliminated. The engine can be further lightened by inclusion of an inter-shaft bearing which eliminates static bearing support structure. Additional reduction in gyroscopic maneuver loads and deflections can also be achieved, thus resulting in multiple benefits to a counter-rotating system with an inter-shaft bearing. Unfortunately, the excitation of backward whirl modes of one rotor, which would normally not be a major concern in a co-rotating engine, can be a significant issue when excited in such a counter-rotating engine through the inter-shaft bearing, which serves as a conduit for forces from the other rotor. However, the logic of the earlier statement regarding the effectiveness of forces applied at, or near, a nodal point led to the hypothesis that optimizing the nodal locations relative to the interface points between the rotors could minimize the responsiveness of the system. This led to the hypothesis that by optimizing the node placement relative to the inter-shaft bearing, it should be possible to minimize the excitation of the backward modes. This paper examines that proposition and demonstrates that considering this aspect during the design of such an engine could lead to significant benefit in terms of minimized dynamic responses.

A Dynamic Investigation of Piping Systems With a Bolted Flange

2002 ◽  
Author(s):  
William H. Semke ◽  
George D. Bibel ◽  
Sukhvarsh Jerath ◽  
Sanjay B. Gurav ◽  
Adam L. Webster
Keyword(s):  
Dynamic Response ◽  
High Strength ◽  
Mode Shapes ◽  
Piping System ◽  
Resonant Frequencies ◽  
Experimental Procedure ◽  
Piping Systems ◽  
Response Output ◽  
Bolted Flange ◽  
Dynamic Investigation

The dynamic response of piping systems with a bolted flange is analyzed. Experimental and numerical analyses and results are presented and show excellent correlation. An overhanging piping system at various span lengths with a flange at mid-length is used. The testing configuration consists of a standard 2-in. (51 mm) schedule 40 steel pipe and an ANSI B16.5 class 300-pound flange. The presence of a spiral wound wire gasket and high strength flange bolts is also assessed. Included are multiple resonant frequencies and their respective mode shapes for various span lengths and gasket configurations. The experimental procedure utilizes an accelerometer to gather the dynamic response output of the piping system due to an impulse. The resonant frequencies are then determined using a Fast Fourier Transform (FFT) method. The numerical analysis is conducted using the commercial Finite Element (FE) code ANSYS®. Both methods take into account the complex interaction between the flange and gasket and their impact on the entire piping system. The dynamic effects of a bolted flange and gasket on a piping system are critical in their use and a summary of the results for a variety of configurations is presented.

scholarly journals Transfer matrix formulation for dynamic response of Timoshenko beams resting on two-parameter elastic foundation subjected to moving load

2021 ◽  
Vol 4 (2) ◽  
pp. 99-110
Author(s):  
Baran Bozyigit
Keyword(s):  
Dynamic Response ◽  
Shear Layer ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Moving Load ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Winkler Foundation ◽  
Foundation Model ◽  
Two Parameter

In this study, the dynamic response of beams resting on two-parameter elastic foundation subjected to moving load is investigated by using the transfer matrix method (TMM). The Timoshenko beam theory (TBT) which considers shear deformation and rotational inertia is used to model the beam. The two-parameter elastic foundation model is selected as Pasternak foundation that takes into account a shear layer at the end of linear springs of Winkler foundation. The TMM which uses the relation between analytically obtained state vectors of each end of the beam is applied to solve the free vibration problem. After performing the free vibration analysis, the mathematical model is simplified into an equivalent single degree of freedom (SDOF) system by using the exact mode shapes to obtain dynamic responses. The generalized displacement is calculated for each mode by using the Runge-Kutta algorithm. A numerical case study is presented for a simply-supported Timoshenko beam on the Pasternak foundation subjected to a concentrated load. The natural frequencies obtained from finite element method (FEM) results of SAP2000 are presented with the results of TMM for comparison purposes using the Winkler foundation. The effects of shear layer on the natural frequencies of the model are revealed. The mode shapes are plotted. The proposed approach for calculating dynamic responses is validated by using the results of FEM for Winkler foundation model. Then, the effects of Winkler springs and shear layer of the foundation model on the dynamic responses are presented in figures. The effects of modal damping are discussed. Finally, the critical velocities for the model are calculated for various elastic foundation scenarios and the effects of elastic foundation parameters on the dynamic response of beam model subjected to moving load with high velocity are observed.

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

Dynamic Response of Spiral Cantilever Undergoing Magnetic Coupling

2014 ◽  
Vol 14 (08) ◽  
pp. 1440021
Author(s):  
Xiaoling Bai ◽  
Yumei Wen ◽  
Ping Li ◽  
Jin Yang ◽  
Xiao Peng ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Cantilever Beam ◽  
Magnetic Force ◽  
Coupling Effect ◽  
Magnetic Coupling ◽  
Resonant Frequencies ◽  
Energy Harvesters ◽  
Magnetic Transducer ◽  
Underlying Mechanisms ◽  
Tip Mass

Cantilever beams have found intensive and extensive uses as underlying mechanisms for energy transduction in sensors as well as in energy harvesters. In magnetoelectric (ME) transduction, the underlying cantilever beam usually will undergo magnetic coupling effect. As the beam itself is either banded with magnetic transducer or magnets, the dynamic motion of the cantilever can be modified due to the magnetic force between the magnets and ME sensors. In this study, the dynamic response of a typical spiral cantilever beam with magnetic coupling is investigated. The spiral cantilever acts as the resonator of an energy harvester with a tip mass in the form of magnets, and a ME transducer is positioned in the air gap and interacts with the magnets. It is expected that this spiral configuration is capable of performing multiple vibration modes over a small frequency range and the response frequencies can be magnetically tunable. The experimental results show that the magnetic coupling between the magnets and the transducer plays a favorable role in achieving tunable resonant frequencies and reducing the frequency spacings. This will benefits the expansion of the response band of a device and is especially useful in energy harvesting.

3-D elastic coupling vibration and acoustical radiation characteristics of cracked gear under elastic support condition

2015 ◽  
Vol 23 (9) ◽  
pp. 1548-1568 ◽  
Author(s):  
Shao Renping ◽  
Purong Jia ◽  
Xiankun Qi
Keyword(s):  
Dynamic Response ◽  
Support System ◽  
Three Dimensional ◽  
Elastic Support ◽  
Dynamic Responses ◽  
Tooth Root ◽  
Support Condition ◽  
Elastic Boundary ◽  
Root Crack ◽  
Elastic Disc

According to the actual working condition of the gear, the supporting gear shaft is treated as an elastic support. Its impact on the gear body vibration is considered and investigated and the dynamic response of elastic teeth and gear body is analyzed. On this basis, the gear body is considered as a three-dimensional elastic disc and the gear teeth are treated as an elastic cantilever beam. Under the conditions of the elastic boundary (support shaft), combining to the elastic disk and elastic teeth, the influence of three-dimensional elastic discs on the meshing tooth response under an elastic boundary condition is also included. A dynamic model of the gear support system and calculated model of the gear tooth response are then established. The inherent characteristics of the gear support system and dynamics response of the meshing tooth are presented and simulated. It was shown by the results that it is correct to use the elastic support condition to analyze the gear support system. Based on the above three-dimensional elastic dynamics analysis, this paper set up a dynamics coupling model of a cracked gear structure support system that considered the influence of a three-dimensional elastic disc on a cracked meshing tooth under elastic conditions. It discusses the dynamic characteristic of the cracked gear structure system and coupling dynamic response of the meshing tooth, offering a three-dimensional elastic body model of the tooth root crack and pitch circle crack with different sizes, conducting the three-dimensional elastic dynamic analysis to the faulty crack. ANSYS was employed to carry out dynamic responses, as well as to simulate the acoustic field radiation orientation of a three-dimensional elastic crack body at the tooth root crack and pitch circle with different sizes.

Evaluation of the Dynamic-Response-Based Intact Stability Criterion for Floating Wind Turbines

2015 ◽  
Author(s):  
Marco Masciola ◽  
Xiaohong Chen ◽  
Qing Yu
Keyword(s):  
Wind Speed ◽  
Dynamic Response ◽  
Wind Turbines ◽  
Stability Criterion ◽  
Area Ratio ◽  
Operating Conditions ◽  
Dynamic Responses ◽  
Stability Criteria ◽  
Intact Stability ◽  
Overturning Moment

As an alternative to the conventional intact stability criterion for floating offshore structures, known as the area-ratio-based criterion, the dynamic-response-based intact stability criteria was initially developed in the 1980s for column-stabilized drilling units and later extended to the design of floating production installations (FPIs). Both the area-ratio-based and dynamic-response-based intact stability criteria have recently been adopted for floating offshore wind turbines (FOWTs). In the traditional area-ratio-based criterion, the stability calculation is quasi-static in nature, with the contribution from external forces other than steady wind loads and FOWT dynamic responses captured through a safety factor. Furthermore, the peak wind overturning moment of FOWTs may not coincide with the extreme storm wind speed normally prescribed in the area-ratio-based criterion, but rather at the much smaller rated wind speed in the power production mode. With these two factors considered, the dynamic-response-based intact stability criterion is desirable for FOWTs to account for their unique dynamic responses and the impact of various operating conditions. This paper demonstrates the implementation of a FOWT intact stability assessment using the dynamic-response-based criterion. Performance-based criteria require observed behavior or quantifiable metrics as input for the method to be applied. This is demonstrated by defining the governing load cases for two conceptual FOWT semisubmersible designs at two sites. This work introduces benchmarks comparing the area-ratio-based and dynamic-response-based criteria, gaps with current methodologies, and frontier areas related to the wind overturning moment definition.

scholarly journals Damage Diagnosis in 3D Structures Using a Novel Hybrid Multiobjective Optimization and FE Model Updating Framework

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Nizar Faisal Alkayem ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Structural Damage ◽  
Model Updating ◽  
Complex Problem ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Fe Model ◽  
Modal Strain Energy ◽  
3D Structures ◽  
Multiobjective Particle Swarm Optimization ◽  
Damage Tracking

Structural damage detection is a well-known engineering inverse problem in which the extracting of damage information from the dynamic responses of the structure is considered a complex problem. Within that area, the damage tracking in 3D structures is evaluated as a more complex and difficult task. Swarm intelligence and evolutionary algorithms (EAs) can be well adapted for solving the problem. For this purpose, a hybrid elitist-guided search combining a multiobjective particle swarm optimization (MOPSO), Lévy flights (LFs), and the technique for the order of preference by similarity to ideal solution (TOPSIS) is evolved in this work. Modal characteristics are employed to develop the objective function by considering two subobjectives, namely, modal strain energy (MSTE) and mode shape (MS) subobjectives. The proposed framework is tested using a well-known benchmark model. The overall strong performance of the suggested method is maintained even under noisy conditions and in the case of incomplete mode shapes.

Experimental Investigation on the Dynamic Response of a Three Legged Articulated Type Offshore Wind Tower

2016 ◽  
Author(s):  
Chinsu Mereena Joy ◽  
Anitha Joseph ◽  
Lalu Mangal
Keyword(s):  
Dynamic Response ◽  
Wind Turbine ◽  
Renewable Energy Sources ◽  
Offshore Structures ◽  
Dynamic Responses ◽  
Offshore Wind ◽  
Experimental Investigations ◽  
Offshore Wind Turbine ◽  
Ocean Engineering ◽  
Study Results

Demand for renewable energy sources is rapidly increasing since they are able to replace depleting fossil fuels and their capacity to act as a carbon neutral energy source. A substantial amount of such clean, renewable and reliable energy potential exists in offshore winds. The major engineering challenge in establishing an offshore wind energy facility is the design of a reliable and financially viable offshore support for the wind turbine tower. An economically feasible support for an offshore wind turbine is a compliant platform since it moves with wave forces and offer less resistance to them. Amongst the several compliant type offshore structures, articulated type is an innovative one. It is flexibly linked to the seafloor and can move along with the waves and restoring is achieved by large buoyancy force. This study focuses on the experimental investigations on the dynamic response of a three-legged articulated structure supporting a 5MW wind turbine. The experimental investigations are done on a 1: 60 scaled model in a 4m wide wave flume at the Department of Ocean Engineering, Indian Institute of Technology, Madras. The tests were conducted for regular waves of various wave periods and wave heights and for various orientations of the platform. The dynamic responses are presented in the form of Response Amplitude Operators (RAO). The study results revealed that the proposed articulated structure is technically feasible in supporting an offshore wind turbine because the natural frequencies are away from ocean wave frequencies and the RAOs obtained are relatively small.

scholarly journals Dynamic Response of a Cracked Rotor With Some Comments on Crack Detection

1994 ◽  
Author(s):  
G. Meng ◽  
Eric J. Hahn
Keyword(s):  
Dynamic Response ◽  
Crack Detection ◽  
Harmonic Component ◽  
Major Axis ◽  
Vertical Axis ◽  
Crack Size ◽  
Cracked Rotor ◽  
Response Component ◽  
Crack Location ◽  
Backward Whirl

By considering time dependent terms as external excitation forces, the approximate dynamic response of a cracked horizontal rotor is analysed theoretically and numerically. The solution is good for small cracks and small vibrations in the stable operating range. For each steady state harmonic component the forward and backward whirl amplitudes, the shape and orientation of the elliptic orbit and the amplitude and phase of the response signals arc analysed, taking into account the effect of crack size, crack location, rotor speed and unbalance. It is found that the crack causes backward whirl, the amplitude of which increases with the crack. For a cracked rotor, the response orbit for each harmonic component is an ellipse, the shape and orientation of which depends on the crack size. The influence of the crack on the synchronous response of the system can be regarded as an additional unbalance whereupon, depending on the speed and the crack location, the response amplitude differs from that of the uncracked rotor. The nonsynchronous response provides evidence of crack in the sub-critical range, but is too small to be detected in the supercritical range. Possibilities for crack detection over the full speed range include the additional average (the constant) response component, the backward whirl of the response, the ellipticity of the orbit, the angle between the major axis and the vertical axis and the phase angle difference between vertical and horizontal vibration signals.

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