Use of the Symmetries in the Study of Vibration Response of a Hollow Cylinder

The paper studies the vibration response of an elastic solid that has geometric symmetries. These determine special properties of the equations of motion of such a system, presented in the case of a cylindrical body (hollow cylinder). The properties of the eigenvalues and eigenmodes of these systems are theoretically established. A validation of these results is made using the finite element method. The use of the obtained results can lead to an easing of the vibration analysis of such a system and, consequently, to the decrease of the cost related to the design and manufacture of such a structure. The properties presented and demonstrated in the paper can simplify the numerical calculation and experimental verifications of such a structure. Serving these symmetries, the computation cost decrease substantially and will depend not in the number of the identical parts.

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New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Mathematics ◽

10.3390/math8091401 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1401 ◽

Cited By ~ 1

Author(s):

Sorin Vlase ◽

Adrian Eracle Nicolescu ◽

Marin Marin

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Equations Of Motion ◽

Classical Mechanics ◽

Three Dimensional ◽

Elastic Solid ◽

The Finite Element Method ◽

Governing Equations ◽

Element Analysis ◽

Elastic Multibody System

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

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

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.3007908 ◽

2008 ◽

Vol 4 (1) ◽

Cited By ~ 38

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.

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On the Dynamic Analysis of Curved and Twisted Cylinders Transporting Fluids

Journal of Pressure Vessel Technology ◽

10.1115/1.3454351 ◽

1976 ◽

Vol 98 (2) ◽

pp. 143-150 ◽

Cited By ~ 40

Author(s):

R. W. Doll ◽

C. D. Mote

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Dynamic Analysis ◽

Vibration Analysis ◽

Equations Of Motion ◽

The Finite Element Method ◽

Spectra Analysis ◽

Variable Curvature ◽

End Conditions ◽

Linear Oscillation

The longitudinal, torsional and 2-transverse equations of motion are formulated for the titled problem through application of Hamilton’s Principle. Curvature-torsion conditions under which linear oscillation in a plane can exist are identified. The finite element method with isoparametric elements is used for discretization prior to spectra analysis. Natural frequency calculations over a range of mass transport velocities and cylinder end conditions were carried out for comparison with constant and variable curvature analyses and experiment. These results support the application of the constant curvature, inextensible centerline model for curved cylinder vibration analysis.

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Free Vibration Analysis of Rotating Functionally Graded Beams Using the p-Version of the Finite Element Method

Oct. 17-19, 2017 Dubai (UAE) ◽

10.15242/dirpub.dir1017402 ◽

2018 ◽

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Functionally Graded ◽

The Finite Element Method ◽

Element Method

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Vibration Analysis of a Screw Pump Unit

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.753-755.1727 ◽

2013 ◽

Vol 753-755 ◽

pp. 1727-1730

Author(s):

Yue Zhang ◽

You Hong Xiao ◽

Jun Weng ◽

Wan You Li

Keyword(s):

Mathematical Method ◽

Vibration Analysis ◽

Vibration Spectrum ◽

Vibration Response ◽

Fe Model ◽

Force Response ◽

Pump Unit ◽

Surface Integral ◽

Screw Pump

In this paper, the vibration of a three screw pump was studied. Firstly the vibration response of the pump was tested. Then the FE model of the pump was constructed and the modals of it were calculated. The exactness of the result was confirmed by the testing modals and the reasonable of the FE model was verified at the same time. Finally, the force acted on rotors due to pressure was calculated by the mathematical method of surface integral. The force was loaded on the FE model and the force response was predicted, which represented the basic vibration of the screw pump. Based on the work above, the vibration spectrum of the screw pump was analyzed.

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Uncertain Structural Free Vibration Analysis With Non-Probabilistic Spatially Varying Parameters

ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg ◽

10.1115/1.4041501 ◽

2019 ◽

Vol 5 (2) ◽

Author(s):

Jinwen Feng ◽

Qingya Li ◽

Alba Sofi ◽

Guoyin Li ◽

Di Wu ◽

...

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Natural Frequencies ◽

Free Vibration Analysis ◽

Spatial Dependency ◽

The Finite Element Method ◽

Engineering Structures ◽

Spatially Varying ◽

Computational Strategy ◽

Bounded System

The uncertain free vibration analysis of engineering structures with the consideration of nonstochastic spatially dependent uncertain parameters is investigated. A recently proposed concept of interval field is implemented to model the intrinsic spatial dependency of the uncertain-but-bounded system parameters. By employing the appropriate discretization scheme, evaluations of natural frequencies for engineering structures involving interval fields can be executed within the framework of the finite element method. Furthermore, a robust, yet efficient, computational strategy is proposed such that the extreme bounds of natural frequencies of the structure involving interval fields can be rigorously captured by performing two independent eigen-analyses. Within the proposed computational analysis framework, the traditional interval arithmetic is not employed so that the undesirable effect of the interval overestimation can be completely eliminated. Consequently, both sharpness and physical feasibility of the results can be guaranteed to a certain extent for any discretized interval field. The plausibility of the adopted interval field model, as well as the feasibility of the proposed computational scheme, is clearly demonstrated by investigating both academic-sized and practically motivated engineering structures.

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Performance analysis of retrofit R410a refrigerant with R32 refrigerant on a split air conditioner

Journal of Applied Mechanical Engineering and Green Technology ◽

10.31940/jametech.v2i1.2459 ◽

2021 ◽

Vol 2 (1) ◽

pp. 1-4

Author(s):

I Nengah Ardita ◽

◽

I Gusti Agung Bagus Wirajati ◽

I Dewa Made Susila ◽

Sudirman Sudirman ◽

...

Keyword(s):

System Performance ◽

Air Conditioning ◽

Quantitative Description ◽

Air Conditioner ◽

Experimental Equipment ◽

Evaporation Heat ◽

Before And After ◽

Common Group ◽

The Cost ◽

Design And Manufacture

Split air conditioning (AC) is the most widely used in the community for both commercial and domestic utilities. At the present refrigerant which used in Split AC is mostly common group of HFCs, such as R410a. R410a is a zeotropic refrigerant and if there is a leak in the system, it cannot be added this refrigerant. This will increase the cost of maintenance. The aims of this research is to investigate the retrofit of R410a with R32 on the Split AC system. The R32 is chosen because it has higher latent evaporation heat at the same temperature and has less effect on global warming. The refrigeration effect, the power consumption and the system performance are the main three quantities that want to be examined in this research which are observed before and after retrofit. Experimental investigation conducted during this research, including design and manufacture of experimental equipment, calibration and tools installment, collecting the experimental data and analysis by quantitative description method before and after retrofit. The results informed that cooling effect increased during the research, but the COP system has a slight decrease about 4%. R32 refrigerant is quite feasible as a retrofit refrigerant to R410a refrigerant.

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