Effect of rotatory inertia and load natural frequency on the response of uniform Rayleigh beam resting on Pasternak foundation subjected to a harmonic magnitude moving load

2018 ◽  
Vol 12 (16) ◽  
pp. 783-795
Author(s):  
A. Jimoh ◽  
E. O. Ajoge
Keyword(s):  
Natural Frequency ◽  
Moving Load ◽  
Pasternak Foundation ◽  
Rotatory Inertia ◽  
Rayleigh Beam

On the Response of a Beam Subjected to a Cyclic Moving Load

1969 ◽  
Vol 91 (4) ◽  
pp. 925-930 ◽  
Author(s):  
P. G. Kessel ◽  
A. L. Schlack
Keyword(s):  
Natural Frequency ◽  
Elastic Foundation ◽  
Infinite Number ◽  
Circular Cylindrical Shell ◽  
Moving Load ◽  
Relative Importance ◽  
Steady State Response ◽  
Rotatory Inertia ◽  
State Response ◽  
Load Movement

A theoretical analysis is presented on the damped steady state response of a simply supported beam on an elastic foundation subjected to a cyclic moving load that oscillates longitudinally along the beam about a fixed point. Loadings of this type have been recently shown to yield an infinite number of load movement frequencies that will excite resonance of a given natural frequency of an elastic member or system of members. It is the purpose of this investigation to introduce damping into the problem in order to determine both the absolute and relative importance of this infinite number of load movement frequencies that will excite a given natural frequency of a beam. The mathematical analogy between the problem of a beam resting on an elastic foundation and that of a long circular cylindrical shell with axial and rotatory inertia neglected is noted. Hence the results obtained are applicable to either problem. Numerical results are presented to illustrate the effects of damping, frequency of oscillation of load movement and amplitude of load movement on the dynamic deflection of the beam.

scholarly journals Exponentially Varying Load on Rayleigh Beam Resting on Pasternak Foundation.

2019 ◽  
Vol 16 ◽  
pp. 8449-8458
Author(s):  
Ahamed Jimoh ◽  
Emmanuel Omeiza Ajoge
Keyword(s):  
Dynamical System ◽  
Shear Modulus ◽  
Dynamic Behavior ◽  
Axial Force ◽  
Laplace Transformation ◽  
Convolution Theorem ◽  
Damping Coefficient ◽  
Pasternak Foundation ◽  
Rotatory Inertia ◽  
Rayleigh Beam

This paper investigates the dynamic behavior of uniform Rayleigh beam resting on Pasternak foundation and subjected to exponentially varying magnitude moving the load. The solution techniques are based on finite Fourier sine transformed Laplace transformation and convolution theorem. The results show that for a fixed value of axial force, damping coefficient and rotatory inertia, increases in shear modulus and foundation modulus reduces the response amplitude of the dynamical system. It was also found that increases in axial force, rotary inertia, and damping coefficient for fixed values of shear modulus and foundation modulus lead to decreases in the deflection profile of the Rayleigh beam resting on Pasternak foundation. Finally, it was found that the effect of shear modulus is more noticeable that of the foundation modulus.

Dynamic Response of a Cantilevered Beam Under Combined Moving Moment, Torque and Force

2020 ◽  
Vol 20 (05) ◽  
pp. 2050065
Author(s):  
Denil Chawda ◽  
Senthil Murugan
Keyword(s):  
Dynamic Response ◽  
High Speed ◽  
Moving Load ◽  
Numerical Results ◽  
Moving Loads ◽  
Element Analysis ◽  
Dirac Delta ◽  
Rayleigh Beam ◽  
Moving Force ◽  
Cantilevered Beam

This paper studies the dynamic response of a cantilevered beam subjected to a moving moment and torque, and combination of them with a moving force. The moving loads are considered to traverse along the length of the beam either from fixed-to-free end or free-to-fixed end. The beam is considered to have constant material and geometric properties. The beam is modeled using the Rayleigh beam theory considering the rotary inertia effects. The Dirac-delta function used to model the moving loads in the governing partial differential equations (PDEs) has complicated the solution of the problem. The Eigenfunction expansions coupled with the Laplace transformation method is used to find the semi-analytical solution for the resulting governing PDEs. The effects of moving loads on the dynamic response are studied. The dynamic effects are quantified based on the number of oscillations per unit travel time of the moving load and the Dynamic Amplification Factor (DAF) of the beam’s tip response. Numerical results are also analyzed for the two-speed regimes, namely high-speed and low-speed regimes, defined with respect to the critical speed of the moving loads. The accuracy of the analytical solutions are verified by the finite element analysis. The numerical results show that the loads moving with low speeds have significant impact on the dynamic response compared to high speeds. Also, the moving moment has significant impact on the amplitude of dynamic response compared with the moving force case.

Nonlinear Vibration of Nanobeam With Quadratic Rational Bezier Arc Curvature

2014 ◽  
Author(s):  
Hassan Askari ◽  
Zia Saadatnia ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequency ◽  
Governing Equation ◽  
Oscillation Amplitude ◽  
Beam Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Pasternak Foundation ◽  
Bernoulli Beam ◽  
Linear Frequency ◽  
Euler Bernoulli Beam

Nonlinear vibration of nanobeam with the quadratic rational Bezier arc curvature is investigated. The governing equation of motion of the nanobeam based on the Euler-Bernoulli beam theory is developed. Accordingly, the non-uniform rational B-spline (NURBS) is implemented in order to write the implicit form of the governing equation of the structure. The simply-supported boundary conditions are assumed and the Galerkin procedure is utilized to find the nonlinear ordinary differential equation of the system. The nonlinear natural frequency of the system is found and the effects of different parameters, namely, the waviness amplitude, oscillation amplitude, aspect ratio, curvature shape and the Pasternak foundation coefficient are fully investigated. The hardening and softening responses of the natural frequency of structure are detected for variations of the shape and amplitude of the curvature waviness. It is revealed that the ratio of nonlinear to linear frequency increases with an increase in the oscillation amplitudes. It is found that by increasing the Pasternak foundation coefficient, the ratio of nonlinear to linear frequency decreases.

Nonlinear free vibrations analysis of overhung rotors under the influence of gravity

2019 ◽  
Vol 234 (2) ◽  
pp. 575-588
Author(s):  
M Moradi Tiaki ◽  
SAA Hosseini ◽  
H Shaban Ali Nezhad
Keyword(s):  
Natural Frequency ◽  
High Frequency ◽  
Multiple Scales ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Beat Frequency ◽  
Dynamical Behavior ◽  
Free Vibrations ◽  
Beam Model ◽  
Rayleigh Beam

In this paper, nonlinear free vibration of a cantilever flexible shaft carrying a rigid disk at its free end (overhung rotor) is investigated. The Rayleigh beam model is used and the rotor has large amplitude vibrations. With the assumption of inextensibility, the effect of nonlinear curvature and inertia is considered. The effect of disk mass on the dynamical behavior of the system is studied in the presence and absence of gravity (horizontal and vertical rotors). By using perturbation technique (method of multiple scales), the main focus is on the influence of gravity on equations of motion and on quantities such as amplitude and damped natural frequency. Here, a different behavior is observed due to the rotor weight. Indeed, the combination effects of gyroscopic term, nonlinearity and gravity are studied on the modal behavior of the system. It is shown that the static deflection creates second order nonlinear terms and changes the nonlinear damped natural frequency. With considering of gravity, both beat and high frequency in beat phenomenon increase. With increasing of the rotor weight, the minimum value of amplitude is extremely amplified in the direction of gravity but in the other transverse direction, amplitude of vibrations decreases. In addition, it is found that the weight has directly influence on beat frequency, while the mass ratio between disk and beam affects the high frequency.

Dynamics and stability analysis of a flexible liquid-filled rotor in a constant thermal environment

2021 ◽  
pp. 107754632110224
Author(s):  
Guangding Wang ◽  
Wenjun Yang ◽  
Huiqun Yuan
Keyword(s):  
Thermal Environment ◽  
Rotor System ◽  
Flexible Rotor ◽  
Rotatory Inertia ◽  
Rayleigh Beam ◽  
Comparison Results ◽  
The Stability ◽  
Spinning Speed ◽  
Thermoelastic Theory ◽  
Good Agreement

In this study, the dynamics and stability of a flexible rotor containing liquid in a constant thermal environment are investigated. According to thermoelastic theory, the thermal axial force exerted on the rotor is calculated by using the analytical method. A spinning Rayleigh beam is used as a simplified model of the rotor. Applying the Hamilton principle, the governing equation of motion for the flexible liquid-filled rotor system is derived. Using the obtained model, the stability prediction model and the critical spinning speed for the rotor system are formulated. To demonstrate the validity of the developed model, the present analysis is compared with the results reported in the previous study, and good agreement is observed from the comparison results. Finally, numerical results based on the obtained model are performed for a better understanding of the parameters including filling parameters, mode number, rotatory inertia and thermal effect on the stability, and critical spinning speed of the rotor system.

Dynamic Response of Prestressed Rayleigh Beam Resting on Elastic Foundation and Subjected to Masses Traveling at Varying Velocity

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
S. T. Oni ◽  
B. Omolofe
Keyword(s):  
Dynamic Response ◽  
Elastic Foundation ◽  
Resonance Effect ◽  
Transverse Displacement ◽  
Rotatory Inertia ◽  
Perfect Agreement ◽  
Rayleigh Beam ◽  
Moving Force ◽  
Concentrated Masses ◽  
Vibrating Systems

In this study, the dynamic response of axially prestressed Rayleigh beam resting on elastic foundation and subjected to concentrated masses traveling at varying velocity has been investigated. Analytical solutions representing the transverse-displacement response of the beam under both concentrated forces and masses traveling at nonuniform velocities have been obtained. Influence of various parameters, namely, axial force, rotatory inertia correction factor, and foundation modulus on the dynamic response of the dynamical system, is investigated for both moving force and moving mass models. Effects of variable velocity on the vibrating system have been established. Furthermore, the conditions under which the vibrating systems will experience resonance effect have been established. Results arrived at in this paper are in perfect agreement with existing results.

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