Influence Of Spring Stiffness Research Articles

Free vibration of spinning stepped functionally graded circular cylindrical shells in a thermal environment

This paper investigates the free vibration of spinning stepped functionally graded material (FGM) circular cylindrical shells with general boundary conditions in a thermal environment. The artificial spring is implemented to simulate the general boundary constraints. Temperature-dependent material properties change constantly along the thickness direction. The Donnell-Mushtari shell theory is applied to derive the energy functions of thin stepped circular cylindrical shells, where the effect of centrifugal force and Coriolis force is taken into account. The modified Fourier-Ritz method is utilized to derive the frequency equations of the spinning stepped FGM circular cylindrical shells. The influences of spring stiffness, power-law index, and temperature on the traveling wave frequencies are investigated. The influence of configuration on the forward wave frequency and critical speed of three stepped shells, including the one-end thickened, the two-end thickened, and the middle-thickened stepped shells, is discussed. For each configuration, design strategies for the stepped shells are proposed.

Study of backflow volume due to check valve’s lag motion in liquid hydrogen piston pump

The liquid hydrogen piston pump is the key equipment in the process of storage, transportation, and refueling of liquid hydrogen. The timely motions of suction and discharge valves are beneficial to the transport performance and volumetric efficiency of the pump. This study sets up an operation frame of the liquid hydrogen piston pump in which reciprocating pistons and check valves with a conical spool interact. Backflow occurs when there is a delay in the spool’s motion, which is more common in suction valves than in discharge valves. The influence of spring stiffness and spool-head angle of the valve cone on the suction valve’s backflow volume is analyzed and further optimized. The results indicate that there exists an optimal spool-head angle and spring stiffness for minimizing backflow volume during the closing phase of the suction valve. This research contributes to enhancing the volumetric efficiency of the liquid hydrogen piston pump.

Free Vibration Analysis of Trapezoidal Bi-Stable Laminates Supported at the Elastic Midpoint of the Median Line

This study investigates the natural vibration of trapezoidal bi-stable laminates (TBL) with elastic supports at the midpoints of the median lines. Configuration of the midplane of the TBL is expressed by a polynomial with 17 parameters. Then, the first order shear deformation theory, curing temperature, and nonlinear strain displacement relations combining energy principles are applied to obtain the bi-stable shapes numerically. Three translational springs and two rotational springs are added at the midpoint of the median line in the trapezoidal bi-stable laminate to acquire elastic point supports. And, by varying the stiffness of the springs, arbitrary elastic point support boundary conditions can be achieved. Chebyshev polynomials are applied to characterize the mode shape function of the TBL. The vibration mode functions of the TBL are mapped to a square area under the new coordinate system by using the coordinate mapping method. Furthermore, the effects of geometry, layup sequence, and spring stiffness on the natural vibrations of the TBL are analyzed, which provides a reference for research in this field. The innovation and highlights lie in the following: (1) the natural frequencies and modes of trapezoidal bi-stable plates are solved; (2) arbitrary elastic support is achieved by a set of artificial springs; (3) the influences of spring stiffness, layer sequence, and trapezoidal base angle on the natural vibration of a trapezoidal bi-stable plate are studied.

Thrust Enhancement of DTMB 5415 with Elastic Flapping Foil in Regular Head Waves

Recent studies indicate that bow foil biomimetic systems can significantly improve ship propulsion in waves. In this paper, the DTMB 5415 ship model is taken as the object and a semi-active elastic flapping foil is proposed to install at its bow underwater position. When a ship sails in head wave, heave and pitch motion will occur, which will drive the bow foil to form heave motion. According to the working characteristics of elastic foil, bow foil can generate forward thrust under drive of given heave motion. At first, co-simulation of the ship with self-pitching bow foil in head waves is realized by ISIS-CFD solver and preliminarily realizes drag reduction and thrust increase effect of the bow foil. At the same time, it is found that the effect of bow foil on hull drag reduction is reflected in two aspects, one is the additional thrust generated by the bow foil and the other is that suppression of the bow foil on hull motion also reduces hull resistance in waves. Then, in order to optimize the working characteristics of elastic bow foil, the influence of spring stiffness and span length of the bow foil on drag reduction and thrust increase effect is discussed. A preliminary spring optimization result is obtained, as well as the influence of the span length of the bow foil on the system.

Numerical Simulation and Experimental Test of the Sliding Core Dynamics of a Pressure Controlled Jet Crushing Tool for Natural Gas Hydrate Exploitation

A pressure-controlled jet crushing tool (PJCT) for the exploitation of deep-sea natural gas hydrate (NGH) was invented to achieve sediment crushing and cavity creation. The opening and closing of tool is controlled by changing the internal flow rate remotely. It can realize the controllable continuous switching of the working state between horizontal well drilling and cavity creation. A dynamic simulation model of the sliding core was established based on the innovative design scheme of the PJCT and the motion law of its slide core was analyzed under the influence of spring stiffness, friction coefficient, and flow rate loading scheme. Moreover, an engineering prototype of the PJCT was manufactured so that a sliding core motion experiment of the prototype was carried out. When the drilling fluid flow rate reaches 455 L/min, the PJCT can stably complete the self-locking and unlocking functions. Its sliding core needs more time to stabilize with an increase in spring stiffness. Meanwhile, the PJCT could achieve continuous fast switching between the mechanical drilling state and the jet crushing state within a cycle of continuous flow changes. Finally, the kinematic and dynamic working mechanism of the PJCT is verified by the combination of the numerical simulation and the experimental analysis above.

Torsional vibration reduction of rotating shafts for multiple orders using centrifugal double pendulum vibration absorber

Centrifugal Pendulum Vibration Absorbers (CPVAs) reduce the torsional fluctuations of rotating shafts at fixed vibration order by changing the natural frequency in accordance with the excitation frequency. Attenuation of multiple orders is necessary in the case of the rear wheel drive vehicle and cylinder deactivation applications for achieving refined vehicle performance. Single pendulum vibration absorbers attenuate only one vibration order at a time and the pendulum length must be reduced for higher orders in the order of (1/n2) times the distance between the center of rotation and pivot point to attenuate nth order vibration. Use of single pendulum absorbers for reducing higher orders has limitations due to manufacturing inaccuracies and occurrence of wear of joints over prolonged usage which reduces the effectiveness of absorber in reducing the torsional vibration. In this study, a centrifugal double pendulum vibration absorber (CDPVA) is proposed to make the design easy for higher orders by deploying two pendulums in series. The CDPVA is designed to attenuate the fundamental excitation order (n) and its second harmonic (2n) without significant reduction in the pendulum length hence making the design robust for prolonged usage. The mass and length values of the double pendulum are tuned to match the two natural frequencies correspond to the fundamental and second harmonic order of the torsional vibration excitation. Torsional springs are used at the pivot joints of the double pendulum to counteract the gravitational effects at low speeds and the influence of spring stiffness on the natural frequencies is analyzed. The nonlinear second order equations of motion of pendulum masses and rotor are solved analytically using method of multiple time scales and the stability characteristics of pendulum motion are analyzed at the excitation frequencies with different torque levels. Numerical simulation of complete nonlinear equations is carried out and the analytical results are compared with the simulation results. The designed CDPVA for 2nd and 4th order is tested on a 4-cylinder the rear wheel drive vehicle and considerable reduction is achieved in the torsional vibration of the drive shaft and also in the vibration levels at seating locations. The proposed methodology helps in designing the CDPVAs for attenuating the torsional vibration of multiple higher orders yet avoiding impacts in low speed operation.

Fluid-Structure Coupling Vibration of an Elastically Restrained Circular Plate

In this paper, an analytical method is presented to calculate the fluid-structure coupling vibration of an elastically restrained circular plate. The displacement of the plate is expanded in series of dry mode shapes and the motion of the fluid is described by velocity potential function. Considering the equilibrium differential equation of the plate and the velocity continuous conditions at the interface of fluid and structure, the Galerkin method and expansion of Fourier-Bessel series are used to establish the governing equations of the system. The free vibration characteristics of the circular plate in contact with fluid are studied and the present method is verified by comparison with numerical results. Furthermore, the influence of spring stiffness and fluid depth on the free vibration characteristics of the circular plate is investigated.

Sensitivity on the non-continuous supported laminated cylindrical shell to boundary conditions and lamination schemes

In this paper, the free vibration of laminated composited cylindrical shells with two kinds of non-continuous supported boundary condition are investigated. The artificial springs are used to simulate the arcs supported and points supported boundary condition. The equations of motion are derived by using the Chebyshev polynomials and the Lagrange equation, and Donnell’s shell theory is employed in this process. The accuracy of the present method compared with that of literature, and convergence analysis is carried out at the same time. Then, the influences of spring stiffness, the number of supported point, and the lamination schemes of non-continuous supported laminated composite cylindrical shells on frequency parameter are studied. The results show that the method can accurately deal with the free vibration of laminated shells with arbitrary non-continuous boundary and arbitrary lamination schemes.

On Generating Expected Kinetostatic Nonlinear Stiffness Characteristics by the Kinematic Limb-Singularity of a Crank-Slider Linkage with Springs

Being different from avoidance of singularity of closed-loop linkages, this paper employs the kinematic singularity to construct compliant mechanisms with expected nonlinear stiffness characteristics to enrich the methods of compliant mechanisms synthesis. The theory for generating kinetostatic nonlinear stiffness characteristic by the kinematic limb-singularity of a crank-slider linkage is developed. Based on the principle of virtual work, the kinetostatic model of the crank-linkage with springs is established. The influences of spring stiffness on the toque-position angle relation are analyzed. It indicates that corresponding spring stiffness may generate one of four types of nonlinear stiffness characteristics including the bi-stable, local negative-stiffness, zero-stiffness or positive-stiffness when the mechanism works around the kinematic limb-singularity position. Thus the compliant mechanism with an expected stiffness characteristic can be constructed by employing the pseudo rigid-body model of the mechanism whose joints or links are replaced by corresponding flexures. Finally, a tri-symmetrical constant-torque compliant mechanism is fabricated, where the curve of torque-position angle is obtained by an experimental testing. The measurement indicates that the compliant mechanism can generate a nearly constant-torque zone.

Surface Effects on a Coated Fiber with an Imperfect Interface Subjected to Plane Compressional Wave

With the rapid development of nanotechnology, nano-components and nano-materials will be widely concerned and applied. At the nano-scale, due to the obvious increase the ratio of surface area to the volume effect and surface effect of nano-components and nano-materials are significant, making their mechanical properties significantly different from the material properties under the macroscopic conditions. And in the practical cases, the interface is not always perfect and smooth, they always have a certain form of defects. Therefore, the wave function expansion method is used in the analytical solutions of dynamic stress concentration factor (DSCF) around a coated fiber with an imperfect interface at nano-scale. The stress boundary conditions on the interface are obtained by using the generalized Young-Laplace equation and the imperfect displacement boundary conditions on the interface are modeled by a spring model. Considering the effects of surface and spring model, the influence of spring stiffness, the number of incident wave and the surface effects on the DSCF are analyzed. The results show that the frequency of incident wave, the spring stiffness and the surface energy have significant effects on the dynamic stress concentration distributions of the nano-sized coated fiber. The smaller the spring coefficient is, the stronger the interface imperfection is, and the stronger the stress concentration at the boundary is. When the spring coefficient reaches a certain value, it is almost close to the dynamic stress value under the ideal interface. The DSCF are obviously different under different incident wave frequencies.

Dynamic Behavior of Reciprocating Plunger Pump Discharge Valve Based on Fluid Structure Interaction and Experimental Analysis.

The influence of spring stiffness and valve quality on the motion behaviors of reciprocating plunger pump discharge valves was investigated by fluid structure interaction (FSI) simulation and experimental analysis. The mathematical model of the discharge valve motion of a 2000-fracturing pump was developed and the discrete differential equations were solved according to FSI and results obtained by ANDINA software. Results indicate that spring stiffness influences the maximum lift, the opening resistance and shut-off lag angle, as well as the fluid velocity of the clearance, the impact stress and the volume efficiency of the pump valve in relation to the valve quality. An optimal spring stiffness parameter of 14.6 N/mm was obtained, and the volumetric efficiency of the pumping valve increased by 4‰ in comparison to results obtained with the original spring stiffness of 10.09N/mm. The experimental results indicated that the mathematical model and FSI method could provide an effective approach for the subsequent improvement of valve reliability, volumetric efficiency and lifespan.

English

This paper treats the dynamic and energy absorption responses of nonlinear spring-mass system using a developed two dimensional solver code. The influence of spring stiffness and various mass configurations on the impact response was investigated using validated models. Results are quantified in terms of important impact response and indicate that an assembly of spring-mass system can be employed to examine the impact response of energy absorption system prior to the detailed numerical analysis and experiment. The developed solver code will be useful for educational purposes to preliminarily understand the behavior and impact response of energy absorbing system without learning a piece of complicated nonlinear commercial finite element codes namely LS-DYNA. The developed code could facilitate the early stage of evaluation for impact applications.   Key words: Spring-mass, dynamic, solver, energy absorption, finite element, impact.

Dynamic Analysis of Elastic Support Beam Subject to Moving Load

The dynamics of elastic support beam are studied and the latent equation of the freely vibration modes of elastic bearing beam is deduced. The equation of the forced vibration of an elastically supported beam is obtained by the Lagrange equations and the influence of spring stiffness and moving load speed are analyzed. Calculation results show: the elastic supports have great effects on responses of beams, the dynamic amplification of deflections and stresses increases with the spring stiffness; the dynamic response of beam also increase with the increase of the speed of moving loads.

Investigation of acoustic emission accompanying stick-slip movement of rock samples at different stiffnesses of spring–block system

Understanding of friction process, especially, transition from stable to stick-slip motion, is very important in various fields from mechanical engineering to seismology. It seems that analysis of acoustic emission (AE) accompanying the friction process can be a sensitive tool for revealing fine details of the friction process. In the present work, acoustic emission accompanying the stick-slip movement of basalt samples has been investigated in laboratory slider-spring device. Exactly, the influence of spring stiffness on the statistical and dynamical characteristics of stick-slip generated AE has been studied. Different time series compiled from recorded AE wave trains have been analyzed using statistical and dynamical data analysis methods. We found that statistical and dynamical changes in acoustic emission of stick-slip movement depend on the stiffness of spring in spring–block system. The obtained results show that dynamics of stick-slip process undergoes both qualitative and quantitative changes at transition from stick-slip to stable sliding friction caused by increased stiffness of frictional system. Extent of regularity in stick-slip process, assessed by analysis of AE temporal distribution characteristics, increases at stiffer springs.

Analysis of cold-formed zed-purlins partially restrained by steel sheeting

This paper presents an analysis model for cold-formed purlin-sheeting systems subjected to wind uplift loading in which the restraint of the sheeting to the purlin is taken into account by using two springs representing the translational and rotational restraints provided by the sheeting. The model yields a set of three differential equations corresponding to one torsion and two bending equations. The set of equations is solved by means of trigonometric series. The influence of spring stiffness and fixing position of the purlin and sheeting on the stresses resulted in the cross-section of the purlin is discussed. The results obtained from this study not only highlight the influence of the sheeting restraints on the results of stresses but also can be used as an input to the finite strip code for carrying out the linear elastic buckling analysis of the sections.

Influence of spring stiffness and anisotropy on stick-slip atomic force microscopy imaging

This paper presents a detailed analysis of high-load friction atomic force microscopy (AFM) images of layered structures in terms of a discrete stick-slip model. It turned out that based on a geometric approach, the characteristics of slip behavior can be linked to the cantilever/sample spring anisotropy. In particular, the use of polar scans is emphasized to analyze and to quantify these characteristics. The measured stiffness as derived from the slip behavior is in correspondence with the stiffness inferred from static friction. It is concluded that the combined stiffness of substrate and cantilever is constant during an AFM scan in a given direction, which supports the simple stick-slip model.