scholarly journals The effect of influence of conservative and tangential axial forces on transverse vibrations of tapered vertical columns

2017 ◽  
Vol 4 (20) ◽  
pp. 333-342
Author(s):  
Jerzy Jaroszewicz ◽  
Leszek Radziszewski ◽  
Łukasz Dragun
Keyword(s):  
Boundary Value Problem ◽  
Natural Frequency ◽  
Critical Loads ◽  
Cauchy Function ◽  
Axial Forces ◽  
Transverse Vibrations ◽  
Cantilever Length ◽  
Tangential Forces ◽  
Elastically Supported ◽  
Good Agreement

The Cauchy function and characteristic series were applied to solve the boundary value problem of free transverse vibrations of vertically mounted, elastically supported tapered cantilever columns. The columns can be subjected to universal axial point loads which considerate – conservative and follower /tangential/ forces, and to distributed loads along the cantilever length. The general form of characteristic equation was obtained taking into account the shape of tapered cantilever for attached and elastically secured. Bernstein-Kieropian double and higher estimators of natural frequency and critical loads were calculated based on the first few coefficients of the characteristic series. Good agreement was obtained between the calculated natural frequency and the exact values available in the literature.

The Study of the Effect of Static Axial Loads on Vertically-Mounted Tapered Cantilever Transverse Vibrations Using the Cauchy Function

2015 ◽  
Vol 712 ◽  
pp. 49-54 ◽  
Author(s):  
Jerzy Jaroszewicz ◽  
Leszek Radziszewski ◽  
Łukasz Dragun
Keyword(s):  
Natural Frequency ◽  
Cantilever Beams ◽  
Axial Loads ◽  
Concentrated Mass ◽  
Cauchy Function ◽  
Transverse Vibrations ◽  
Cantilever Length ◽  
Tangential Forces ◽  
Elastically Supported ◽  
Good Agreement

The Cauchy function and characteristic series were applied to solve the boundary value problem of free transverse vibrations of vertically mounted, elastically supported tapered cantilever beams. A concentrated mass was attached at the same distance from the base. The beams were subjected to universal axial loads - conservative and follow wing tangential forces - and distributed loads along the cantilever length. The general form of characteristic equation was obtained taking into account the shape of the tapered cantilever, elastic foundation and nonhomogeneous material. Bernstein-Kieropian double estimators of natural frequency were calculated based on free coefficients of the characteristic series. Good agreement was obtained between the calculated natural frequency results and the exact values available in the literature.

scholarly journals Triangular buckling patterns of twisted inextensible strips

2010 ◽  
Vol 467 (2125) ◽  
pp. 285-303 ◽  
Author(s):  
A. P. Korte ◽  
E. L. Starostin ◽  
G. H. M. van der Heijden
Keyword(s):  
Boundary Value Problem ◽  
Critical Load ◽  
Critical Loads ◽  
Equilibrium Shape ◽  
Boundary Value ◽  
Mode Number ◽  
Force Extension ◽  
Higher Modes ◽  
Post Buckling ◽  
Good Agreement

When twisting a strip of paper or acetate under high longitudinal tension, one observes, at some critical load, a buckling of the strip into a regular triangular pattern. Very similar triangular facets have recently been found in solutions to a new set of geometrically exact equations describing the equilibrium shape of thin inextensible elastic strips. Here, we formulate a modified boundary-value problem for these equations and construct post-buckling solutions in good agreement with the observed pattern in twisted strips. We also study the force–extension and moment–twist behaviour of these strips by varying the mode number n of triangular facets and find critical loads with jumps to higher modes.

scholarly journals Analysis of natural frequency of flexural vibrations of a single-span beam with the consideration of Timoshenko effect

2018 ◽  
Vol 3 (21) ◽  
pp. 215-232
Author(s):  
Jerzy Jaroszewicz ◽  
Krzysztof Łukaszewicz
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Boundary Value ◽  
Rotational Inertia ◽  
Cauchy Function ◽  
Simply Supported Beam ◽  
Good Convergence ◽  
Simply Supported ◽  
Elastic Characteristics

This paper presents general solution of boundary value problem for constant cross-section Timoshenko beams with four typical boundary conditions. The authors have taken into consideration rotational inertia and shear strain by using the theory of influence by Cauchy function and characteristic series. The boundary value problem of transverse vibration has been formulated and solved. The characteristic equations considering the exact bending theory have been obtained for four cases: the clamped boundary conditions; a simply supported beam and clamped on the other side; a simply supported beam; a cantilever beam. The obtained estimators of fundamental natural frequency take into account mass and elastic characteristics of beams and Timoshenko effect. The results of calculations prove high convergence of the estimators to the exact values which were calculated by Timoshenko who used Bessel functions. Characteristic series having an alternating sign power series show good convergence. As it is shown in the paper, the error lower than 5% was obtained after taking into account only two first significant terms of the series. It was proved that neglecting the Timoshenko effect in case of short beams of rectangular section with the ratio of their length to their height equal 6 leads to the errors of calculated natural frequency: 5%÷12%.

Investigating the vibrational behaviour of a rotating two-blade propeller by using a self-tracking method

2018 ◽  
Vol 233 (3) ◽  
pp. 835-847 ◽  
Author(s):  
Mohammad-Reza Ashory ◽  
Farhad Talebi ◽  
Heydar R Ghadikolaei ◽  
Morad Karimpour
Keyword(s):  
Natural Frequency ◽  
Measurement Errors ◽  
Mode Shapes ◽  
Model Parameters ◽  
Test Results ◽  
Modal Assurance Criterion ◽  
Tracking Method ◽  
Strong Resemblance ◽  
Test Scenarios ◽  
Good Agreement

This study investigated the vibrational behaviour of a rotating two-blade propeller at different rotational speeds by using self-tracking laser Doppler vibrometry. Given that a self-tracking method necessitates the accurate adjustment of test setups to reduce measurement errors, a test table with sufficient rigidity was designed and built to enable the adjustment and repair of test components. The results of the self-tracking test on the rotating propeller indicated an increase in natural frequency and a decrease in the amplitude of normalized mode shapes as rotational speed increases. To assess the test results, a numerical model created in ABAQUS was used. The model parameters were tuned in such a way that the natural frequency and associated mode shapes were in good agreement with those derived using a hammer test on a stationary propeller. The mode shapes obtained from the hammer test and the numerical (ABAQUS) modelling were compared using the modal assurance criterion. The examination indicated a strong resemblance between the hammer test results and the numerical findings. Hence, the model can be employed to determine the other mechanical properties of two-blade propellers in test scenarios.

Investigation of Sensitivity Effect Based on Mass and Stiffness Modification in Automobile Crankshaft

2015 ◽  
Vol 752-753 ◽  
pp. 839-844
Author(s):  
R.M.S. Zetty ◽  
B.A. Aminudin ◽  
L.M. Aung ◽  
M.K. Khalid ◽  
H.M.Y. Norfazrina ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Natural Frequency ◽  
Dynamic Characteristics ◽  
Differential Analysis ◽  
Partial Differential ◽  
Mechanical Parts ◽  
Stiffness Reduction ◽  
Experiment And Simulation ◽  
Good Agreement

A modeling through sensitivity analysis is one of the promising methods to investigate the dynamic characteristics of complex mechanical parts. This study aimed to investigate the effect of sensitivity based on mass and stiffness modification in automobile crankshaft as a function of natural frequency. Verification for the crankshaft model that is used in the experiment and simulation was done and both results showed good agreement and small errors percentage. The modification was also done by reducing the different percentage of crankshaft’s mass and stiffness. Partial differential analysis was used in the sensitivity analysis in order to figure out the natural frequency after every set of modification. According to the results, we also found that there were changes of sensitivity value by changes in mass value but the stiffness value remains unchanged. However, there is no significant effect of stiffness reduction on vibration was found in this research.

Analysis of a Natural Frequency Tracking System for MEMS Fatigue Testing

2001 ◽  
Author(s):  
Xiaotian Sun ◽  
Roberto Horowitz ◽  
Kyriakos Komvopoulos
Keyword(s):  
Control System ◽  
Natural Frequency ◽  
Averaging Method ◽  
Fatigue Testing ◽  
Tracking System ◽  
Frequency Tracking ◽  
At Resonance ◽  
Mems Resonator ◽  
Control Gain ◽  
Good Agreement

Abstract A nonlinear control system that can track the natural frequency of a MEMS resonator was developed in this study. Due to the evolution of fatigue damage, the natural frequency of the resonator decreases. To maintain the device at resonance, a phase-locked loop system is used to track the frequency decay and adjust the driving force accordingly. A model for the control system is introduced and the system behavior is analyzed using an averaging method. A quantitative criterion for selecting the control gain to achieve stability is derived from the analysis. Simulation results are shown to be in good agreement with the prediction of the theoretical analysis.

scholarly journals INFLUENCE OF INCONSTANT DISTRIBUTION OF DEADWOOD BEARING STIFFNESS COEFFICIENTON NATURAL FREQUENCY OF THE SHAFT TRANSVERSE VIBRATIONS

2019 ◽  
pp. 89-96
Author(s):  
Guriy Kushner ◽  
Victor Andreevich Mamontov
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Uniform Distribution ◽  
Natural Frequency ◽  
Stiffness Coefficient ◽  
Propeller Shaft ◽  
Shaft Length ◽  
Slide Bearing ◽  
Transverse Vibrations ◽  
Stiffness Distribution

One of the most significant factors affecting the natural frequency of transverse vibrations of shaft-slide bearing systems is the stiffness coefficient of the slide bearing. The need to consider the influence of heterogeneity of stiffness coefficient of the bearing on its natural frequency is caused by the fact that when the bearing is worn, the modulus of longitudinal elasticity of the material changes, and since the bearing wears unevenly, the non-uniform distribution of the stiffness coefficient occurs. The problem of determining the natural frequency of transverse vibrations of a ship propeller shaft based on the foundation with a variable stiffness coefficient along the length has been studied. The differential equation of the propeller shaft vibrations written taking into account the stiffness coefficient variable along the shaft length is considered. It has been noted that, in the general case, this equation is a fourth-order partial differential equation and cannot be integrated in quadratures for an arbitrary stiffness distribution function along the shaft length. A numerical-analytical method for determining the natural frequency of a system based on approximation of the stiffness distribution function by a piecewise-linear function is proposed. The method is applied to calculate the natural frequencies of the pipeline section taking into account the functions describing the change in the stiffness coefficient. The proposed method allows to consider the section of the shafting enclosed in the stern bearing, subject to the non-uniform distribution of the stiffness coefficient of the bearing, and is the basis for improving the accuracy of finding the true natural frequency of transverse vibrations of the shafting.

Vibrations of an Intermediately Supported U-Bend Tube

1975 ◽  
Vol 97 (1) ◽  
pp. 23-32 ◽  
Author(s):  
L. S. S. Lee
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Experimental Tests ◽  
Bending Stiffness ◽  
Stiffness Ratio ◽  
Plane Vibration ◽  
Straight Beam ◽  
Out Of Plane ◽  
Straight Segments ◽  
Good Agreement

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

Study on Dynamic Characteristics and Parameter Sensitivity of Three Spans Prestressed Continuous Beam

2013 ◽  
Vol 351-352 ◽  
pp. 386-391
Author(s):  
Lu Ning Shi ◽  
Hao Xiang He ◽  
Wei Ming Yan ◽  
Yan Jiang Chen ◽  
Da Zhang
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Frequency Equation ◽  
Dynamic Parameters ◽  
Continuous Beam ◽  
Analytical Expression ◽  
Beam Dynamic ◽  
Frequency Sensitivity ◽  
The Impact ◽  
Good Agreement

Established the three spans prestressed continuous beam dynamic equation, obtained analytical expression of frequency equation. To solve the frequency equation for natural frequency, and compared with the finite element numerical analysis results, the frequency both with analytical expression and with finite element are in good agreement. The formula can be obtained accurately the dynamic parameters of three spans prestressed continuous beam such as frequency. At the same time, the paper also studied the natural frequency sensitivity analysis of three spans prestressed continuous beam, and focuses on the impact on the frequency with effective prestress and prestressed eccentricity.

The Use of Vibration as a Means of Industrial Drive

1947 ◽  
Vol 157 (1) ◽  
pp. 20-31
Author(s):  
C. A. M. Thornton
Keyword(s):  
Natural Frequency ◽  
Transverse Vibration ◽  
Vibration Amplitude ◽  
Electrical Excitation ◽  
Advantages And Disadvantages ◽  
Transverse Vibrations ◽  
Industrial Drive ◽  
The Subject ◽  
And Control

The application of vibration as a means of industrial drive has been considerably developed in the last twenty years. Starting from the obvious application of screening, it has been extended to conveying, heat interchanging, consolidation of material in packages to reduce shipping space, keeping material “fluid” in hoppers and chutes, hammering, etc. The paper discusses that part of the subject involved in the production and control of the vibration by mechanical or electrical means under all conditions of load. Formulae are developed for calculation of spring strength and for the calculation of the spring dimensions, and for the avoidance of spring fatigue. The various methods of electrical excitation are compared, and the relative advantages and disadvantages are discussed. The desirable instrument equipment is described, including the remote indication of vibration amplitude. A method is outlined by which it is claimed that vibration can be maintained constant at all loads and at any desired frequency. The testing of vibrating drives at the manufacturer's works and on site is discussed. In an Appendix to the paper the problem of transverse vibrations in long vibrating conveyors is treated mathematically, and a formula is developed for the natural frequency of transverse vibration of a conveyor of any uniform section and of any length.

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