Dynamics of Double-Beam System with Various Symmetric Boundary Conditions Traversed by a Moving Force: Analytical Analyses (original) (raw)
Related papers
VIBRATIONS OF NON-UNIFORM CONTINUOUS BEAMS UNDER MOVING LOADS
Journal of Sound and Vibration, 2002
The dynamic behavior of multi-span non-uniform beams transversed by a moving load at a constant and variable velocity is investigated. The continuous beam is modelled using Bernoulli}Euler beam theory. The solution is obtained by using both the modal analysis method and the direct integration method. The natural frequencies and mode shapes used in the solution of this problem are obtained exactly by deriving the exact dynamic sti!ness matrices for any polynomial variation of the cross-section along the beam using the exact element method. The mode shapes are expressed as in"nite polynomial series. Using the exact mode shapes yields the exact solution for general variation of the beam section in case of constant and variable velocity. Numerical examples are presented in order to demonstrate the accuracy and the e!ectiveness of the present study, and the results are compared to previously published results.
Vibration of Beams with General Boundary Conditions Due to a Moving Harmonic Load
Journal of Sound and Vibration, 2000
Vibrational behavior of elastic homogeneous isotropic beams with general boundary conditions due to a moving harmonic force is analyzed. The analysis duly considers beams with four di!erent boundary conditions; these include pinned}pinned, "xed}"xed, pinned}"xed, and "xed}free. The response of beams are obtained in closed forms and compared for three types of the force motion: accelerated, decelerated, and uniform motion. The e!ects of the moving speed and the frequency of the moving force on the dynamic behavior of beams are studied in detail.
Modal Analysis of Pinned-Pinned Beam using Numerical, Analytical and Experimental Techniques
2021
Research Student, Department of Mechanical Engineering, Islamic University of Science and Technology Awantipora, Pulwama-192301-india ----------------------------------------------------------------------------***-------------------------------------------------------------------------AbstractIn this study, Modal analysis of rectangular cross-section uniform beam is investigated numerically, analytically and experimentally under the boundary conditions (pinned-pinned) simply supported. Modal analysis is a technique for determining the system's normal modes, normal shapes and frequencies as well as for better understanding the system as a whole. In this paper transverse vibration modal analysis of simply supported wooden beam is carried out 3 by different approaches. Numerical analysis is accomplished by ANSYS based FEA software, Analytical solution is carried out by Euler-Bernoulli’s beam theory under the assumption effect of rotary inertia and shear deformation of beam is negle...
On the Response of Vibration Analysis of Beam Subjected to Moving Force and Moving Mass
African Journal of Science and Nature
In this paper, vibration of beam subjected to moving force and moving mass is considered. Finite Fourier Sine transform with method of undetermined coefficient is used to solve the governing partial differential equation of order four. It was found that the response amplitude increases as the mass of the load increases for the case of moving mass while the response amplitude for the case of moving mass is not affected by increase in mass of the load. Also analysis shows that the response amplitude for the case of moving force is greater than that of moving mass.
Modal Analysis of Vibration of Euler-Bernoulli Beam Subjected to Concentrated Moving Load
Iraqi journal of science, 2020
This paper investigates the modal analysis of vibration of Euler-Bernoulli beam subjected to concentrated load. The governing partial differential equation was analysed to determine the behaviour of the system under consideration. The series solution and numerical methods were used to solve the governing partial differential equation. The results revealed that the amplitude increases as the length of the beam increases. It was also found that the response amplitude increases as the foundation increases at fixed length of the beam.
Vibration Analysis of a Beam Carrying a Moving Mass
2007
This paper deals with the linear dynamic response of a cracked cantilever beam subjected to a moving mass. The velocity of the moving mass is assumed to be constant. The present analysis in its general form may well be applied to beams with various boundary conditions. Results from the numerical solutions of the differential equations of motion are shown graphically. Moreover, when considering the maximum deflection for the end point of the beam, the critical speeds of the moving mass have been evaluated. Experiments have been conducted to compare with the numerical results. It is observed that the experimental results are in good agreement with the numerical one.
Chinese Journal of Engineering, 2013
The study of the dynamic properties of beam structures is extremely important for proper structural design. This present paper deals with the free in-plane vibrations of a system of two orthogonal beam members with an internal elastic hinge. The system is clamped at one end and is elastically connected at the other. Vibrations are analyzed for different boundary conditions at the elastically connected end, including classical conditions such as clamped, simply supported, and free. The beam system is assumed to behave according to the Bernoulli-Euler theory. The governing equations of motion of the structural system in free bending vibration are derived using Hamilton's principle. The exact expression for natural frequencies is obtained using the calculus of variations technique and the method of separation of variables. In the frequency analysis, special attention is paid to the influence of the flexibility and location of the elastic hinge. Results are very similar with those o...
Vibration analysis of beams traversed by uniform partially distributed moving masses
Journal of Sound and Vibration, 1995
An investigation into the dynamic behavior of beams with simply supported boundary conditions, carrying either uniform partially distributed moving masses or forces, has been carried out. The present analysis in its general form may well be applied to beams with various boundary conditions. However, the results from the computer simulation model given in this paper are for beams with simply supported end conditions. Results from the numerical solutions of the differential equations of motion are shown graphically and their close agreement, in some extreme cases, with those published previously by the authors is demonstrated. It is shown that the inertial effect of the moving mass is of importance in the dynamic behavior of such structures. Moreover, when considering the maximum deflection for the mid-span of the beam, the critical speeds of the moving load have been evaluated. It is also verified that the length of the distributed moving mass affects the dynamic response considerably. These effects are shown to be of significant practical importance when designing beam-type structures such as long suspension and railway bridges. 7
NON-LINEAR VIBRATIONS OF A BEAM-MASS SYSTEM UNDER DIFFERENT BOUNDARY CONDITIONS
Journal of Sound and Vibration, 1997
An Euler-Bernoulli beam and a concentrated mass on this beam are considered as a beam-mass system. The beam is supported by immovable end conditions, thus leading to stretching during the vibrations. This stretching produces cubic non-linearities in the equations. Forcing and damping terms are added into the equations. The dimensionless equations are solved for five different set of boundary conditions. Approximate solutions of the equations are obtained by using the method of multiple scales, a perturbation technique. The first terms of the perturbation series lead to the linear problem. Natural frequencies and mode shapes for the linear problem are calculated exactly for different end conditions. Second order non-linear terms of the perturbation series appear as corrections to the linear problem. Amplitude and phase modulation equations are obtained. Non-linear free and forced vibrations are investigated in detail. The effects of the position and magnitude of the mass, as well as effects of different end conditions on the vibrations, are determined.
A numerical–analytical combined method for vibration of a beam excited by a moving flexible body
International Journal for Numerical Methods in Engineering, 2007
The vibration of a beam excited by a moving simple oscillator has been extensively studied. However, the vibration of a beam excited by an elastic body with conformal contact has attracted much less attention. This is the subject of the present paper. The established model is more complicated but has a much wider range of applications than the moving-oscillator model.