Modeling of dynamic response of beam-type vibration absorbing system excited by moving mass

A numerical simulation to calculate the dynamic response of a beam attached with beam vibration absorber through a viscoelastic layer subjected to a moving load is presented in this paper. The mathematical model is formulated by using Euler-Bernoulli theory to calculate the vertical response of the system. The effect of the inertia of the moving load is included in the model to study its effect on the beam response at the mid span. The viscoelastic layer is introduced as uniformly distributed stiffness and damping and the concept of mixed damping ratio is implemented which allows the system to be modeled for different rigidity ratio. The response is calculated using time integration method for different moving mass inertia, rigidity ratio of the beams and the stiffness and damping of the visco-elastic layer. The effect is investigated for different values of mass and speed of the moving load

Response of beams resting on viscoelastically damped foundation to moving oscillators

The response of beams resting on viscoelastically damped foundation under moving SDoF oscillators is scrutinized through a novel state-space formulation, in which a number of internal variables is introduced with the aim of representing the frequency-dependent behaviour of the viscoelastic foundation. A suitable single-step scheme is provided for the numerical integration of the equations of motion, and the Dimensional Analysis is applied in order to define the dimensionless combinations of the design parameters that rule the responses of beam and moving oscillator. The effects of boundary conditions, span length and number of modes of the beam, along with those of the mechanical properties of oscillator and foundation, are investigated in a new dimensionless form, and some interesting trends are highlighted. The inaccuracy associated with the use of effective values of stiffness and damping for the viscoelastic foundation, as usual in the present state-of-practice, is also quantified

Oscillating Modes of Driven Colloids in Overdamped Systems

Microscopic particles suspended in liquids are the prime example of an overdamped system because viscous forces dominate over inertial effects. Apart from their use as model systems, they receive considerable attention as sensitive probes from which forces on molecular scales can be inferred. The interpretation of such experiments rests on the assumption, that, even if the particles are driven, the liquid remains in equilibrium, and all modes are overdamped. Here, we experimentally demonstrate that this is no longer valid when a particle is forced through a viscoelastic fluid. Even at small driving velocities where Stokes law remains valid, we observe particle oscillations with periods up to several tens of seconds. We attribute these to non-equilibrium fluctuations of the fluid, which are excited by the particle's motion. The observed oscillatory dynamics is in quantitative agreement with an overdamped Langevin equation with negative friction-memory term and which is equivalent to the motion of a stochastically driven underdamped oscillator. This fundamentally new oscillatory mode will largely expand the variety of model systems but has also considerable implications on how molecular forces are determined by colloidal probe particles under natural viscoelastic conditions.Comment: Accepted with Nat. Comm. (originally submitted version, complying with Nature policies). 10 pages, 8 figure

Interaction of a non-self-adjoint one-dimensional continuum and moving multi-degree-of-freedom oscillator

Peer reviewedPostprin

Determination of mechanical properties of excised dog radii from lateral vibration experiments

Experimental data which can be used as a guideline in developing a mathematical model for lateral vibrations of whole bone are reported. The study used wet and dry dog radii mounted in a cantilever configuration. Data are also given on the mechanical, geometric, and viscoelastic properties of bones

Indian railway track analysis for displacement and vibration pattern estimation

This paper presents the dynamic response of the Indian Railway track. Two track models are considered for the dynamic response in terms of vertical displacement and acceleration at different wheel speeds, keeping the moving point load at constant magnitude. The rail is treated as a beam either on viscoelastic foundation or on the discrete elastic support system. The governing equation is implemented in finite element analysis using ANSYS 14.0. For the validation of result from system equation are compared with those available in published literature and the maximum deviation for displacement at the midpoint of rail is found to be within 5 %. Different wheel speed generates variation in displacement and acceleration of the rail track. The study can be viewed as the foundation for the comparison of FEA based simulation of rail track to specify its dynamic response useful to provide better safety and comfort to commuters

Modeling a Viscoelastic Support Considering Its Mass-Inertial Characteristics During Non-Stationary Vibrations of the Beam

Peer reviewedPublisher PD

Dynamic response of an embedded railway track subjected to a moving load

A dynamic computational model for the embedded railway track subjected to a moving load is developed in this paper. The model consists of two-layer Euler-Bernoulli beams and continuous viscoelastic elements. The lower beam, the upper beam are employed to model the concrete slab and the rail, respectively, whilst the continuous viscoelastic elements model the soil reaction and the fill material. The problem is solved by employing Newmark-β numerical integration method. The effects of the speed of the moving loads, the rail type, and the spring stiffness of rail supports are studied. Results indicate that the dynamic response of rail and slab increases with the larger moving load speeds, whilst the response of rail and slab decreases with the increase of spring stiffness and heavier rail used

DYNAMIC RESPONSE OF A SIMPLY SUPPORTED VISCOELASTIC BEAM OF A FRACTIONAL DERIVATIVE TYPE TO A MOVING FORCE LOAD

In the paper, the dynamic response of a simply supported viscoelastic beam of the fractional derivative type to a moving force load is studied. The Bernoulli-Euler beam with the fractional derivative viscoelastic Kelvin-Voigt material model is considered. The Riemann-Liouville fractional derivative of the order 0 < ¬ 1 is used. The forced-vibration solution of the beam is determined using the mode superposition method. A convolution integral of fractional Green's function and forcing function is used to achieve the beam response. Green's function is formulated by two terms. The first term describes damped vibrations around the drifting equilibrium position, while the second term describes the drift of the equilibrium position. The solution is obtained analytically whereas dynamic responses are calculated numerically. A comparison between the results obtained using the fractional and integer viscoelastic material models is performed. Next, the effects of the order of the fractional derivative and velocity of the moving force on the dynamic response of the beam are studied. In the analysed system, the effect of the term describing the drift of the equilibrium position on the beam deflection is negligible in comparison with the first term and therefore can be omitted. The calculated responses of the beam with the fractional material model are similar to those presented in works of other authors