International Journal of Applied Mechanics

This paper presents the dynamic response of a rotating beam with elastic restraints in forward flight. The motion equations of the system are established by Hamilton’s principle. The structure model is established by Euler-Bernoulli beam theory. The influence of elastic restraints and centrifugal force is considered in the form of potential energy. The aerodynamic model is established by Greenberg theory and considered in the form of an external force. A modified Fourier series method is used to expand the displacement field. The stiffness intervals of boundary springs corresponding to the elastic restraints are determined by natural frequencies. The effects of advance ratios on the dynamic response of the system are studied. Then, the effects of spring stiffness in different directions are compared. The results show that the displacements and velocities of the rotating beam increase with the advance ratio. The displacement amplitudes of the rotating beam increase as the stiffness of boundary springs decrease.

Multi-Layered viscoelastic composite laminates are commonly designed as damping structures in non-isothermal environments to avoid unnecessary vibration and ensure the safety of structures working in vibration engineering, such as reducing the unwanted vibration and noise of aircraft structures and vehicles. In recent years, there have been extensive research works that contributed to evaluate and predict the influences of relaxation time parameters, nonlocal elastic/thermal parameters, and temperature related material properties on the dynamic thermo-viscoelastic responses of such structures. Nevertheless, the effects of fractional derivatives and related parameters are rarely reported on this topic. This paper aims to construct a mathematical model of transient structural thermo-mechanical response of multi-layered viscoelastic composite laminates with non-idealized interfacial conditions (i.e., the thermal contact resistance and elastic wave impedance) by introducing the new definitions of the Caputo-Fabrizio (CF), Atangana-Baleanu (AB), and Tempered-Caputo (TC) fractional derivatives. The Laplace transform method is applied to obtain the transient solutions. The dimensionless results reveal that the new fractional derivatives, non-idealized interfacial conditions and material constants ratios significantly affect the wave propagations and transient thermo-viscoelastic responses, and the harmful heat/stress isolation at interface are improved to some extent.

To study the impact of on/off-ramps on traffic stability in heterogeneous traffic flow, a novel lattice hydrodynamic model was presented. The new model’s stability condition was determined using the linear stability analysis method. The theoretical results reveal that traffic flow stability is influenced by the proportion of vehicles with different maximum speeds and safe headway, as well as the presence of on-ramps and off-ramps to a certain degree. Through the approximate perturbation method, the mKdV equation and the kink–antikink solution of the traffic density at the jam area are obtained. In order to verify the effectiveness and feasibility of the new model, numerical simulations were conducted to demonstrate on/off ramp effect and different proportions of vehicles which possess bigger maximum velocity or safe space headway affect the traffic stability. The numerical results indicate that in heterogeneous traffic flow scenarios, increasing the ratio of vehicles which possess bigger maximum velocity or bigger safe space headway can lead to a deterioration of traffic stability. The effect of on-ramp could cause traffic instability, while the effect of off-ramp is beneficial for easing traffic congestion.

Micro-channels with built-in shape memory alloys (SMAs) can respond intelligently to channel temperature variations without applying an external force and control the flow rate. In this work, a 2D micro-channel with a shape memory alloy (SMA) valve is designed and studied using fluid–structure interaction (FSI) conditions. The behavior of the SMA valve, which includes bending under the effect of force loading and inlet fluid pressure, and the recovery of the shape of the valve, has been investigated in this study. The temperature at which the valve is completely recovered and the output fluid reaches the lowest value is called the closing temperature. This research investigates the impact of different geometrical and functional parameters on closing temperature, such as fluid inlet pressure and velocity, channel height and valve thickness. The outlet fluid flow rate of the SMA micro-channel is evaluated by employing a relevant constitutive equation to model the SMA valve behavior and implement it in Finite Element Method (FEM) multiphysics frameworks. The results show that the outlet flow rate relies on the shape recovery of the SMA valve and the fluid velocity field in the FSI simulations.

Our previous study observed a non-monotonic time-dependent deformation from the long-term isothermal tensile creep tests, indicating the significant influence of physical aging on viscoelastic behavior. In this work, a new physical mechanism-based thermo-rheological complex constitutive relation that combines Ngai’s coupling model and Schapery’s nonlinear viscoelastic framework is established. A piecewise function was used to represent the non-monotonic time-varying compliance, in which molecular cooperativity and the interaction between different relaxing units were considered. The strength of the interaction is presented by a coupling strength parameter. The effects of stress and temperature on the deformation are represented by not only two shift factors but also are associated with the coupling strength parameter, which is modeled as a function of the fictive temperature. The physical aging effect is also incorporated into the evolution of the fictive temperature. The proposed model was verified by a comparison of the experimental and finite element simulated results. Finally, the physical meanings of the model parameters and their correlation with the macroscopic deformation of the laminates were discussed.

Improving the ability of nonlinear energy sink (NES) to suppress large vibrations under strong excitation has been widely concerned. Moreover, distributing NES to suppress multimodal resonances is also an issue that deserves more attention. This paper investigates the distribution strategy of the series NES in suppressing the vibration of a two-degree-of-freedom (2-DOF) system. Dynamic models are developed for two strategies: centralized and distributed series NES. The vibration reduction efficiency of these strategies is compared, and the approximate results obtained from the analytical analysis were verified using numerical methods. The research results indicate that distributing the series NES among different vibration sources can lead to improved vibration reduction performance. Moreover, the distributed vibration reduction strategy exhibits greater adaptability to different modes of primary system. Furthermore, while keeping the total additional weight of the NES unchanged, the effects of the series NES and 1DOF NES on vibration control were compared. The results demonstrate that, under large amplitude excitation, the series NES has a better vibration reduction effect than the 1DOF NES when using distributed NES to control the vibration of a 2-DOF system. Additionally, by studying the energy transfer between NES oscillators in series, the series NES with high stiffness asymmetry exhibits superior vibration reduction. The findings of this study contribute to the advancement of research on the NES control of strong excitation vibration and multi-mode structure vibration.

This article develops a mathematical formulation to investigate the nonlinear forced vibration of curved viscoelastic beam with nonlinear viscoelastic boundary conditions around buckled position numerically, for the first time. The nonlinear integro-differential equation of buckling problem and the corresponding nonlinear nonhomogeneous boundary conditions are discretized by the differential integral quadrature method (DIQM) and after that, they are solved via Newton-iterative method to compute the nonlinear static deflection paths. By employing DIQM, the linear vibration problem is converted to a linear eigenvalue problem that is solved easily. The Galerkin technique is implemented to reduce the nonlinear partial integro-differential equation governing the nonlinear dynamic problem into Duffing-type equation. The Duffing equation is discretized via periodic spectral differentiation matrix operators. Finally, the pseudo-arc length continuation algorithm is applied to solve the nonlinear eigenvalue problem resulting from the discretized duffing equation. Validation of numerical techniques implemented in the solutions is proved with previous works. Parametric studies are conducted to deliberate the influences of the amplitude of initial curvature, axial load, linear and nonlinear support parameters on the static and dynamic behaviors of straight and curved beams. It should be noted that the proposed algorithm computes both stable and unstable solutions.

This work proposes an improved weak-form quadrature element (IWQE) method for analyzing non-homogeneous space truss structures. The present method combines the high accuracy of the traditional WQE method with the universality of the standard finite element (FE) method. In the analysis, the structure is divided into a series of non-homogeneous elements with large sizes, and discrete function values are used to describe unknown mechanical properties in an element. Chebyshev–Lobatto differential quadrature and Gauss–Lobatto integral quadrature are used to deal with the energy variation of the element. Therefore, the endpoints of the element are included in the quadrature points, resulting in symmetric and positive definite stiffness matrix and diagonal mass matrix that represent internal point displacements by its endpoints in advance, significantly reducing order. All the elements can be easily and conveniently implemented as in FE. Both displacement and force boundary conditions are considered, leading to easier element assembly and smaller global matrices than traditional WQE while maintaining higher accuracy than FE. A non-homogeneous space truss composed of 40 bars is taken as an example to demonstrate the merits of the proposed method in accuracy, efficiency and robustness. The order of the global matrix equation is only 51 in present method.

Soft dielectric elastomers (SDEs) represent a category of intelligent electroactive materials utilized in electro-mechanical actuation technology. The dynamic performance of these materials during actuation is notably affected by intrinsic factors like crosslinks, entanglements and the limited extensibility of polymer chains. In this paper, we provide a theoretical framework for modeling the dynamic behavior of a balloon actuator made up of soft dielectric elastomer. To account for the inherent characteristics of polymer chain networks, we employ a physics-based nonaffine material model proposed by Davidson and Goulbourne. The governing equation for dynamic motion is established using Euler–Lagrange’s equation of motion for conservative systems. The reported dynamic modeling framework is then utilized to explore the transient response, stability, periodicity and resonance properties of a dielectric elastomer balloon (DEB) actuator for varying levels of polymer chain crosslinks, entanglements and finite extensibility parameters. To assess the periodicity and stability of the nonlinear vibrations exhibited by the DEB actuator, we present Poincaré maps and phase-plane plots. The results demonstrate that changes in the density of polymer chain entanglements lead to transitions between quasi-periodic and aperiodic vibrations. These findings represent an essential initial step toward the design and production of intelligent soft actuators with diverse applications in future technologies.

The gap between the theoretical solution of the load and the field measurement is too large to guide the support design while the primary support of deep-buried soft rock tunnels shares a large surrounding rock load. In this study, the flexible support effect of the primary support and the rheological effect of the surrounding rock were considered. The calculation procedure of load shared by the primary support when the surrounding rock is in the accelerated, uniform velocity and decelerated stages was proposed. Then, the reliability of the computational method of the study was verified by numerical simulation methods. The analysis shows that the surrounding rock in the accelerated, uniform and decelerated stages of the load sharing of the primary support presents increasing, unchanged and decreasing states and that the formation of the primary support load is mainly concentrated in the stage of accelerated movement of the surrounding rock. Enhancement of the primary support parameters, while significantly increasing the support safety factor, has a limited effect on reducing load shared by the primary support. Thus, it is recommended that the advanced support can be strengthened to reduce the pre-deformation of the surrounding rock in the unsure soft rock section to reduce the load shared by the primary support. The primary support design of tunnels with rheological rock should account for the long-term rheological load effect of the surrounding rock. The results of this study can provide guidance for the prediction of primary support load sharing for dynamic tunnel construction.

To achieve broadband energy harvesting under weak excitations, this paper comprehensively investigates a novel tri-magnet levitating bistable electromagnetic energy harvester with variable potential wells (BEEH-VP). The bistable nonlinear mechanism is realized using the single-sided bipolarity of the ring magnets. Auxiliary springs are integrated into the ring magnets to dynamically self-adjust the spacing of the ring magnets, causing variable potential wells. The analytical model of BEEH-VP is derived and verified experimentally. The performance of the proposed BEEH-VP is compared with that of the bistable electromagnetic energy harvester with featuring fixed potential wells (BEEH-FP). The comparative results clearly demonstrate that the BEEH-VP exhibits superior capabilities in terms of energy output under weak excitation and possesses a broader frequency bandwidth. Bifurcation analysis for the excitation conditions reveals that the proposed structure features complex dynamic behaviors, such as intra-well, chaotic, harmonic inter-well and subharmonic inter-well vibrations. In comparison to BEEH-FP, BEEH-VP requires lower acceleration to perform the snap-through and has a larger vibration amplitude, facilitating improved output performance.

In recent years, researchers have shown interest in using elastomers with high dielectric constant and good elasticity in capacitive MEMS. This paper aims to investigate how the performance of capacitive sensors/actuators is affected by the temperature-dependent behavior of gap-filling Polydimethylsiloxane (PDMS). As a case study, a model is created, consisting of a proof mass with two attached flexible microbeams parallel to a stationary electrode, under electrostatic actuation. The actuation is directly proportional to the temperature-dependent dielectric constant. To reduce resistance stiffness, the bulk PDMS was assumed to have porosity, resulting in a nonlinear displacement-dependent Young’s modulus. The system’s static and dynamic responses were obtained by solving the governing nonlinear equations using Galerkin-based numerical procedures. Additionally, a physically gradient-descent-based learning method was used to predict the nonlinear frequency response of the system. The results have shown that using PDMS instead of an air gap significantly reduces the required actuation voltage, although this difference is less pronounced at higher temperatures. In addition, the inclusion of PDMS alters the resonance behavior of the system and also reducing the temperature diminishes the nonlinear softening behavior of the system under specific bias and AC voltages.

Bolted joints have been widely used in rotor assemblies of aircraft engines. A typical bolt joint is composed of two metal parts connected mechanically with pre-tensioned bolts. During operations, the bolting pretensions can vary with the changing contacting relationship between the parts, which makes the connection stiffness of the joint nonlinear on the macroscopic scale. The fundamental problems of the dynamical analysis for bolted joints are (1) to identify the transition of the change of the connection stiffness and properly model the overall connection stiffness and (2) to investigate the influence of such variable stiffness on the rotor vibration. In this paper, an analytical model is proposed considering the effect of bolted joints. The bolt of the joint is simplified as a two-node spring-like connection element considering different axial tension and compression stiffness, non-uniform preload of bolts and the contact interface friction described based on Coulomb friction. The dynamic equations of the rotor system are established based on the lumped mass modeling and the proposed connection element, and numerically solved through the Runge–Kutta method. The results indicate that the rotor system exhibits a variety of states, such as period-1 motion, multi-period motion, quasi-periodic motion and chaotic motion. The effects of friction coefficient and preload of the bolts on the nonlinear dynamic behaviors of the bolted rotor system are demonstrated in detail.

A customized MATLAB algorithm is developed for internally separated laminated composite panels experiencing large geometric deformations. The algorithm is designed to calculate nonlinear deflection responses under the effect of combined hygro-thermo-mechanical (HTM) loading. The hygrothermal (HT) load on the panel is in-plane, whereas the mechanical load acts upon the structure transversely. The analysis has adopted various kinematic theories and finite element (FE) techniques to determine the deformations computationally. The deflection behavior of the composite is characterized through a macro mechanical model considering the nonlinearity in geometry with and without accounting for the stretching effects across the panel thickness. Additionally, the changes in composite properties due to the environment and/or loadings are adopted to achieve a realistic response, preserving continuity assumptions between the individual layers of the weakly bonded structure. Moreover, various numerical examples are examined through different models to illustrate the influences of environmental factors and design-specific parameters on the flexural strength of weakly bonded structures. The findings strongly emphasize the necessity of employing diverse kinematic models when examining laminated structures, both with and without HT loading, while also acknowledging the potential for debonding.

Application of porous electrode materials has sparked significant interest as a strategy to mitigate traditional electrode mechanical failure arising from its intercalation-induced large volume change. In this work, a thermal analogy method is employed for implementing the coupled chemo-mechanical model into the finite element (FE) package ABAQUS via user subroutines UMATHT and UMAT, which is used to model the lithium (Li) diffusion and the resulting deformation of the electrode during charge-discharge cycling. This work presents a Direct FE² method for modeling the chemo-mechanically coupled behavior of porous electrode materials by establishing the macro-microscopic scale transitions through concentration and displacement DOFs and the representative volume element (RVE) volume scaling relationship. The two-scale numerical simulations can be implemented in a single computational scheme. Within the present computational framework, the Li diffusion and mechanical deformation in the porous silicon electrode during charging and discharging are easily simulated in the typical FE package. Benchmarked against the traditional direct full-field numerical computational method, the Direct FE² method is validated to present significant computational efficiency improvements through two numerical examples, the constrained expansion and the pre-compression expansion of porous electrode, by 99.27% and 94.55%, respectively, while maintaining the high precision.