Spring Stiffness Research Articles

Stability of Running Stride Biomechanical Parameters during Half-Marathon Race

This study explores the stability of biomechanical parameters of the running stride of male trained athletes during a half-marathon competition. Using a field-based descriptive design, eight male athletes from a local training group were monitored throughout an official half-marathon race under identical conditions, assessing biomechanical parameters including ground contact time (GCT), leg spring stiffness (LSS), vertical oscillation (VO), and stride length (SL) recorded via the Stryd Summit Power Meter. A repeated measures analysis of variance (RM ANOVA) was conducted to detect significant changes in biomechanical parameters as the race progressed. Results demonstrated minimal changes in all parameters, with no significant differences observed for GCT (F = 0.96, p = 0.38), VO (F = 0.23, p = 0.87), and SL (F = 1.07, p = 0.35), and a small (η2 = 0.004) yet statistically significant difference in LSS (F = 5.52, p = 0.03) between the first and second segments, indicating that athletes were able to maintain stable biomechanical parameters throughout the race. The conclusion highlights the need for personalized training programs tailored to the unique biomechanical adaptations and demands of endurance running.

Modelling and simulation of a novel secretary bird-inspired vibration isolator

Abstract In this article, a novel secretary bird-inspired vibration isolator (SBIVI) is presented and investigated. The vibration isolator consists of an X-shaped stiffness adjustment mechanism and a lever arm structure that mimics the leg and wing of the secretary bird respectively. The biodynamics of the secretary bird is briefly introduced. The structure mapping from the body of the secretary bird to the scheme of the proposed SBIVI is analyzed. For the purpose of confirming the isolation performance of the SBIVI, the theoretical dynamics model is built while the virtual prototype simulation is carried out. By adjusting the values of the inertial mass and spring stiffness, the SBIVI can be easily installed with optimal operating conditions. From the simulation results, it is concluded that the vibration suppression ability of the SBIVI surpasses the traditional X-shaped structure within the interest of the frequency bandwidth.

Non-smooth nonlocal mechanical diode

In this paper, we proposed a new mechanical diode with non-smooth and nonlocal elastic, which support a backflow of the input mechanical energy. It is composed of a nonlinear converter connecting with nonlocal bilinear springs and linear phononic crystal. The asymmetrical stiffness of bilinear springs can be utilized to periodically modulate the stiffness of converter, generate non-reciprocal propagation of mechanical waves, thereby decompose the excitation frequency into multiple sub-bands. Utilizing this characteristic of converter, during the forward propagation of mechanical diodes, it is possible to effectively surpass the cutoff frequency of phononic crystals, ensuring higher energy transmission efficiency and achieving wideband performance of mechanical diodes. Nonlocal connections induce a roton-like dispersion in the wave propagation, resulting in negative group velocities and partial energy backflow. The Runge-Kutta method is utilized to simulate wave propagation and verified by experimental. It is shown that the low-frequency impinging wave is rectified and nearly 100% contrast ratio is observed. Our work provide a new platform for mechanical wave manipulation and energy harvesting.

Development and validation of a hysteretic model for a novel self-centering friction damper

This study aimed to develop a novel self-centering friction damper (SC-FD) consisting of the winding rope, the friction shaft and the self-centering spring. The theoretical model and equations for the mechanical properties of the SC-FD were derived. Then, the dynamic performance test of the SC-FD and finite element simulation were done to validate the theoretical mechanical model of the SC-FD. Finally, the influence of the main parameters on the dynamic performance of SC-FD was analyzed and design recommendations were made. The study showed that the SC-FD exhibited stable flag-type hysteretic behavior, with good energy dissipation capability and self-centering performance. The theoretical model and equations derived in this study can be used to predicate the behavior of the SC-FD accurately. The parameters, such as the initial inclination angle of the winding rope, winding turns of the winding rope and the stiffness of the self-centering spring and so on, had significant influences on the mechanical performance of SC-FD, which should be optimized in the designing of the SC-FD in order to get excellent mechanical performance.

A semi-active quasi-zero-stiffness vibration isolation system through controllable lateral spring stiffness

A semi-active quasi-zero-stiffness vibration isolation system through controllable lateral spring stiffness

Numerical Simulation Study Considering Discontinuous Longitudinal Joints in Soft Soil under Symmetric Loading

In shield tunneling, the joint is one of the most vulnerable parts of the segmental lining. Opening of the joint reduces the overall stiffness of the ring, leading to structural damage and issues such as water leakage. Currently, the Winkler method is commonly used to calculate structural deformation, simplifying the interaction between segments and soil as radial and tangential Winkler springs. However, when introducing connection springs or reduction factors to simulate the joint stiffness of segments, the challenge lies in determining the reduction coefficient and the stiffness of the springs. Currently, the hyperstatic reflection method cannot simulate the discontinuity effect at the connection of the tunnel segments, while the state space method overlooks the nonlinear interaction between the tunnel and the soil. Therefore, this paper proposes a numerical simulation method considering the interaction between the tunnel and the soil, which is subjected to compression rather than tension, and the discontinuity of the joints between the segments. The model structure and external load are symmetrical, resulting in symmetrical calculation results. This method is based on the soft soil layers and shield tunnel structures of the Shanghai Metro, and the applicability of the model is verified through deformation calculations using three-dimensional laser scanning point clouds of sections from the Shanghai Metro Line 5. When the subgrade reaction coefficient is 5000 kN/m3, the model can effectively simulate the deformation of operational tunnels. By adjusting the bending stiffness of individual connection springs, we investigate the influence of bending stiffness reduction on the bending moment, radial displacement, and rotational displacement of the ring. The results indicate that a decrease in joint bending stiffness significantly affects the mechanical response of the ring, and the extent and degree of this influence are correlated with the joint position and the magnitude of joint bending stiffness.

Flow-Induced Vibration Analysis by Simulating a High-Speed Train Pantograph

This paper investigates the aerodynamic behavior and dynamic characteristics of high-speed train pantographs under various operating conditions using advanced aerodynamic simulations and dynamic analyses. The simulations show significant fluctuations in aerodynamic loads during tunnel entry and exit, heavily influenced by train speed and pantograph position (raised/lowered). Modal simulations reveal distinct low-frequency vibrations in pantographs, significantly impacted by external aerodynamic forces. Importantly, the lowered position exposes the pantograph to upward aerodynamic forces, leading to increased bow-net contact force and off-line rate, ultimately compromising current collection stability. Both maximum contact force and off-line rate further increase with higher train speeds. To improve pantograph design, the paper proposes adjustments to the airbag’s equivalent spring stiffness and the bow head’s density. These modifications aim to mitigate contact force and enhance the stability and reliability of pantographs at high speeds. This research offers theoretical and practical insights, aiding in the design, optimization, and refinement of future pantograph systems.

Vibration analysis of graphene-reinforced porous aluminum-based variable-walled thickness sandwich joined conical-conical panel with elastic boundary conditions using differential quadrature method

In this paper, a unified solution is proposed to investigate the vibration characteristics of the variable-walled thickness graphene-reinforced porous aluminum-based (GRPA) sandwich joined conical-conical panel (JCCP) with the arbitrary elastic support boundary conditions by using the differential quadrature method (DQM). The two surfaces of the sandwich JCCP are made of metallic aluminum and the central core layer is the GRPA. The core thickness of each conical plate varies linearly with its generatrix. Three types of the graphene distributions and two types of porosity distributions are considered along the core thickness direction. Based on the first-order shear deformation theory (FSDT), von-Karman strain displacement relationship, constitutive relationship and Hamiltonian principle, the partial differential governing equations of motion are obtained for the variable wall thickness GRPA sandwich JCCP. Using the DQM, the dynamic equation is discretized into the ordinary differential equation. The matrix of the characteristic equation is analyzed to solve the frequencies and mode shapes of the variable wall thickness GRPA sandwich JCCP. The effects of the spring stiffness, boundary conditions, graphene distributions, porosity distributions and geometric parameters on the vibration properties are studied for the variable wall thickness GRPA sandwich JCCP with two interesting elastic supported boundary conditions. At the same time, this article provides a useful approach for studying the arbitrary boundary coupled plate and shell structures with the variable wall thickness.

Nonlinear dynamic analysis of a spring coupled double beam based piezoelectric energy harvester under parametric base excitation

This paper proposes a base excited, spring coupled double cantilever beam with attached tip mass based piezoelectric energy harvester. The dimensions of the beams are so chosen that the system experiences 1:1 internal resonance. The governing coupled electro-mechanical equations of motion of the system are obtained by using the Lagrange principle which is reduced to the temporal form by using generalized Galerkin’s method. The governing temporal equations of motion are in the form of that of a parametrically excited coupled system with geometric and inertial nonlinearities. These nonlinear equations are solved using the method of multiple scales and the results are compared with those solved by numerical method (4th order Runge Kutta method) for principal parametric resonance conditions. Parametric studies are conducted by varying the tip masses of the beams, coupled spring stiffness, load resistance, external excitation frequency and excitation amplitude. Results show that by introducing spring coupling, the system operational frequency range increases significantly and also energy transfer process takes place due to the internal resonance. Significant enhancement of voltage and power are observed in the present work in comparison to the earlier studied equivalent single beam-based energy harvester.

Influence of fractal-based contact friction coefficient on the stiffness of disc springs: Experimental and numerical studies

In order to study the influence of friction coefficient on the stiffness of disc spring, A series of disc springs ( D = 71 mm) were selected in this paper. The tension and compression experiments of disc spring components were carried out by universal testing machine. The load-displacement characteristic curves of disc springs with different friction surfaces were obtained. The results show that in the loading process, the friction effect hinders the increase of the deformation of the disc spring, so that the actual stiffness of the disc spring is improved and the actual compensation amount is reduced, so this result is worthy of attention. In order to further study the influence of friction coefficient on the loading process of disc spring, according to the load-deformation formula of disc spring in A-L method, the tangential stress caused by friction is added, and the stiffness calculation model of corresponding disc spring is established by Workbench finite element software. The coefficients of different friction surfaces are used as variables for numerical calculation. The results show that the theoretical calculation, numerical calculation and experimental results of stiffness increase with the increase of friction coefficient under 0.55 h (the compensation displacement of A71 disc spring under the working displacement of corrugated tube ±10 mm). Among them, the numerical calculation results are close to the experimental results, and the error value is less than 1%. The numerical calculation results are corrected by using the experimental data, and the corrected model calculation results are in good agreement with the measured results.

A Numerical Study of the Performance of Point Absorber Wave Energy Converters

Free-floating and submerged wave energy converters (SWECs) are regarded as promising technologies for renewable energy production. These converters rely on a heave-motion buoy to capture the kinetic energy of ocean waves and convert it into electrical energy through power conversion systems. To better understand the impact of various factors on power generation and efficiency, the effects of different buoy shapes (rectangular, circular cylinder, and trapezoidal fin), submergence depths (0, 0.1, and 0.2 m), wave heights (0.04, 0.06, and 0.1 m), and spring stiffness (50 and 100 N/m) were investigated. A 2D numerical wave tank with a buoy was simulated, and the results were validated against experimental data. Information on vorticity, vertical displacement, power absorption, and efficiency are provided. The findings indicate that the buoy shape and wave height significantly affect power absorption and efficiency. Additionally, this study reveals that increasing submergence leads to higher power absorption and lower conversion efficiency.

Weak bond evaluation of lap bonding structures by SH guided waves using EMATs

ABSTRACT In this research, simulations and experiments were conducted for the bonding quality evaluation of an aluminum bonding structure, based on the SH guided wave analysis. In order to simulate the propagation of SH waves in the bonded structure, a 3D finite element model was established based on interfacial spring stiffness modeling. The frequency-wavenumber diagram was obtained by doing Fourier transform along the spatial axis in the time frequency domain simulation results. At the same time, the influence of the bonding interface weakening on the propagation characteristics of the guided wave was analyzed. The simulated dispersion curves of SH-guided waves in different bonding states were in good agreement with the theoretically results. In addition, a periodic permanent magnet electromagnetic acoustic transducer (PPM-EMAT) 3D finite element model was established. An optimized transducer was fabricated to excite pure SH0 mode. Then, a series of aluminum lap bonding structures with different bonding states were prepared. The effect of bonding interfaces on the propagation characteristics of SH waves was investigated. The interfacial spring stiffness can be determined when the STFT of the SH waves matches the theoretical dispersion curves. Thus, this method demonstrated an ultrasonic way to distinguish the weakening of the bonding structures.

Seismic displacement response analysis of Friction Pendulum Bearing under friction coupling and collision effects

Friction Pendulum Bearing (FPB) with shearing keys will exhibit friction-coupling effect and collision phenomenon subjected to horizontal orthogonal ground motions. This paper establishes a numerical analysis model of FPB with four shear keys and viscous damping, considering the impact of the friction coupling effect and collision between the FPB and the shear keys on its displacement response. The influence of parameters of FPB on seismic displacement response with considering collision effect under horizontal orthogonal ground motions was studied. The results suggest that adjustments in damping and equivalent stiffness exclusively impact the amplitude of the displacement response, maintaining the response waveform. Conversely, variations in friction significantly alter the response waveform, as friction induces changes in the natural frequency of FPB. A heightened collision impact is noted with reduced spring stiffness. The displacement response is particularly amplified when the collision occurs at the vicinity of peak displacement in the time-history response of FPB. When the restoring stiffness and Peak Ground Acceleration (PGA) are low, the friction coupling effect significantly reduces the amplification of displacement response caused by collision effects. Viscous damping can considerably reduce the impact of collisions on the peak displacement of FPB and prevent the collision effects from noticeably amplifying or diminishing the peak displacement of FPB.

A3-DOF frog-inspired quasi-zero stiffness isolator and its vibration control performance

To pursue a nonlinear isolator with simpler structure, better load adaptability, and wider quasi-zero stiffness (QZS) region, a 3-DOF bionic vibration isolation device is proposed and analyzed inspired by the superior landing performance of the frog's leg structure. The mechanism's dynamical equation is established using Lagrange's principle. The dynamic model is validated using ADAMS simulation. The effects of spring stiffness and rod length on static mechanical characteristics are analyzed. The vibration attenuation performance of the structure is analyzed under independent three-directional excitation and three-directional coupled excitation. Compared with the typical X-shaped QZS isolator and the traditional QZS isolator, the designed structure's advantages is demonstrated. By tuning the parameters and building a control route based on variable-stiffness dielectric elastomer, optimization of the device's vibration isolation performance under coupled excitation was accomplished.

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.

Advances in Pulse Tube Cooler with Dual-opposed Ambient Temperature Displacers

The pulse tube cooler offers several advantages, such as low vibration, high reliability, and no moving parts at the cold end. However, its efficiency is hindered by the limited phase modulation capability and acoustic power dissipation in the phase shifter. In response to this, Lihan Cryogenics has developed a Stirling pulse tube cooler employing ambient displacers. This innovative cooler comprises a moving magnet compressor with dual-opposed pistons and a co-axial cold finger. By utilizing ambient displacers, the cooler can recover expansion work and enhance cooling efficiency. This article highlights recent advancements in this type of cooler. To simplify manufacturing and increase reliability, the displacers now adopt a rod structure, reducing the requirement for supporting spring stiffness. Additionally, the cooler incorporates dual-opposed room temperature displacers, positioned orthogonally to the compressor piston axis (referred to as “OrthoCoolTM”). This arrangement results in low vibration, reduced flow resistance, and eased assembly and production challenges. Experimental tests demonstrate that compared to the cooler employing inertance tube phase modulation, the new ambient displacer structure effectively enhance system efficiency, achieving a cooling capacity of 100W at 77K with 1455W input electric power. The corresponding relative Carnot efficiency is 20%.

Effect of spatial setting angle on vibration of elastically restrained rotating beams

For a fully articulated rotor system, there may exist a spatial setting angle and elastically restrained root for each individual blade in rotation procedure due to flapping, drag and pitch hinges. Most of previous studies on rotating blades or beams focused on pitch angle and clamped root. In this paper, a three-dimensional dynamic model is proposed for elastically restrained rotating beams with spatial setting angle. The elastic deformation of the beam is expressed by three scalar variables in three-dimensional space including stretch deformation instead of the conventional axial deformation. The longitudinal shrinkage is considered to capture centrifugal forces. The penalty method is adopted to deal with the elastic constraints, which greatly simplifies the construction of admissible functions. A unified formulation is derived by a variational principle combined with Chebyshev orthogonal polynomials. One of the advantages of the present method is that any linearly independent and complete basis functions can be used as admissible function regardless of boundary conditions, and another advantage is that the present method is capable of handling arbitrary boundary conditions by only adjusting the values of penalty factor. The convergence and accuracy of the present method are validated by comparison, and the effects of boundary conditions, angular velocity and spatial setting angle on vibration characteristics are discussed in detail. The results show that natural frequencies increase as the spring stiffness rises in a certain range and the spatial setting angle plays a more significant role on dynamic characteristics for rotating beams.

Column-based programmable damper for impact protection and vibration suppression of jacket structures

Steel jacket structures subjected to environmental impacts exhibit severe dynamic responses, potentially causing local fatigue failure, plastic damage, and even catastrophic collapse. Therefore, a structure with adjustable stiffness and large damping is ideal for coping with complex environmental loads and dissipating kinetic energy. A novel programmable damper was designed by connecting N-layer coupling elements composed of a linear spring, wire ropes, and an asymmetric column. Analytical models for the elastic buckling behavior of the damper were derived and mutually verified with finite element analysis (FEA). Based on the analytical models, the dependence of the mechanical responses of the damper on the number of elements and the spring stiffness was investigated for design guidance. The results indicate that the N-layer damper has 2N different stiffnesses, and the total dissipation capacity increases by approximately 2.6N times compared with a single asymmetric column. For potential applications, the dynamic decay responses of representative jacket structures assembled with the damper were simulated using the FE software ABAQUS combined with user-defined-material (UMAT) code, which demonstrated that the programmable damper is an advanced device that simultaneously achieves adjustable stiffness and significant damping.

Pilot Study Investigating Effects of Changing Process Variables on Elastic and Energy-Absorbing Characteristics in Polyurethane/Agglomerated Cork Mix for Use in Micro-Transport Helmet.

This pilot investigation identifies the influence that changing the process variables of curing pressure, curing temperature, and mix ratio of a polyurethane/agglomerated cork matrix has on the mechanical properties of energy absorption, Young's modulus of elasticity, and spring stiffness in safety helmets intended for micro-transport riders. The results are compared to expanded polystyrene, a material commonly used in micro-transport helmets. Mechanical testing of the various samples found that, over the range tested, curing pressure had no effect on any of the mechanical properties, while increasing amounts of resin caused a stiffer structure, and increasing curing temperature led to increased energy absorption. Consistent with the elastic modulus findings, all polyurethane/agglomerated cork test samples demonstrated higher median levels of spring stiffness, ranging from 7.1% to 61.9% greater than those found for expanded polystyrene. The sample mixed at a 1.5:1 binder/cork ratio and cured at 40 °C displayed the closest spring stiffness to EPS. While the mechanical properties of the eco-friendly polyurethane/agglomerated cork matrix did not match those of expanded polystyrene, the difference in performance found in this study is promising. Further investigation into process variables could characterise this more ecologically based matrix with equivalent energy-absorbing and structural characteristics, making it equivalent to currently used expanded polystyrene and suitable for use in micro-transport helmets.

Development and performance assessment of different squeal index metrics based on experimental data

As an NVH problem observed in automotive brake systems, the significance of brake squeal phenomenon still persists; and the estimation of squeal propensity is a crucial operation. Thus, developing different means to define squeal propensity is an important task. As being one metric, squeal index is widely used for this purpose; and there already exists several different squeal index formulations in the available literature. The main objective of this study is to develop new squeal index formulations and assess their performances. Though, unlike the existing formulations, not only the measured data but also the operating and design parameters of the system of interest are also incorporated in the proposed formulations. The experimental data used for squeal index formulations are obtained on a mass-sliding belt experiment, where squeal-like behavior can successfully be observed. Experiments are conducted at different operating and design parameter conditions. First, cases with presence and absence of squeal-like behavior are observed on the measured data in time and frequency domains. Then, eight different squeal index formulations are developed, where different set of parameters are utilized in each formulation. Some of these parameters are extracted from the measured data (time and frequency domains), and the rest are adopted from the key operating and design parameters. Finally, the performances of proposed squeal indexes are assessed through their relative amplitude variations. In conclusion, the second squeal index formulation is found to have superior performance for distinguishing the effects of operating and design parameters on the occurrence of squeal-like behavior. Furthermore, the sixth squeal index formulation is found to have the best performance for differentiating the effect of spring stiffness on the initiation of squeal-like behavior.