Dynamic Response and Vibration of a Cantilevered Beam under an Accelerated Moving Mass

In this research we investigate dynamic responses and vibration of a cantilevered beam subjected to a moving mass with variable speeds. Governing equations of motion under a moving mass are derived by Galerkin's mode summation method considering the effects of all forces acting on the beam (gravity force, Coriolis force, inertia force caused by a slope of the beam, and transverse inertia of the beam). A Runge-Kutta integration method is then applied to calculate dynamic responses of the beam. The effects of the speed, acceleration and the magnitude of the moving mass on the response of the beam are investigated in these numerical analyses. Furthermore, experimental tests are conducted to validate our analysis.

Vibration of a Microbeam Under Ultra-Short-Pulsed Laser Excitation Considering Momentum and Heating Effect

In this study, vibration of a microbeam excited by an ultra-short-pulsed laser considering the momentum and heating effect of the laser beam is investigated. When the laser impacts the microbeam, portion of the photons is absorbed by the beam and their energy will be transformed into heat while the others are reflected. The momentum change of the absorbed and reflected laser photons is considered and modeled as a distributed force on the beam. The absorbed thermal energy yields non-uniform thermal stress causing the beam to vibrate. According to short duration of laser pulse, the non-Fourier conduction equation which takes into account the finite propagation speed of thermal energy, is implemented to the problem and Euler-Bernoulli assumption is made for the beam. The coupled partial differential equations for the deflection and temperature are solved implementing the mode summation method and Laplace transform. Effect of reflectivity, pulse duration and absorption depth are investigated. It should be noted that depth of the thermal absorption and reflectivity can be managed to control the vibration amplitude and phase of the beam vibration.

Drill string instability reduction by optimum positioning of stabilizers

The main aim of this article is to find the optimum positions of the stabilizers that reduces the vibration and leads to the largest weight on bit (WOB) in drill strings. In this work, the potential energy of drill strings has been derived by considering the drill string weight and WOB. The potential energy of this continuous system is considered as a multi-degree-of-freedom system by the mode summation method. The equilibrium position of the system and its stability is determined by finding the roots of the first derivative and the sign of the second derivative of the potential energy, respectively. Using this formulation, the best positions of stabilizers that lead to the largest WOB can be found for different numbers of stabilizers. The best arrangement of the stabilizer's position on a drill string with one, two, and three stabilizers is investigated.

A Tunable Vibration Absorber Design to Suppress Chatter in Boring Manufacturing Process

Dynamic vibration absorbers are used to reduce the undesirable vibrations in many applications such as electrical transmission lines, helicopters, gas turbines, engines, bridges and etc. One type of these absorbers is tunable vibration absorber (TVA) which can act as a semi-active controller. In this paper, by applying a (TVA), chatter vibration is suppressed during boring process in which boring bar is modeled as a cantilever Euler-Bernoulli beam. The optimum specifications of absorber such as spring stiffness, absorber mass and its position can be determined by developing an algorithm based upon mode summation method. Finally, using the SIMULINK Toolbox of MATLAB, the analog simulated block diagram of the problem is developed. The advantage of this simulation is that, one can analyze the effect of other types of excitations such as step, ramp, etc on the absorbed system.

Low Cost Pipe-crawling Pneumatic Robot

A pipes inspection robot prototype was built and a mathematical modeling of its dynamics was developed. In order to pass over complicated pipeline networks, the robot was constructed with a flexible rubber structure moved by pneumatics power The robot locomotion was inspired by the inch-worm gait kinematics. Because of significant acceleration values revealed during the robot gait, the robot dynamics was mathematically formulated either by a single degree of freedom model or by the assumed mode summation method. A set of experiments were conducted for obtaining all the parameters required for models formulation. Finally the models were validated by comparing the numerical and experimental robot gait with time.

ZERO-POINT ENERGY OF A DILUTE DIELECTRIC BALL IN THE MODE SUMMATION METHOD

In the (ε1-ε2)2-approximation the Casimir energy of a dilute dielectric ball is derived using a simple and clear method of the mode summation. The addition theorem for the Bessel functions enables one to present in a closed form the sum over the angular momentum before the integration over the imaginary frequencies. The linear in (ε1-ε2)2 contribution into the vacuum energy is removed by an appropriate subtraction. The role of the contact terms used in other approaches to this problem is elucidated.