Effect Of Bending Stiffness Research Articles

Analytical Framework for Tension Characterization in Submerged Anchor Cables via Nonlinear In-Plane Free Vibrations

Submerged tensioned anchor cables (STACs) are pivotal components utilized extensively for anchoring and supporting offshore floating structures. Unlike tensioned cables in air, STACs exhibit distinctive nonlinear damping characteristics. Although existing studies on the free vibration response and tension identification of STACs often employ conventional Galerkin and average methods, the effect of the quadratic damping coefficient (QDC) on the vibration frequency remains unquantified. This paper re-examines the effect of bending stiffness on the static equilibrium configuration of STACs, and establishes the in-plane transverse free motion equations considering bending stiffness, sag, and hydrodynamic force. By introducing the bending stiffness influence coefficient and the Irvine parameter, the exact analytical solutions of symmetric and antisymmetric frequencies and modal shapes of STACs are derived. An improved Galerkin method is proposed to discretize the nonlinear free motion equations ensuring the accuracy and applicability of the analytical results. Additionally, this paper presents an analytical solution for the nonlinear free vibration response of the STACs using the improved averaging method, along with improved frequency formulas and tension identification methods considering the QDC. Through a case study, it is demonstrated that the improved methods introduced in this paper offer higher accuracy and wider applicability compared to the conventional approaches. These findings provide theoretical guidance and reference for the precise dynamic analysis, monitoring, and evaluation of marine anchor cable structures.

Effect of bending stiffness and impact of key system parameters on the in-plane free vibration behavior of a two-cable network

Effect of bending stiffness and impact of key system parameters on the in-plane free vibration behavior of a two-cable network

Tensile-shear properties of steel-Al adhesively bonded dissimilar joints and the effect of Al plate thickness

Lap shear dissimilar joints between aluminium (Al) alloy, A6061-T6, and stainless steel, type 304, were fabricated by adhesive bonding. Three Al plates with different thicknesses were used to investigate the effect of the Al plate thickness on the tensile-shear properties, namely the effect of bending stiffness of Al plates. The maximum tensile-shear loads increased with increasing Al plate thicknesses. The fracture through the adhesive layer (cohesive fracture) occurred when the Al plate was the thickest, while the interface fracture between Al plate and adhesive layer appeared on the fracture surface with decreasing Al plate thickness. Fatigue strengths also increased with increasing Al plate thickness. When the fatigue strengths were normalized by the tensile strengths, the effect of the plate thickness became negligible. FEM analyses revealed that the stress concentration at the edge of adhesive on Al side decreased with increasing Al plate thickness, which could be related to the dependence of tensile and fatigue properties on the Al plate thickness.

Interacting effects of AFO stiffness, neutral angle and footplate stiffness on gait in case of plantarflexor weakness: A predictive simulation study

To maximize effects of dorsal leaf ankle foot orthoses (AFOs) on gait in people with bilateral plantarflexor weakness, the AFO properties should be matched to the individual. However, how AFO properties interact regarding their effect on gait function is unknown. We studied the interaction of AFO bending stiffness with neutral angle and footplate stiffness on the effect of bending stiffness on walking energy cost, gait kinematics and kinetics in people with plantarflexor weakness by employing predictive simulations.Our simulation framework consisted of a planar 11 degrees of freedom model, containing 11 muscles activated by a reflex-based neuromuscular controller. The controller was optimized by a comprehensive cost function, predominantly minimizing walking energy cost. The AFO bending and footplate stiffness were modelled as torsional springs around the ankle and metatarsal joint. The neutral angle of the AFO was defined as the angle in the sagittal plane at which the moment of the ankle torsional spring was zero. Simulations without AFO and with AFO for 9 bending stiffnesses (0–14 Nm/degree), 3 neutral angles (0–3-6 degrees dorsiflexion) and 3 footplate stiffnesses (0–0.5–2.0 Nm/degree) were performed.When changing neutral angle towards dorsiflexion, a higher AFO bending stiffness minimized energy cost of walking and normalized joint kinematics and kinetics. Footplate stiffness mainly affected MTP joint kinematics and kinetics, while no systematic and only marginal effects on energy cost were found.In conclusion, the interaction of the AFO bending stiffness and neutral angle in bilateral plantarflexor weakness, suggests that these should both be considered together when matching AFO properties to the individual patient.

Study on initial stiffness of high strength steel T-stubs considering bending stiffness of bolts

The formula of initial stiffness of high strength steel T-stubs is proposed based on the continuous beam model with consideration of bolts bending stiffness in this paper. The accuracy of this formula is verified through comparison with numerical results obtained from validated finite element models. The influence of flange thickness and bolt position is investigated via a parametric study. The results show that the effect of bending stiffness of bolts increases with the decrease of flange thickness and the increase of distance between the flange edge and bolt axis. Concerning mild steel T-stubs, the difference corresponding to the calculation results of initial stiffness of T-stubs taking bolts bending stiffness into account or not is less than 5%, while concerning high strength steel T-stubs, the difference increases to 21%. Therefore, it is indispensable to consider the bolts bending stiffness in the calculation of the initial stiffness of high strength steel T-stubs.

Nonlinear Vibration of Bolted Rotor Bearing System Accounting for the Bending Stiffness Characteristics of the Connection Interface

This paper considers the discontinuous characteristics of a real aero-engine rotor system, that is, the existence of bolted connection characteristics, and establishes a new bolted connection rotor system model. Taking into account the bending stiffness and the nonlinear Hertzian contact force of the rolling bearing, the Newmark-[Formula: see text] numerical method is used to solve the system response, and the influence of the bending stiffness on the system is studied. Moreover, the effects of bending stiffness and eccentricity on the system dynamics are analyzed. The results show that the nonlinear phenomena of the system are more abundant and the critical speed of the system is higher when the bending stiffness is involved. With the increase of bending stiffness, the critical speed of the system increases, and the frequency component of the system becomes more complex. Then, the influence of eccentricity on the system is studied based on the bending stiffness. It is found that the greater the eccentricity, the greater the critical speed of the rotor and the greater the amplitude of the main frequency. In the case of the same eccentricity, the main frequency increases as the rotational speed increases, and the frequency doubling component appears in the 2-period motion. This paper provides a basis for predicting the nonlinear response of bolted rotor-bearing system.

Effect of wear rings on buckling load capacity of Two-Stage hydraulic cylinder

In a two-stage hydraulic cylinder, the rod is a critical component for stability against buckling failure. A small disturbance in the rod may increase the instability that may lead to catastrophic failure. A small support against the instability may increase the system's flexural strength to make it more stable. The wear rings provide an elastic support against the rod and cylinder's instability and increase the flexural strength of the connections. In this paper, a theoretical model for the buckling load of a pin-pin-mounted two-stage hydraulic cylinder is proposed. The buckling load calculation by the proposed approach is in close match (6.96% deviation) with the experimental results reported in the literature for the case of single-stage hydraulic cylinders. The effect of bending stiffness on stability is considered by considering the stiffness of the rod and cylinder along with the wear rings. A hyperelastic model is used to determine the bending stiffness of wear rings in three different cases: first when all wear rings are present, second when three wear rings are present, and third when only two wear rings are present. The stiffness of the rod and piston head is determined with the help of the conjugate beam method. Eigenvalue buckling analysis (finite element method) is carried out to verify the buckling load of a two-stage hydraulic cylinder with two, three, and four wear rings. Theoretical results are observed to be in good agreement with the numerical simulations (FEA) results, with a percentage deviation of 0.22 % − 9.22 % for different cases of wear rings positions. It is observed that when all four wear rings are present, the buckling load capacity increases by 1.14 times, whereas the removal of wear rings on the gland side decreases it by 0.96 times.

Natural vibration characteristics of short-span submarine power cables with bending stiffness and sag

Based on a continuum model that governs the dynamics of submarine power cables, analytical solutions of the natural frequencies and modal shapes for free spanning cables are derived. The effects of sag, axial and bending stiffness are all included. The cable sag calculation has considered the effects of bending stiffness on the static profile. The accuracy of the derived solutions is validated by the results from a laboratory experiment. The applicable ranges of these solutions and that of Ricciardi (Ricciardi and Saitta, 2008) [15] are determined. Also, the effects of static profile, boundary conditions and non-dimensional parameters (ξ and λ2) on the cable natural frequencies and modal shapes are discussed. The results show that the static profile and boundary conditions have significant effects on the modal properties for free spanning submarine power cables. It must be noted that, for lower ξ values, the frequencies of the symmetric modes show a non-monotonic dependence on bending stiffness. The single-degree-of-freedom approach is adopted to further analyze the mechanisms of the non-monotonic behavior.

Combined effect of bending stiffness and streamwise length of the attached flexible splitter plate on the vortex-induced vibration of a circular cylinder

A flexible splitter plate attached to the rear stagnation point of a circular cylinder is applied to control the vortex-induced vibration. The influence of its bending stiffness on the control effect is experimentally investigated for two streamwise lengths of 1D and 2D (D is the cylinder diameter). Five dimensionless bending stiffnesses are selected: 0.979 (P1), 3.123 (P2), 6.797 (P3), 23.087 (P4), and 47.484 (P5). The characteristics of cylinder vibration, flow field, lift, and plate dynamics are synchronously studied. The results show that the effect of the bending stiffness depends on the streamwise length of the plate. For the flexible splitter plate of 1D, the best suppression effect of cylinder vibration is achieved for the P2 case, where maximum vibration amplitude is reduced by 93%, while the galloping-like vibration is excited for P4 and P5 cases. According to the analysis of the plate dynamics and the wake development, a large plate vibration is expected to suppress the galloping-like vibration. The bending stiffness affects the vibration state of the flexible splitter plate, and consequently, the wake vortex development and dynamic response of the cylinder are changed. For the flexible splitter plate of 2D, the vibration amplitude response of the cylinder can be divided into three categories based on the variation of amplitude versus the reduced velocity. For P2-P5 cases, a beneficial phenomenon that a frequency branch is larger than the natural frequency occurs.

Effect of bending stiffness on the polymer adsorption onto a heterogeneous stripe-patterned surface

Adsorption of a single homopolymer chain with bending stiffness onto a heterogeneous regular stripe-patterned surface consisting of adsorbing and non-adsorbing stripes is studied theoretically in the framework of the lattice model and the generating functions approach. The stiffness is introduced by assigning a statistical weight to a trans-isomer (a straight segment) with respect to a gauche-isomer (a kink). The temperature is taken as the main control parameter since it affects both the strength of the monomer units’ attraction to the adsorbing stripes and the chain stiffness. It is shown that the adsorption transition temperature is a non-monotonic function on the bending energy having a minimum. The position of this minimum depends on the stripes’ width and only slightly deviates from zero bending energy. Temperature dependences of the main conformational and thermodynamic characteristics of the adsorbed chain are obtained. It is demonstrated that in most of the studied cases the adsorption is accompanied by the chain localization on a single adsorbing unit stripe and the chain stiffness enhances this effect.

Analytical investigation of the main cable bending stiffness effect on free flexural vibration of suspension bridges with a 3D cable system

This paper proposed a dimensionless continuum model of suspension bridges to comprehensively study the bending stiffness effect of the 3D cable system on the structural free flexural vibration, which has seldom been investigated in previous studies. In this model, coupled differential equations including the cable bending resistance term are derived via the Galerkin method. The equations are then nondimensionalized from a set of key design parameters, including the lateral inclination of hangers. The precision of the model is validated with the finite element (FE) method through an example. Then, parametric comparative studies of the effect under dimensionless parameters are conducted between 3D and 2D cable system suspension bridges. The results show that, the bending stiffness effects of the 3D cable system are more evident on the high order modes and antisymmetric modes of suspension bridges, which is similar with those effects of the 2D cable system. The hanger lateral inclination restrains the effect on the structural frequencies following a relationship of linear negative correlation; when the inclination angle varies from 30 to 60 degrees, the effect ratio of 3D to 2D cable system correspondingly varies from 0.33 to 0.67. Under a given hanger lateral inclination (48.6 degrees) with other identical conditions, the variation trend of the effects on the high order frequencies are similar between 3D and 2D cable systems; the effect value of the 3D cable system is on average 0.625 times that value of the 2D cable system.

Scaling laws for drag-to-thrust transition and propulsive performance in pitching flexible plates

The propulsion of a pitching flexible plate in a uniform flow is investigated numerically. The effects of bending stiffness ( $K$ ), pitching amplitude ( $A_L$ ) and frequency ( $St$ ) on the wake patterns, thrust generations and propulsive performances of the fluid–plate system are analysed. Four typical wake patterns, i.e. von Kármán, reversed von Kármán, deflected and chaotic wakes, emerge from various kinematics, and the $St-A_L$ wake maps are given for various $K$ . The drag-to-thrust transitions (DTT) and the wake transitions (WT) between the von Kármán and reversed von Kármán wakes are examined. Results indicate that the WT and DTT boundaries can be scaled by the chord-averaged distance of travel, $\mathcal {L}$ , which leads to $\mathcal {L}\times St \approx 1$ and $\mathcal {L}\times St \approx 1.2$ , respectively. Further, the resonance mechanism for the performance enhancement is revealed and confirmed in a wide range of parameters. The dimensionless average speed of plate, $\mathcal {U^*}\left (=\mathcal {L}\times St\right )$ , is adopted merely to characterize the propulsive performances. For the first time, the $\mathcal {U^*}$ -based scaling laws for the thrust and power are revealed in pitching rigid and flexible plates for various $A_L$ and $St$ . This study may deepen our understanding of biological swimming and flying, and provide a guide for bionic design.

Vesicle Geometries Enabled by Semiflexible Polymer.

Understanding and controlling vesicle shapes is fundamental challenge in biophysics and materials design. In this paper, we employ the Monte Carlo method to investigate the shape of soft vesicle induced by semiflexible polymer outside in two dimensions. The effect of bending stiffness of polymer and the strength of attractive interaction between vesicle and polymer on the shape of vesicle is discussed in detail in the present paper. It is found that the shape of vesicle is influenced by and . Typical shape of vesicles is observed, such as circular, cigar-like, double vesicle, and racquet-like. To engineer vesicle shape transformations is helpful for exploiting the richness of vesicle geometries for desired applications.

Semi-Active Cable Damping to Compensate for Damping Losses Due to Reduced Cable Motion Close to Cable Anchor

The relative motion of transverse cable dampers is smaller than predicted by the taut string model because of the effects of bending stiffness and fixed support conditions. As a result of the reduced damper motion, the dissipated energy per cycle is reduced as well, which may explain why damping measurements on real stay cables with transverse dampers often show lower cable damping ratios than expected from the taut string theory. To compensate for the reduced damper motion and damper efficiency, respectively, a semi-active cable damper is proposed. The controllable damper is realized by a hydraulic oil damper with real-time controlled bypass valve whereby the resulting damper force is purely dissipative. The proposed control law is clipped viscous damping with negative stiffness. The viscous coefficient is adjusted in real time to the actual frequency of vibration to generate optimum modal damping while the negative stiffness component partially compensates for the reduced damper motion due to the flexural rigidity and fixed support conditions of the cable. The measurements of the prototype semi-active hydraulic damper are used to derive a precise model of the semi-active damper force including the control force constraints due to the fully open and fully closed bypass valve. This model is used to compute the cable damping ratios of the first four cable modes, for typical damper positions, for a taut string model and for a cable model with flexural rigidity and fixed supported ends. The obtained cable damping ratios are compared to those resulting from the passive linear viscous damper being optimized to the first four cable modes. The results demonstrate that the proposed semi-active cable damper with the consideration of the minimum and maximum control force constraints significantly enhances the cable damping of the first four modes compared to the linear viscous damper.

Minimal requirements for the vibration-based identification of the axial force, the bending stiffness and the flexural boundary conditions in cables

This paper aims at presenting the guidelines to follow in order to set up an identification procedure which is able to determine the axial force, the flexural rigidity and the rotational end stiffnesses of slender and tensioned structural elements, based on measurements of their natural frequencies and mode shapes. First of all, when such an element is slightly affected by bending stiffness effects, perturbation methods can be applied to get a composite approximation for its natural frequencies and an asymptotic expression for its mode shapes. These simple analytical formulas allow to understand the role played by each model parameter in the modal response and show that the axial force, the flexural rigidity and the rotational end stiffnesses can be correctly identified under some conditions, which are established and provided in this document. Among others, it is necessary that the identification procedure relies on the first few natural frequencies and mode shapes, which are measured near each extremity of the element, as well as some natural frequencies associated with higher modes.

Conformational behavior and self-assembly of disjoint semi-flexible ring polymers adsorbed on solid substrates.

The conformational behavior and spatial organization of self-avoiding semi-flexible ring polymers, that are fully adsorbed on solid substrates, are investigated via systematic coarse-grained molecular dynamics simulations. Our results show that both conformations and spatial organization of the polymers depend strongly on their bending stiffness, κ, and on their areal number density, ρ. For ρ < ρ*, where ρ* is the overlap density, and for low values of κ, thermal fluctuations lead to weakly anisotropic instantaneous conformations of the polymers. The interplay between thermal fluctuations and polymer stiffness leads to a non-monotonic dependence of the polymers elongation on κ with a maximum elongation at some intermediate κ. Regardless of κ, the polymers elongation is almost independent of ρ for ρ ⪅ ρ*, then increases with ρ. At ρ ≈ ρ* and high κ, the almost circularly-shaped polymers self-assemble into a triangular lattice with quasi-long range order. For ρ above ρ* and high κ, crowding of the polymers leads to their self-assembly into liquid-crystalline phases. In particular, for ρ moderately above ρ* and high κ, the polymer conformations are obround and self-assemble into domains with smectic-A-like order. At higher densities, the polymer have a biconcave geometry and self-assemble into domains with smectic-C-like order.

In-plane modal responses of two-cable networks considering cable bending stiffness effect

Cross-tie solution has proven to be effective in mitigating cable vibrations on cable-stayed bridges. In the formed cable network, the consisting cables are divided into shorter segments by cross-ties and thus significantly reduced their effective length. While bending stiffness plays an important role in the behavior of shorter cables, its effect has not been considered in any existing cable network analytical models. To assess the impact of cable bending stiffness on the in-plane dynamic response of cable networks, in the current study, an existing analytical model of a two-cable network is refined by taking into account the cable bending stiffness in the formulation. A set of closed-form solutions are derived to clearly reveal the impact of cable bending stiffness on the modal response of two-cable networks having different configurations. The proposed analytical model is validated by numerical simulations and the modal analysis results are compared with those of the corresponding taut-cable networks. It is found that the cable bending stiffness would influence all the modes of a cable network by increasing their modal frequencies, with the stiffening effect on the high order global and local modes being more considerable. If neglected, an underestimation of network fundamental frequency up to 7.1% could occur. Further, the cable bending stiffness has more effect on local modes than global modes. Some local modes could evolve into global modes. Nevertheless, the modal order is not affected by the presence of cable bending stiffness.

Effect of bending stiffness on the in-plane free vibration characteristics of a cable network

Stay cables of cable-stayed bridges are connected by cross-ties to form a cable network, or the slings of the same suspension points on a suspension bridge are connected by vibration absorbers to form a sling network. As a result, the cable network’s in-plane free vibration characteristics are different from independent, single cables. However, stay cables or slings have certain bending stiffnesses, which directly affect the cable network’s free vibration characteristics. Therefore, to clarify the real dynamic behavior of a cable network and to improve the accuracy of cable network measurements, a multi-node, cross-tied, multilayer beam analytical model that considers the bending stiffness is proposed. The system equilibrium equation is established and the free vibration frequencies and modes of the system are obtained by analytical algorithm. Then, numerical simulations and field experiments, are carried out to verify the analytical results. In addition, parameter analyses with different configurations are performed on a multilayer stay-cable network and on a double-layer sling network to study the influence of bending stiffness on the cable network’s free vibration characteristics with different parameters.

Nonlinear stability of steel cooling towers with semirigid connections

Based on the experimental and numerical bending-rotation (M-Φ) curves of a new semirigid connection, the finite element model (FEM) of a semi-rigidly jointed reticulated steel (SJRS) cooling tower structure is established. Considering the connection stiffness (including rigid and semirigid), height, and mesh size, the dual nonlinear stability behavior of the SJRS cooling tower is analyzed. The complete load–displacement curves, buckling modes, and percentage of different connection statuses (linear, elastic–plastic, plastic, and unloading states) in the structure are obtained. Further, the influence rules of each parameter on the structural stability performance are analyzed in detail. Three main buckling modes, two local buckling modes (Mode-I and Mode-II), and one overall buckling mode (Mode-III) are obtained for the SJRS cooling towers with different connection stiffnesses. The results indicate the good carrying capacity of the steel cooling towers, and that the effect of bending stiffness on the stability of the SJRS cooling towers varies significantly with height, and the bending stiffness of the connection around the z-axis is the key factor affecting the critical load and buckling mode of the cooling towers.

Influence of Bending Stiffness on Snap Loads in Marine Cables: A Study Using a High-Order Discontinuous Galerkin Method

Marine cables are primarily designed to support axial loads. The effect of bending stiffness on the cable response is therefore often neglected in numerical analysis. However, in low-tension applications such as umbilical modelling of ROVs or during slack events, the bending forces may affect the slack regime dynamics of the cable. In this paper, we present the implementation of bending stiffness as a rotation-free, nested local Discontinuous Galerkin (DG) method into an existing Lax–Friedrichs-type solver for cable dynamics based on an hp-adaptive DG method. Numerical verification shows exponential convergence of order P and P+1 for odd and even polynomial orders, respectively. Validation of a swinging cable shows good comparison with experimental data, and the importance of bending stiffness is demonstrated. Snap load events in a deep water tether are compared with field-test data. The bending forces affect the low-tension response for shorter lengths of tether (200–500 m), which results in an increasing snap load magnitude for increasing bending stiffness. It is shown that the nested LDG method works well for computing bending effects in marine cables.