Natural Frequency

Passive means of vibration attenuation have been employed successfully and efficiently in machining systems such as turning and milling. Traditional approach to controlling vibration in a milling system is to develop control mechanisms for cutting tools or machine spindles. However, due to the nature of milling operations where the cutting tools rotate at high speed, the passive vibration control methods

We use the meshless local Bubnov–Galerkin (MLPG6) formulation to analyze free and forced vibrations of a segmented bar. Three different techniques are employed to satisfy the continuity of the axial stress at the interface between two materials: Lagrange multipliers, jump functions, and modified moving least square basis functions with discontinuous derivatives. The essential boundary conditions are satisfied in all cases by the method of Lagrange multipliers. The related mixed semidiscrete formulations are shown to be stable, ...

To model the impact dynamics of a golf drive, finite element (FE) models of the ball and the clubhead are created and combined to simulate the collision of the two bodies. A three-piece golf ball is modelled using only solid elements, while the clubhead is modelled using solid elements for the crucial area of the impact, i.e. the clubface, and using shell elements for the rest of the clubhead to improve the computational efficiency of the simulation. The correct transfer of forces and moments in the transition area between the shell and solid elements is assured by introducing kinematic nodal constraints using rigid elements. The FE model is used to optimize the shape of the clubface in three steps to maximize the launch velocity of the golf ball for central impacts. A final clubface shape is reached and a total improvement of 4.8 m/s over the initial design is obtained. This is a 7% gain in launch velocity, which results in a driving length advantage of approximately 20 m (or 22 yards) until the first contact with the ground. During the optimization process, the mechanical impedances of the two colliding bodies were recorded and compared. It is shown that the optimal clubhead geometry does not agree with the impedance matching theory by comparing the optimization results to those obtained from a simple lumped parameter model.

Autoparametric interaction and the associated phenomenon of amplitude saturation are experimentally observed in a physical model of cable-and-beam structure. In this system, the horizontal beam is fixed at one end and supported at the other end by an inclined taut cable. The longitudinal axes of beam and cable are in a vertical plane. Three natural frequencies of the system are approximately of the ratio 1:1:2. This is a combination of two conditions that are very likely to occur in relatively long-span, multi-stay-cable bridges, namely, 1:1 tuning and 1:2 superharmonic tuning. While the beam is vertically excited with sufficiently large force near a primary resonance, the cable vibrates horizontally at half of excitation frequency. The beam also vibrates horizontally at half-frequency, as well as vertically. As the vertical excitation on the bean is further increased in amplitude, the vertical vibration amplitude gets saturated instead of increasing proportionately. A 3DOF analytic...

Despite the extensive research and model testing of high-rise structures, there is still a significant degree of uncertainty associated with the estimation of the response of tall buildings under dynamic excitations. To reduce this uncertainty, a suite of accelerometers and Global Positioning Systems (GPS) are installed to monitor the accelerations and displacements of three tall buildings in Chicago to determine

A Chimney is a structure that is used for removing hazardous gases from furnace and from big industry plants to outdoor atmosphere. Chimneys are generally vertical structure as far as possible to make sure that the hazardous gases flow easily and quickly by taking air into the combustion. Industrial Chimneys are having greater heights and slender structures with circular cross-sections. The height of a chimney determines its capability to pass gases to the outside environment via stack effect. Also, the dispersion of hazardous gases at greater heights can minimize their effect on the immediate surroundings. The project is based on the design concepts of chimneys according to Indian codes provisions and analyse through finite element method. Different types of steel chimney models are made by varying its height, geometry and diameter. The main objective of this study is to perform vibration analysis of steel chimney for dynamic wind loads using different critical velocity. Natural frequency and time period has been found out using analysis in Ansys. All the models are modelled in the Ansys Software.

The transverse free vibration of a class of variable-cross-section beams is investigated using the Wentzel, Kramers, Brillouin (WKB) approximation. Here the governing equation of motion of the Euler-Bernoulli beam including axial force distribution is utilized to obtain a singular differential equation in terms of the natural frequency of vibration and a WKB expansion series is applied to find the solution. Based on this formulation, a closed form solution is obtained for determination of natural vibration mode shapes and the corresponding frequencies. The first four terms of this asymptotic solution are simplified for homogenous beams to give a compact third-order WKB approximation. Next, the resulting solution is employed to determine the natural frequencies and mode shapes of some examples with and without axial force distribution. The results are then been compared with those in the literature and very good agreement is achieved.

Eccentric rotor motion induces an unbalanced magnetic pull between the rotor and stator of cage induction motors. Recently, a linear parametric model of this eccentricity force due to the arbitrary rotor motion was presented. The purpose of this study is to combine this electromagnetic force model with a simple mechanical rotor model, and further, to demonstrate the rotordynamic response induced

This paper describes an experimental study of a skew bridge model conducted at the Federal Highway Administration Turner-Fairbank Highway Research Center. The objectives of the experiment are: (1) to perform a pilot study on the design, construction, instrumentation, testing and data processing of a skew bridge model, (2) to provide experimental data to validate a 3D finite element model developed

A method is proposed to estimate the degradation of the first natural frequency of vibration of earthen dams with increase in strain levels induced due to seismic events. A synthesised wave, referred to as the 'sum of sines', generated by the superposition of sinusoidal waves with frequencies ranging from 0.01 Hz to 25 Hz, is scaled to different peak accelerations and used to simulate seismic excitations at the base of the dam. The natural frequency is then determined by studying the response of the structure in the frequency domain. For this study, four dams with varying complexities of geometry, constituent material properties, and known natural frequencies were at first selected from previously published literature to establish the validity of the proposed method for determining natural frequencies of the dams at small strain levels. Plane strain models of these structures were constructed and analysed, using a commercially available finite element method-based software that is capable of performing time-history analyses. Results from the analyses indicate a good agreement between the natural frequencies predicted using the proposed method and the frequency values reported in the literature for the corresponding structures at small strain levels. The method was later used to determine the strain-dependent natural frequency of a hydraulic-fill dam in North Texas. Twenty-one different earthquake conditions, with different peak ground accelerations, frequency contents, and mean periods, were used to thoroughly validate the applicability of the developed methodology. Numerical analyses indicate that the strain-dependent variation of the first natural frequency follows a similar trend as that obtained using the 'sum of sines' excitation when the dam is subjected to widely different earthquake conditions.