Papers by Keyword: Transverse Vibration

Abstract: In this study, we have investigated the band structure of elastic waves propagating in a phononic crystal, consisting of an epoxy matrix reinforced by Al₂O₃ inclusions in a square and hexagonal lattices. We also studied the influence of the inclusion geometry cross section – circular, hollow circular, square and rotated square with a 45° angle of rotation with respect to the x, y axes. The plane wave expansion (PWE) method is used to solve the wave equation considering the wave propagation in the xy plane (longitudinal-transverse vibration, XY mode, and transverse vibration, Z mode). The complete band gaps between the XY and Z modes are observed to circular, square and rotated square cross section inclusion and the best performance is for rotated square cross section inclusion in a square lattice. We suggest that the Al₂O₃/epoxy composite is feasible for vibrations management.

Abstract: In the one bar method, one of the standardized high velocity tensile testing techniques for thin steel plate, sometimes it shows an apparent effect of transverse vibration of an output bar on dynamic behavior of the plate. Suppressing the lateral vibration of the loading end of the bar is the most important factor to decrease the apparent effect, as pointed by Yoshida, Kuriyama, Uenishi and Takahashi in 2002, and the present author in 2011. He proposed an output-bar supporting technique with a polytetrafluoroethylene (PTFE) collar. In the former work, the lateral vibration was not fully suppressed, because the collar had some clearance to the output bar. He convinced that, in order to eliminate the clearance, it was worthy to give some transverse pre-load on the bar from the outer surface of the collar. However, the output bar is a load-sensing elastic body with strain gages adhered on it. The axial strain signal is a source of load detection. If such transverse compression is applied to the output bar, the axial skin strain of it is reduced to some extent. The key factor is the collar material, PTFE. This solid polymer possesses the lowest coefficient of friction in the situation of PTFE on steel, typically 0.05-0.10. The present author has modified an output-bar supporting stand to apply the lateral compressive load to the output bar with the divided PTFE collars which allow the smooth axial movement of the bar. The transverse compressive load is varied as 0, 70, 200 and 420 N. Obtained dynamic stress-strain curves at the strain rate of 500 s^-1 are compared each other to indicate the effect of the lateral compression on the bar. As a result, the lateral compression of 200 N is found as the most suitable condition.

Abstract: The dynamic characteristics and stability of the thermoelastic coupling moving rectangular plate are investigated. Based on the heat conduction equation involving the thermoelastic coupling term and the differential equation of motion of the plate subjected to the thermal shock, the thermoelastic coupling differential equation of the moving plate is derived. Dimensionless complex frequencies of the thermoelastic coupling moving rectangular plate with two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The results show that the first mode behaves divergent instability firstly, and the critical divergent moving speed of the first mode increase with the increase of the thermoelastic coupling factor for the two kinds of boundary conditions.

Abstract: In this paper the transverse vibration of a fixed-fixed end beam will be investigated by experimental measurement. This paper is concerned with the classical theory formula as well as the analysis and design of the dynamic vibration absorber (DVA) which is composed by a flexible beam with two masses symmetrically mounted at its both sides. The fixed end beam clamped to a static structure where dynamic vibration absorber then being attached onto it. One side of end of the beam is harmonically excited in transversal direction by an electric shaker. The structure equipped with accelerometer sensor to measure its vibration response amplitudes and natural frequencies. The dynamic vibration absorber arrangement located under motor near the beam end was then being vibrated and done in two conditions; before and after mounting dynamic vibration absorber. The comparison amplitudes before and after equipped dynamic vibration absorber were compared and discussed. From the experimental results, proved that the DVA has successfully absorbed the beam vibration hence reduced the vibration amplitude of the beam structure. The knowledge and result obtained from this study can help engineers control the vibration level of beam structure.

Abstract: Analytical solution of the free vibration of the isosceles right triangle membrane with several different boundary conditions was obtained. Some qualities of the solution were studied, especially, the completeness’s of the analytical solution were proved.

Abstract: Axially moving fabric can be met in many textile devices. In most cases, the transverse vibrations of fabric can cause a series of negative influents to the product. In this paper, the transverse vibration of axially accelerating moving fabric, which is excited by velocity fluctuations, is investigated by experimental method. The harmonic varying velocity is achieved through a brushless DC motor controlled by PWM technology based on the embedded microcontroller LPC1768. An inductive non-contact displacement sensor is used to measure transversal vibration of fabric. The motor speed is measured by a photoelectric encoder. The experimental data is processed by measurement platform based on Labview and the analysis is given. Laboratory measurements demonstrate the effect of velocity fluctuations on transverse vibration of fabric, particularly near the parametric resonance region.

Abstract: The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli, the form of pin rocker bearing in the analysis of transverse vibration in the paper. According the principle of Hamilton, after a series of variation, exchanging the order of integral and integration by parts, the transverse vibration differential equation of pipe is obtained without fluid. Considering different boundary consitions, the solving process is carried out. By utlization of MALAB language, the numerical example is analyzed, considering fluid and foundation. Thus, the fluid-solid coupling interaction is not ignored in transverse vibration in the buried pipeline.

Abstract: The vibration of buried pipeline is influenced by inner fluid and outer constrained soil. Euler-Bernoulli beam is analyzed in the vibration model of buried pipeline, using the Hamilton principle. In addition, the differential equations of transverse vibration of buried pipeline deduced by the mechanical model are transformed into basic form of dynamics equations, considering earthquake excitation as random wave. Using the method of the elasticity time-travel analysis to programming, the pipe element, the soil parameter and the earthquake dynamic parameter are analyzed in the Matlab software. With soil from soft to hard, the response of piping displacement becomes smaller and smaller. In the same soil, the earthquake damage rate of the piping becomes increaser and increaser with earthquake intensity increasing.

Abstract: Analysis of transverse vibration of beams is presented in this paper. Unfortunately, complexities which appear in solving differential equation of transverse vibration of non-uniform beams, limit analytical solution to some special cases, so that the numerical method is presented. DTM is a numerical method for solving linear and some non-linear, ordinary and partial differential equations. In this paper, this technique has been applied for solving differential equation of transverse vibration of conical Euler-Bernoulli beam. Natural circular frequencies and mode shapes have been calculated. Comparing results with the cases which exact solution have been presented, shows that DTM is a strong method especially for solving quasi-linear differential equations.

Abstract: Recursive and inexplicit differential equation of the second order with variable coefficients is derived from the fourth order linear homogeneous differential equation with variable coefficients of transverse vibration of non-uniform beam, which is about deflection and bending moment according to boundary conditions and order reduction. By finite difference method, numerical computation and accuracy are studied for natural frequency of transverse vibration for simply supported beam of non-uniform. Theoretical analysis and orthogonal computation examples show that numerical computation algorithm is very simple, and accuracy of computation depends on variety rate of gradually changed cross section in vertical direction and numbers of computation step, which is independent of width and length of beam; numerical accuracy of computation is estimable for given length or numbers of computation step; and reasonable length or numbers of computation step is determinable for given accuracy demand.