Vibration of viscoelastic beams subjected to an eccentric compressive force and a concentrated moving harmonic force (original) (raw)
Related papers
Vibration of Viscoelastic Beams Subjected to Moving Harmonic Loads
2004
The transverse vibration of a beam with intermediate point constraints subjected to a moving harmonic load is analyzed within the framework of the Bernoulli-Euler beam theory. The Lagrange equations are used for examining the dynamic response of beams subjected to the moving harmonic load. The constraint conditions of supports are taken into account by using Lagrange multipliers. In the study, for applying the Lagrange equations, trial function denoting the deflection of the beam is expressed in the polynomial form. By using the Lagrange equations, the problem is reduced to the solution of a system of algebraic equations. The system of algebraic equations is solved by using the direct time integration method of Newmark (8). Results of numerical simulations are presented for various combinations of constant axial velocity, excitation frequency,
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.
Geometrically nonlinear free and forced vibrations of Euler-Bernoulli multi-span beams
MATEC Web of Conferences
The objective of this paper is to establish the formulation of the problem of nonlinear transverse forced vibrations of uniform multi-span beams, with several intermediate simple supports and general end conditions, including use of translational and rotational springs at the ends. The beam bending vibration equation is first written at each span and then the continuity requirements at each simple support are stated, in addition to the beam end conditions. This leads to a homogeneous linear system whose determinant must vanish in order to allow nontrivial solutions to be obtained. The formulation is based on the application of Hamilton's principle and spectral analysis to the problem of nonlinear forced vibrations occurring at large displacement amplitudes, leading to the solution of a nonlinear algebraic system using numerical or analytical methods. The nonlinear algebraic system has been solved here in the case of a four span beam in the free regime using an approximate method developed previously (second formulation) leading to the amplitude dependent fundamental nonlinear mode of the multi-span beam and to the corresponding backbone curves. Considering the nonlinear regime, under a uniformly distributed excitation harmonic force, the calculation of the corresponding generalised forces has led to the conclusion that the nonlinear response involves predominately the fourth mode. Consequently, an analysis has been performed in the neighbourhood of this mode, based on the single mode approach, to obtain the multi-span beam nonlinear frequency response functions for various excitation levels.
Viscoelastic Analysis of a Bernoulli-Navier Beam Resting on an Elastic Medium
This paper deals with the problem of the determination of the response of a Bernoulli-Navier beam having viscoelastic behavior, and resting on an elastic medium. Assuming uniaxial bending, the displacement of the beam axis is governed by an integro-differential equation. The compatibility of the displacements between the beam and the elastic medium is in general imposed through an integral equation. In this case, the solution has to be pursued numerically, and a specific algorithm is presented. On the contrary, in the case of a Winkler's medium the compatibility is expressed by a linear finite relationship, which allows the analytical solution of the problem for both hereditary and aging behavior of the beam.
The governing equation of motion for free vibration of a uniform Euler-Bernoulli beam is given as
2017
EVERAL techniques have been used to carry out the vibration analysis of beams with a view to determining their vibration characteristics. Lai, et al. [1] analysed the free vibration of uniform Euler-Bernoulli beam with different elastically supported conditions using Adomian decomposition method (ADM). Li [2] had earlier studied the vibration characteristics of a beam having general boundary conditions. The displacement of the beam was sought in form of a linear combination of a Fourier series and an auxiliary polynomial function. Kim and Kim [3] also applied Fourier series to determine the natural frequencies of beams having generally restrained boundary conditions. Later, Liu and Gurram [4] adopted the He’s variational iteration method to estimate the vibration frequencies of a uniform Euler-Bernoulli beam for various supporting end conditions. Natural frequencies for the first six modes of vibration were presented in their work. Malik and Dang [5] employed the differential transf...
Journal of Mechanical Science and Technology, 2010
In this paper the dynamic response of a simply-supported, finite length Euler-Bernoulli beam with uniform cross-section resting on a linear and nonlinear viscoelastic foundation acted upon by a moving concentrated force is studied. The Galerkin method is utilized in order to solve the governing equations of motion. Results are compared with the finite element solution for the linear foundation model in order to validate the accuracy of the solution technique. A good agreement between the two solution techniques is observed. The effect of the nonlinearity of foundation stiffness on beam displacement is analyzed for different damping ratios and different speeds of the moving load. The results for the time response of the midpoint of the beam are presented graphically.
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.
Journal of Sound and Vibration, 2007
The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of the machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. An exact solution for the title problem is obtained in closed-form fashion, considering general boundary conditions by means of translational and rotatory springs at both ends. The model allows to analyze the influence of the masses and their rotatory inertia on the dynamic behavior of beams with all the classic boundary conditions, and also, as particular cases, to determine the frequencies of continuous beams. r
Nonlinear vibrations of the Euler-Bernoulli beam subjected to transversal load and impact actions
In this work vibrations of a flexible nonlinear Euler-Bernoulli-type beam, driven by a dynamic load and with various boundary conditions at its edge, including an impact, are studied. The governing equations include damping terms, with damping coefficients ε 1 , ε 2 associated with velocities of the vertical deflection wand horizontal displacement u,respectively. Damping coefficients ε 1 , ε 2 and transversal loads q 0 and ω p serve as the control parameters in the problem. The continuous problem is reduced to a finite-dimensional one by applying finite differences with respect to the spatial coordinates, and is solved via the fourth-order Runge-Kutta method. This approach enables the identification of damping coefficients, as well as the investigations of elastic waves generated by the impact of rigid mass moving at constant velocity V.
MATEC Web of Conferences
This paper deals with the geometrically nonlinear free and forced vibration analysis of a multi-span Euler Bernoulli beam resting on arbitrary number N of flexible supports, denoted as BNIFS, with general end conditions. The generality of the approach is based on use of translational and rotational springs at both ends, allowing examination of all possible combinations of classical beam end conditions, as well as elastic restraints. First, the linear case is examined to obtain the mode shapes used as trial functions in the nonlinear analysis. The beam bending vibration equation is first written in each span. Then, the continuity requirements at each elastic support are stated, in addition to the beam end conditions. This leads to a homogeneous linear system whose determinant must vanish in order to allow nontrivial solutions to be obtained. Numerical results are given to illustrate the effects of the support stiffness and locations on the natural frequencies and mode shapes of the B...