Vibration Response Curves Research Articles

The frequency analysis of the gun barrel vibration based on road simulation test

Aiming at the problem that the gun barrel vibration affects the firing accuracy during tank moving, based on the road simulation test, under the excitation of the different road levels (C, D and E), the acceleration vibration response curves of the barrel under different road levels and different vehicle speeds were obtained by arranging acceleration sensors on the barrel surface. Based on the power spectrum analysis method, the frequency response characteristics of the barrel vibration were analyzed, and the main frequency of barrel vibration during moving is obtained. It has been shown that, the main frequency of the barrel response is mainly distributed in three frequency ranges: 1~3Hz, 14~15Hz and 24~26Hz. The main frequency of the barrel vibration is different with different roads. The main frequency of the barrel response is mainly in the frequency range of 1~3Hz under C level road, and in the frequency range of 1~3Hz and 24~26Hz under D lever road. And under the E level road, the main frequency of barrel response is within the three frequency ranges of 1~3Hz, 14~15Hz and 24~26Hz. And the main frequency is 25Hz as the measuring point is far away from the muzzle. The results will provide support for obtaining the vibration characteristics of barrel as tank moving and explaining the vibration response law of the barrel.

Numerical simulation of stability and responses of dynamic systems under parametric excitation

The stability and responses of dynamic systems under parametric excitation are often encountered in many fields of science and engineering, such as slender columns and thin plates under axial loadings. This paper proposes a novel numerical simulation method to simultaneously construct stability diagrams and predict the responses of multiple degree-of-freedom (DOF) dynamic systems under arbitrary parametric loadings. The method divides an arbitrary load into discrete segments to approximate the variable excitation function by a step function and then accumulates the system responses of each segment using a matrix method. Dynamic stability and response analysis of undamped and damped 1DOF, 2DOF, 3DOF, and multiple DOF systems are conducted, and numerical examples are compared to conventional methods to show the accuracy and advantage of the proposed numerical simulation method. The instability diagrams are also substantiated by vibration response curves obtained from the same method. The method is applied to calibrate the validity and ranges of applicability of the Hill infinite determinants in the Floquet theory of 1DOF Mathieu-Hill equations. The second order approximation of the first instability region from the Hill determinant is acceptable. However, the fourth order approximation of the second instability region must be used to obtain a relatively accurate result. For 2DOF, 3DOF, and multi-parameter linear periodic systems, the method can simultaneously render four types of instability regions in a single procedure: no resonances, simple parametric resonances, combination additive resonances, and combination differential resonances. These results could provide a better understanding of stability and responses of dynamic systems under parametric excitation.

Dynamic Stability and Responses of Beams on Elastic Foundations Under a Parametric Load

This paper is concerned with numerical simulation of both dynamic stability and responses of beams on elastic foundations under a pulsating axial parametric load in a single matrix method. First, the equation of motion of a beam on an elastic foundation with damping is derived and decoupled into a Mathieu–Hill equation. Three different elastic foundations are considered and compared: Winkler, Pasternak, and Hetenyi models. Then a novel numerical simulation algorithm is proposed to investigate both the dynamic stability and the responses of the beam simultaneously. Accurate instability diagrams are obtained by the numerical simulation and are substantiated by vibration response curves obtained from the same method. These numerically accurate diagrams are used to calibrate the approximate instability boundaries of various orders of Hill infinite determinants from the classical Bolotin method for the first time. A detailed discussion is presented on effects of various aspects including elastic foundation models, damping, and static and dynamic loads. The results provide insights into the efficient and safe application of beams on elastic foundations in engineering. The proposed numerical method can be extended to analyze dynamic stability and vibrations of systems under arbitrary parametric excitations where Mathieu–Hill equations are involved.

Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam

The nonlinear forced vibration of bidirectional functionally graded porous material beams where the material components gradient change in both thickness and axial directions are studied in this study. Combining von Karman’s geometric nonlinearity and first-order shear deformation theory, the governing equations describing the coupled deformations are formulated as a system of nonlinear partial differential equations. Utilizing the Galerkin method, the formulated continuous model is transformed to a coupled nonlinear ordinary differential dynamic system. By accomplishing bifurcation calculation for periodic response of the discrete system using pseudoarclength technique, the vibration response curves are obtained by extracting the max-min amplitude of periodic motions. To highlight the effect of nonlinearity, the linear and nonlinear dynamic responses of beam are demonstrated. It is found that the periodic motion of beam may undergo cyclic-fold bifurcation. Numerical results are presented to examine the effects of the system parameters, e.g., gradient indexes, porosity, damping coefficients, and aspect ratio.

Dynamic motion analysis of impeller for the development of real-time flow rate estimations of a ventricular assist device.

Implantable ventricular assist devices are used in heart failure therapy. These devices require real-time flow rate estimation for effective mechanical circulatory support. We previously developed a flow rate estimation method using the eccentric position of a magnetically levitated impeller to achieve real-time estimation. However, dynamic motion of the levitated impeller can compromise the method's performance. Therefore, in this study, we investigated the effects of dynamic motion of the levitated impeller on the time resolution and estimation accuracy of the proposed method. The magnetically levitated impeller was axially suspended and radially restricted by the passive stability in a centrifugal blood pump that we developed. The dynamic motions of impeller rotation and whirling were analyzed at various operating conditions to evaluate the reliability of estimation. The vibration response curves of the impeller revealed that the resonant rotational speed was 1300-1400 revolutions per minute (rpm). The blood pump was used as a ventricular assist device with rotational speed (over 1800 rpm) sufficiently higher than the resonant speed. The rotor-dynamic forces on the impeller (0.03-0.14 N) suppressed the whirling motion of the impeller, indicating that the dynamic motion could be stable. Although the temporal responsiveness should be determined based on the trade-offs among the estimation accuracy and time resolution, the real-time estimation capability of the proposed method was confirmed.

Quick Suppression of Vibration of Robot via Hybrid Input Shaping Control Strategy

When the vibration amplitude and resonant frequency bandwidth of each mode are different in the multiple-modal system, the response time of a system is increased but the residual vibration is effectively reduced by the positive impulses multiple-modal input shapers. However, a negative impulses hybrid multiple-modal input shaping method can solve those problems. The basic principle of this control strategy and a 3-DOF parallel robot were introduced. Six negative impulses hybrid input shapers to reduce vibration of the first two modes were constructed based on the robot. Using simulation methods, the response time and vibration suppression abilities of various negative impulses hybrid two-modal input shapers (NHTIS) were obtained by analyzing the vibration response curves of these input shapers, and comparing with positive and negative impulses two-modal input shapers, respectively. The results show that the NHTIS can improve the response speed of the system while significantly reducing the multiple-modal residual vibration.

Non-linear vibrations of nuclear fuel rods

Abstract Single zirconium alloy nuclear fuel rods with clamped-clamped boundary conditions and subjected to harmonic excitation at various force levels were experimentally studied. Different configurations were implemented, and the fuel rods were tested in air and submerged in quiescent water. Moreover, the effect of the contained fuel pellets was also reproduced by representative metallic pellets inside the rods. Non-linear stiffness and damping parameters were extracted from experimental vibration response curves by means of a specifically-developed identification tool. For the cases where the fuel pellets were removed or axially compressed, it was found that the axial-symmetry of the fuel rod resulted in a pronounced one-to-one internal resonance. The internal motion of the fuel pellets is a source of friction and impacts during vibrations, thus complicating further the linear and non-linear dynamic behavior of the system. A very significant increase of the viscous modal damping with the vibration amplitude was observed during geometrically non-linear vibrations, which is particularly relevant and in advantage of safety.

Vibration Analysis and Optimal Design in Hydraulic Leveling System

In the process of launching, some launch bearing platforms will bear large impact force, thus causing severe vibration of the platform. There exists coupling relationship between this kind of vibration and the hydraulic system. In this paper, we established the vibration model according to the coupling vibration system in bearing platform and hydraulic system, and realized decoupling. Then we derived the vibration controlling equation and transfer function of coupling vibration between bearing platform and hydraulic system. Further more, we simulate the actual situation in software Simulink, and it gave vibration response curves under different parameters. In this way, it provides basis for reducing platform vibration.

Generation Mechanism of Sidebands about Gear Mesh Vibration Considering Amplitudes Asymmetricity

Sidebands of mesh harmonic frequencies are considerable components in gear vibration spectrum. In this study, generation mechanism and characteristics of sidebands are investigated based on a single-degree-of-freedom vibration model of a cylindrical gear pair. Time-varying mesh stiffness and contribution of tooth surface form are formulated in the model. In addition to mesh harmonic components, the first order component of gear rotation is incorporated into each of the time-varying mesh stiffness and the tooth surface form as the effect of gear eccentricity. This model presents that the product of mesh harmonics and low order component of gear rotation frequency produces sidebands on either side of the mesh frequency. Asymmetrical property of sideband amplitudes about mesh frequency is dependent on frequency response function of gear vibration system. Vibration response curves of the sidebands have pseudo resonance peak. These sideband characteristics are verified by comparing simulation result of the gear model with experiment using a single-stage helical gearing.

Damping and Forced Vibration Analyses of Viscoelastic Shells

The forced vibration response curves and damping characteristics of viscoelastic and sandwich viscoelastic shells are studied by a combination of the finite element and perturbation methods. The mathematical formulation is developed in a general form in order to take into account various viscoelastic models in the frequency domain. Frequency dependent Young modulus based on various Maxwell's model is used for viscoelastic materials modeling. The series-continuation and Padé-continuation procedures are elaborated for harmonic responses of elastic, viscoelastic and sandwich arches, panels, and cylindrical shells. Passive vibration control, response curves, and equivalent damping characteristics are obtained at large frequency ranges.

Interference effect of an upstream larger cylinder on the lock-in vibration of a flexibly mounted circular cylinder

Experiments have been carried out to investigate the flow-induced vibration response of a flexibly mounted circular cylinder located in the vicinity of a larger cylinder and subjected to cross-flow. The interfering larger cylinder was placed upstream and had a diameter twice that of the vibrating cylinder. Complex interaction was observed between the flow over the two cylinders. The vibration responses of the flexible cylinder were classified into different regimes according to the relative positions of the two cylinders. In the-side-by-side arrangement and the tandem or near-tandem arrangement, flow-induced vibrations of the flexible cylinder were greatly suppressed. In the staggered arrangement which covered a large portion of the relative cylinder positions being investigated, vibrations of the smaller cylinder were greatly amplified. The vibration response curves were also largely modified with a broadening of the lock-in resonance range. A shift of the peak reduced velocity for maximum vibration response was also found. Flow visualizations and wake velocity measurements suggested that the modifications of the vibration responses were related to the presence or absence of constant or intermittent flow through the gap region between the two cylinders. The proposed mechanisms of flow interactions and the resulting vibration response characteristics could explain previous observations on flow-induced vibrations of two equal-sized circular cylinders reported in the literature.

Experimental Measurements of Actively Controlled Bearing Damping With an Electrorheological Fluid

Selection criteria and design evaluations of several types of bearing dampers with active control for application to aircraft engines were described in a companion paper. A disk type electrorheological (ER) damper was chosen for further study and testing. The results of the tests and the final conclusions of the study are described in this paper. Experimental results including stiffness and damping coefficients are presented for the ER bearing damper with two types of ER fluid, 350 CS and 10 CS (centistokes) viscosity. The vibration attenuation performance of the ER damper was measured on a rotordynamic test rig in the form of free vibration decay, rotor orbits, and runup unbalance responses. The results show that the ER fluid with lower viscosity has the better characteristics for rotordynamic applications. It was found that ER fluids produce both Coulomb and viscous damping. If only the damping is considered, the Coulomb type is less desirable, but with active control it can also achieve control of rotor stiffness. A feedback control system was developed and applied to the ER damper with the objective of improving the overall rotordynamic performance of the rotor bearing system, considering both vibration amplitudes and dynamic bearing forces. A “bang–bang” (on and off) simple control logic was found to work better in practice than more sophisticated schemes. The measured runup response of the rotor-bearing system with this control approximated the desired vibration response curves fairly well. The tests highlighted some of the practical considerations that would be important for aircraft engine applications, such as the ER fluid limitations, the electrical power supply requirements, the electrical insulation requirements, the nonlinear relationship between the voltage and the damping, and the relative benefits of active control. It is concluded that active control of bearing damping is probably not a practical improvement over the passive squeeze film dampers currently used in most aircraft gas turbine engines. [S0742-4795(00)01202-3]

Analysis of Vibration of Timing Belt. Under a Moving Load.

Analytical results are presented for vibration of a wide timing belt under a moving load. The equation of motion is derived from Hamilton's principle, and approximate solutions to the basic equation are obtained using the Galerkin method. The steady-state responses are calculated using the harmonic balance method. Analytical results are presented which show the contributions of moving load position and moving load value to response curves. The response amplitude that varies with the width of timing belt. In the case of variable velocity, the response value shows very complicated behavior with pulley rotation. The response curves of vibration are greatly influenced by the moving load and the velocity.

Geotechnical interpretation of vibration response curves of piles (in French) : Rev Fr Geotech, N8, Aug 1979, P15–21 Davis A., Guillerman P.

Geotechnical interpretation of vibration response curves of piles (in French) : Rev Fr Geotech, N8, Aug 1979, P15–21 Davis A., Guillerman P.

Some Experimental Results on Wing Flutter

The present paper represents a progress report of some experiments being carried out in the aerodynamics laboratory of Harvard University, The first part of the experimental investigation consisted in the measurement of the vibration response curves of a wing in the wind tunnel. A wing, free to vibrate in bending and in torsion, was subjected to a forced vibration at various air speeds up to the flutter speed. These measurements are of interest in that they show how the two natural frequencies of the wing come together as the flutter velocity is approached. The peaks of these response curves are also of interest in that they determine the maximum stresses which are experienced, for instance, by a propeller which is subjected to periodic impulses from the engine. The second part of the investigation deals with the problem of flutter above the stall. Measurements show that at angles of attack above the positive stalling angle and below the negative stalling angle the flutter speed is decreased to less than one-third of the flutter speed of the unstalled wing. This flutter seems to be associated with an instability which arises when the slope of the lift curve becomes negative. Experiments on a metal wing supported as a cantilever indicate that the flutter at the stall may also be associated with an excitation from a system of Karman vortices.