Sprung Mass Research Articles

Graph oscillators: Physics-guided graph modeling of mass–spring–damper systems for trajectory prediction and damage localization

Recognizing that a multiple-degree-of-freedom mass–spring–damper system can be viewed as a group of connected nodes, this paper presents a novel computational framework that learns such coupled oscillations by a graph, a mathematical structure describing pairwise connections between objects. Further reinforced by an incomplete equation of motion, distributed neural networks and an anti-symmetric coupling constraint, we can learn unknown coupling mechanisms (or nodal interactions in the language of graph models) using limited data. The proposed physics-data-hybrid method demonstrates a promising predictive capability even for unseen control inputs, outperforming three black-box and grey-box counterparts in synthetic and experimental studies. In addition to its predictive capability, the distributed parameterization of nodal interactions allows us to identify local anomalies by evaluating updates after short transfer learning. While limits of the current method exist, it displays the potential of a generalizable and interpretable meta-model for predicting nonlinear trajectories and identifying the system’s status.

A Dual Triggering Scheme to Adaptive Fuzzy Resilient Control of Switched Nonlinear Systems Against Mixed Attacks.

A dual event-triggered adaptive fuzzy resilient control scheme for a class of switched nonlinear systems with vanishing control gains under mixed attacks is proposed in this article. The scheme proposed achieves dual triggering in the channels of sensor-to-controller and controller-to-actuator by designing two new switching dynamic event-triggering mechanisms (ETMs). An adjustable positive lower bound of interevent times for each ETM is found to preclude Zeno behavior. Meanwhile, mixed attacks, that is, deception attacks on sampled state and controller data and dual random denial-of-service attacks on sampled switching signal data, are handled by constructing event-triggered adaptive fuzzy resilient controllers of subsystems. Compared with the existing works for switched systems with only single triggering, more complex asynchronous switching caused by dual triggering and mixed attacks and subsystem switching is addressed. Further, the obstacle caused by vanishing control gains at some points is eliminated by proposing an event-triggered state-dependent switching law and introducing vanishing control gains into a switching dynamic ETM. Finally, a mass-spring-damper system and a switched RLC circuit system are applied to verify the obtained result.

Multiple scattering analysis of phononic crystals

Multiple scattering theory allows for the computation of states and scattering fields on a diverse variety of wave systems. Through rigorous analysis, this theory provides insights into wave phenomena such as diffraction, reflection, and transmission, contributing to a comprehensive understanding of the intricate dynamics of classical systems. Our study focuses on flexural waves in thin elastic plates, with point-like mass spring resonators serving as scatterers attached the plate’s top surface. Finite clusters of scatterers will be analysed without imposing symmetries or periodicity in the system. Despite the apparent simplicity of this model, it proves capable of unveiling and predicting many behaviours related to the latest topics on metamaterials, including phononic crystals, quasicrystals, topological insulators, rainbow trapping effects or spatio-temporal modulation. In essence, this technique offers a foundation for advancements in materials science, structural engineering and all the domains where metamaterials and phononic crystals find application.

Analytical exploration of generic undamped mass–spring chains: A comprehensive study

Analysis of structural vibrations presents challenges due to the coupling between different degrees of freedom, often preventing the derivation of analytical expressions for quantities such as poles, vibration amplitude, etc. While numerical methods are commonly employed to tackle such challenges, their purely numerical nature prevents achieving a comprehensive understanding of the system behaviour. This paper builds on a novel recursive transfer function formulation recently proposed by the authors to analytically characterise the dynamics of generic undamped mass-chain systems. This approach provides fundamental properties and analytical insights that cannot be obtained through current numerical approaches, representing a significant breakthrough in the understanding of vibrations and offering valuable insights for analysing complex vibrating systems. These results presented in this paper allow for a rapid assessment of the minimum phase nature of the vibration system through straightforward stability assessment, and present analytical expressions for sums and multiplications of natural frequencies squared by induction and Vieta’s formulas. Furthermore, it derives conditions for existence of repeated roots using direct analytical derivation of the characteristics equations, including purely imaginary roots and repeated roots at the origin, showing that repeated roots can only occur when some forms of spatial symmetries exist, and confirms bounds for the arithmetic mean of natural frequencies by using inequalities between geometric, arithmetic and quadratic means. Additionally, analytical conditions are established for systems with different degrees of freedom to share the same roots, providing a theoretical foundation for eigenvalue assignment in the time domain or pole placement in the frequency domain. This foundation enables the determination of desired natural frequencies from scratch using transparent analytical conditions, without relying on complex algorithms typically required by current inverse methodologies involving passive structural modifications or active controllers. Moreover, this paper also explores the relationship between independent and coupled vibrations, providing insights for comparing natural frequencies. Overall, this paper contributes to a deeper understanding of structural vibrations through analytical exploration and offers practical guidance for eigenvalue assignment and natural frequency analysis.

An analytical vibration model of a one-dimensional two-stage periodic isolation system for the broadband vibration suppression of an underwater glider

Periodic isolation system is effectively applied in broadband vibration control. To further enhance the broadband vibration attenuation effect, the paper proposes a two-stage periodic isolation system for an underwater glider. The analytical model of the one-dimensional two-stage periodic isolation system is developed through the multi-degree of freedom spring mass model method. For illustrating the superiority of the proposed two-stage periodic isolator, the force transmission ratio and the wave propagation constant of the SDOF isolator, the single-stage periodic isolator, and the two-stage periodic isolator are calculated and compared. In order to obtain the dynamic parameter influences on the vibration isolation performances as the design guidelines of the two-stage periodic isolator, the parametrical study is carried out based on the analytical model. Furthermore, a two-stage periodic isolator is designed for an underwater glider. The application effect of the two-stage periodic isolator is investigated through analytical modeling and finite element method, comparing to the single-stage periodic isolator. The research results from the analytical models show the proposed two-stage periodic isolator could strength the broadband vibration suppression. The parametrical study results demonstrate the vibration attenuation bandgap and attenuation amount are greatly influenced by the designed dynamic parameters, such as the mass unit and the spring unit of the periodic isolator, the intermediate mass of the two-stage isolator, and the number of the periodic cells. In application study of an underwater glider, the finite element results verify that the two-stage periodic isolator has more vibration attenuation effect than the single-stage periodic isolator. The vibration isolation assessment according to the proposed analytical model gives good predictive performance before the finite element model verification.

Adaptive stabilization of stochastic systems with polynomial nonlinear conditions, unknown parameters, and dead‐zone actuator

AbstractMany practical dynamic models always suffer from complex nonlinearities, parameter uncertainties and random noises. Such kind of models are always characterized by uncertain stochastic nonlinear systems. Besides, many factors will lead to dead‐zone actuator, which further adds more challenges to control engineering. This paper studies stabilization issue of stochastic systems with polynomial nonlinear conditions, unknown parameters and dead‐zone actuator. An adaptive control approach is proposed by exploring homogeneous domination control and using dynamic‐gain‐based adaptive design strategy. It shows that all the signals are bounded almost surely and the system states converge to the origin almost surely. The presented method is successfully applied to the mass spring mechanical system.

A mass spring model applied for characterizing mode I fracture in orthotropic materials

A mass spring model applied for characterizing mode I fracture in orthotropic materials

The effect of high-speed railway train on the seismic response of bridge under earthquakes

This study aims to discuss the effect of high-speed railway train on the seismic response of bridge girder under earthquakes especially pay attention to the possible response reduction to the bridge caused by vehicle, utilizing experimental and simulation methods. A 1:10 scale model for the train-track-bridge system was built and a high-speed train running test platform based on shaking table array was constructed for the seismic loading test at varying running speed. To account the effects of different earthquake characteristics, earthquakes under the four types of site soil in the far-field and near-field were selected. The vehicle was modeled in two kinds of ways to distinguish the effects of spring-mass vehicle and additional mass which means a vehicle was set with spring suspension and mass, while another with additional mass only. Through a large amount of numerical simulation dates to determine the distribution interval of specific reduction value caused by the vehicle under the earthquake. Results in running tests and numerical simulation indicate that the lateral acceleration of the bridge girder can be effectively reduced when the train is stationary. The reduced ratios were about 4%− 8% compared without train on bridges. As the speed increases, the response of bridge is generally intense and the reduction is also weakened. Similar reduction was not observed in the response of vertical earthquake excitations, and high-frequency earthquakes have adversely affected this kind of reduction. The main reason for the reduction of lateral seismic response of bridge girder in the presence of static vehicle can be attributed to the phase difference between vehicle and bridge caused by a mass damper-like action, and the additional mass cannot cause similar changes alone.

A Distributionally Robust Optimization Approach to Two-Sided Chance-Constrained Stochastic Model Predictive Control With Unknown Noise Distribution

In this work, we propose a distributionally robust stochastic model predictive control (DR-SMPC) algorithm to address the problem of multiple two-sided chance constrained discrete-time linear systems corrupted by additive noise. The prevalent mechanism to cope with two-sided chance constraints is the so-called risk allocation approach, which conservatively approximates the two-sided chance constraints with two single chance constraints by applying Bool's inequality. In this proposed DR-SMPC framework, an exact second-order cone approach is adopted to abstract the multiple two-sided chance constraints by considering the first and second moments of the noise. With the proposed DR-SMPC algorithm, the worst-case probability of violating safety constraints is guaranteed to be within a pre-specified maximum value. By flexibly adjusting this pre-specified maximum probability, the feasible region of the initial state can be increased for the SMPC problem. The recursive feasibility and convergence of the proposed DR-SMPC are rigorously established by introducing a binary initialization strategy for the nominal state. A simulation study of a single spring and double mass system was conducted to demonstrate the effectiveness of the proposed DR-SMPC algorithm.

Dynamic fracture toughness measurement of graphite material considering inertial effect

Graphite materials are widely used as moderators, reflectors, and core structural materials in high-temperature gas-cooled reactors. During operation, graphite materials in nuclear reactors may be subjected to dynamic loads caused by earthquakes or other factors. Therefore, the dynamic fracture properties of graphite materials need to be investigated. In this study, dynamic three-point bending drop hammer impact experiments were conducted on IG-11 graphite specimens with precracks to measure their dynamic fracture toughness under medium- and low-speed impacts using a digital image correlation method. Traditional methods for measuring fracture toughness based on ASTM standards do not consider the influence of the inertial effect, leading to unreasonably large measurement results. To address this disadvantage, the dynamic fracture toughness of IG-11 graphite was evaluated using a spring–mass model that considers the inertial effects of materials. Results indicated that the measured fracture toughness was significantly lower than that obtained based on the ASTM standard and increased almost linearly with increasing impact velocity. The toughening mechanism was analysed by observing the fracture morphology of the samples using a scanning electron microscope. The results showed that as the impact velocity increased, the fracture mode of the graphite samples gradually changed from intergranular to transgranular fracture, and the samples absorbed sufficient energy, resulting in a noticeable toughening phenomenon.

Unveiling advanced modelling and analysis: the integrated system and formula for mass–spring–damper with hydraulic damper systems

Unveiling advanced modelling and analysis: the integrated system and formula for mass–spring–damper with hydraulic damper systems

Neural Network-Based Adaptive Height Tracking Control of Active Air Suspension System with Magnetorheological Fluid Damper Subject to Uncertain Mass and Input Delay.

In this paper, we present a novel robust adaptive neural network-based control framework to address the ride height tracking control problem of active air suspension systems with magnetorheological fluid damper (MRD-AAS) subject to uncertain mass and time-varying input delay. First, a radial basis function neural network (RBFNN) approximator is designed to compensate for unmodeled dynamics of the MRD. Then, a projector-based estimator is developed to estimate uncertain parameter variation (sprung mass). Additionally, to deal with the effect of input delay, a time-delay compensator is integrated in the adaptive control law to enhance the transient response of MRD-AAS system. By introducing a Lyapunov-Krasovskii (LK) functional, both ride height tracking and estimator errors can robustly converge towards the neighborhood of the desired values, achieving uniform ultimate boundness. Finally, comparative simulation results based on a dynamic co-simulator built in AMESim 2021.2 and Matlab/Simulink 2019(b) are given to illustrate the validity of the proposed control framework, showing its effectiveness to operate ride height regulation with MRD-AAS systems accurately and reliably under random road excitations.

Finite element dynamic modeling and vibration reduction analysis of the double-lap bolted thin plate with partially attached constrained layer damping

The double-lap bolted thin plate is widely used, but it is easy to produce vibration. In this paper, the method of attaching H-shaped constrained layer damping (CLD) is adopted to reduce vibration, and the finite element dynamic model of the double-lap bolted thin plate with H-shaped CLD is investigated. The innovations of the modeling method are described as follows. A composite element with four nodes and 28 degrees of freedom (DOFs) is produced by taking into account the interlaminar shear deformation of the CLD structure and employing complex modulus to quantify the damping characteristics of the viscoelastic layer. A series of transition elements are constructed to conduct the assembly of elements with inconsistent dimensions. Complex stiffness spring components and mass elements are presented to simulate the stiffness, damping, and mass characteristics of the double-lap bolt joint based on the crock-shaped stress distribution in the double-lap bolt joint and taking the bolt effect region into account. Finally, a case study is carried out, and the rationality of the finite element model of the bolted structure in solving the natural characteristics and vibration response parameters is verified by the established experimental tests. At the same time, the test and modeling results show that the H-shaped CLD reduces vibration on the double-lap bolted thin plate. Furthermore, based on the established finite element model, the influence of the attaching position of the H-shaped CLD, thicknesses of the viscoelastic layer, and the constraining layer on the vibration characteristics of the bolted structure are analyzed.

Insights into the flame transitions and flame stabilization mechanisms in a freely falling burning droplet encountering a co-flow

The present study investigates the flame dynamics of a contactless burning fuel droplet under free fall subjected to a co-flow. The dynamic external relative flow established due to co-flow and droplet acceleration results in a series of droplet flame transitions. Different flame structures were observed, including a wake flame, reversed wake flame and enveloped flame. Following ignition, the droplet is allowed to fall through the central tube of a co-flow arrangement, and, at its exit, the droplet flame encounters the co-flow. The wake flame, which was established based on the droplet's instantaneous velocity of descent, encounters the abrupt relative velocity jump due to the co-flow. This causes the droplet flame to go through various transitions as it approaches equilibrium with the surrounding flow. Once it equilibrates, the droplet flame evolves in response to the instantaneous relative flow velocity. The droplet flame evolves by altering both its shape and the stabilization mechanism. Two stabilization mechanisms were identified for the droplet wake flame: edge-flame stabilization and bluff-body stabilization. The stabilization mechanism for different flame structures and the transition events have been theoretically analysed, and the relation between flame shape evolution and flow velocity has been determined based on the flow-field characteristics at the corresponding Re (Reynolds number) range. Furthermore, these correlations are employed in a mathematical formulation based on the spring–mass analogy, which predicts the droplet flame evolution after encountering the co-flow, including all the transition events.

Nonlinear oscillator acceleration and period variation with amplitude

A classic nonlinear spring mass oscillator, the nonlinearity of which could be varied by changing the initial stretching of the spring, was used to investigate how the amplitude dependence of the period and the harmonic content depended on the nonlinearity. The oscillations were measured with a photogate and a MEMS accelerometer, allowing both the oscillation period and the Fourier components of the motion to be precisely determined. The results were in good agreement with theory.

Stability optimization of time-delay systems with zero-location constraints applied to non-collocated vibration suppression

We present an active control method for achieving non-collocated vibration absorption, implemented on a lumped mass system. The task of suppressing vibrations at a number of frequencies, at a target mass is recast into a problem of assigning zeros of the transfer function from the external excitation force to the position of the target mass. The controller design involves computing the controller parameters by utilizing the available output feedback to directly assign a set of zeros on the imaginary axis while simultaneously preserving the overall stability with a sufficient margin. The design also takes into account delays in the feedback path. The presence of delays leads to an infinite dimensional system for which, there exists in general, infinitely many characteristic roots. The requirement of achieving sufficient damping in the resulting closed-loop system together with suppressing vibrations of the desired frequency leads to a constrained optimization problem of minimizing the spectral abscissa function subject to zero-location constraints. These constraints exhibit polynomial dependence on the controller parameters. We present two approaches for controller parameterization for the single and multiple input case. Both approaches are based on constraint elimination and exploit the property that the constraints are affine in a selection of the gain parameters. Finally, the methodology is verified by simulating on a spring–mass–damper system following which, it is then validated experimentally on a laboratory setup.

Adaptive stable backstepping controller based on support vector regression for nonlinear systems

In this paper, a novel adaptive stable backstepping controller(BSC) based on support vector regression (SVR) has been introduced for nonlinear dynamical systems. Stable BSC is designed over Lyapunov stability of the closed-loop system. The nonlinear system dynamics required to constitute the BSC architecture are identified via SVR. The prediction competency of SVR and the stable behavior of BSC are aggregated in this architecture for nonlinear systems. The performance evaluation of the proposed adaptive BSC has been examined on a nonlinear inverted pendulum(IP) and a nonlinear mass–spring–damper(NMSD) system. The acquired results provide a successful and stable BSC control performance for both nonlinear systems.

An improved van der Pol wake oscillator model for a 1DOF circular cylinder undergoing vortex induced vibrations

An optimization procedure is presented for prescribing the empirical coupling parameters of a modified coupled van der Pol (VDP) wake oscillator and mass–spring–damper system for a one degree of freedom (1DOF) circular cylinder system undergoing vortex induced vibrations (VIV). This approach allows for the generalization of the traditional VDP model to cover a large VIV parameter range. The procedure is developed using experimental data covering the parameter space: 3<U∗<11, 8<m∗<20, 0.003<ζ<0.063, ReD=4000. The VDP model contains empirical coupling coefficients that describe the regime specific dynamic damping, ϵ, and wake coupling, β. Two calibration procedures are considered and the improvements over the traditional VDP model in predicting the VIV response are discussed. Subsequently, a regression fit is used to prescribe the two empirical coupling coefficients as functions of m∗, ζ and U∗. The generalized model results in a better prediction of the VIV response in terms of identification of lock-in regimes, lock-in frequency and amplitude response over several regimes when compared to the classical models. The use of a functional representation replaces the need for using tables and reduces user input for determining regime-specific coupling coefficients.

Simplified numerical model for the collapse analysis of RC frame under oblique impact

The objective of this study is to develop a simplified numerical model that can be used to accurately and quickly conduct collapse analysis of a reinforced concrete (RC) frame impacted by a vehicle obliquely at 45°. The simplified numerical model included introduces a simplified RC frame and a simplified vehicle. For the simplified RC frame, a mixed modelling technique was used, in which structural components that experienced serious damage were simulated using detailed elements, while the retained structural components were simulated by larger elements. A constraint algorithm of nodal rigid body in LS-DYNA was adopted to guarantee the displacement compatibility of two kinds of element. For the simplified vehicle model, the spring–mass system was improved on the basis of the energy conservation principle to represent the vehicle in a 45° impact. Combining the simplified RC frame model and vehicle model, the impact response of an RC frame subjected to vehicle impact was studied and compared with the results of a detailed RC frame model impacted by a detailed vehicle. The validation confirmed that these introduced simplifications could significantly improve the computational efficiency and ensure the computational accuracy for the collapse analysis of an RC frame subjected to vehicle impact.

Event-based performance guaranteed tracking control for constrained nonlinear system via adaptive dynamic programming method

An optimal tracking control problem for a class of nonlinear systems with guaranteed performance and asymmetric input constraints is discussed in this paper. The control policy is implemented by adaptive dynamic programming (ADP) algorithm under two event-based triggering mechanisms. It is often challenging to design an optimal control law due to the system deviation caused by asymmetric input constraints. First, a prescribed performance control technique is employed to guarantee the tracking errors within predetermined boundaries. Subsequently, considering the asymmetric input constraints, a discounted non-quadratic cost function is introduced. Moreover, in order to reduce controller updates, an event-triggered control law is developed for ADP algorithm. After that, to further simplify the complexity of controller design, this work is extended to a self-triggered case for relaxing the need for continuous signal monitoring by hardware devices. By employing the Lyapunov method, the uniform ultimate boundedness of all signals is proved to be guaranteed. Finally, a simulation example on a mass–spring–damper system subject to asymmetric input constraints is provided to validate the effectiveness of the proposed control scheme.