External Moment Research Articles

Improved ADRC-Based Autonomous Vehicle Path-Tracking Control Study Considering Lateral Stability

The antidisturbance control problem of autonomous vehicle path tracking considering lateral stability is studied in this paper. This paper proposes an improved active disturbance rejection control (IADRC) control method including an improved extended state observer (IESO) and an error compensator based on LQR, where a new continuous nonlinear function is proposed in the IESO instead of the classical piecewise function. Based on the IADRC, an autonomous vehicle path-tracking controller considering lateral stability is designed. Using the output wheel steering angle and external yaw moment, the IESO estimates the disturbance value and compensates for the disturbance in the feedback to meet the goal of antidisturbance control. Based on the concept of control allocation (CA), the control distributor is designed to distribute the external yaw moment to the four wheels in a reasonable and optimal way to achieve differential braking. Finally, the control scheme is evaluated in the form of CarSim/Simulink cosimulation; the results show that the proposed autonomous vehicle path-tracking control scheme has better path-tracking effect and higher antidisturbance robustness.

The impact of ankle-foot orthosis's plantarflexion resistance on knee adduction moment in people with chronic stroke.

An ankle-foot orthosis (AFO) is used to assist gait of people with chronic stroke. It is widely accepted that AFO's plantarflexion resistance affects sagittal knee moments during their gait. However, its effect on the coronal knee moment remains unclear. This study aimed to examine the effects of varying articulated AFO's plantarflexion resistance on knee adduction moment in people with chronic stroke. Ten people with chronic stroke participated in this study. Gait performance was measured using a Vicon 3-dimensional motion capture system and a Bertec split-belt instrumented treadmill. The participants walked on the treadmill wearing an articulated AFO whose plantarflexion resistance could be systematically adjusted. The ankle joints were set to four distinct levels of plantarflexion resistance (S1 < S2 < S3 < S4). The coronal ankle and knee joint moment, center of pressure, and ground reaction force were analyzed using Visual3D. The external knee adduction moment increased significantly ( P < .001) and the position of the center of pressure trajectory shifted significantly ( P = .003) in the medial direction as the plantarflexion resistance of the AFO was increased from the least resistive condition (S1) to the most resistive condition (S4). The maximum knee adduction moment (median [interquartile range]) was S1: 0.097 (-0.012 to 0.265) Nm/kg; S2: 0.136 (0.040 to 0.287) Nm/kg; S3: 0.160 (0.465 to 0.289) Nm/kg; and S4: 0.192 (0.080 to 0.288) Nm/kg. This study demonstrated that varying AFO's plantarflexion resistance altered the knee adduction moment, likely by altering the center of pressure trajectory while walking, in people with chronic stroke.

Effects of artificially induced bilateral internal rotation gait on gait kinematics and kinetics

BackgroundBilateral internal rotation gait is a common gait abnormality in children with bilateral cerebral palsy, but still not fully understood. Research questionThe aim of this clinical study was to analyze the effects of artificially induced bilateral internal rotation gait on kinematics and kinetics. Our hypothesis was, that the internal rotation gait defined as increased dynamic internal hip rotation itself causes significant alterations in gait kinematics and kinetics. Methods30 typically developing children with a mean age of 12 (SD 3) years (range 8 – 16) performed three-dimensional gait analysis in two different conditions: with unaffected gait and with artificially induced bilateral internal rotation gait with two rotation bandages worn in order to internally rotate the hips. Kinematic and kinetic changes between these two conditions were calculated and compared using a mixed linear model with “gait condition” as fixed effect and both “limb” and “patient” as random effects. ResultsThe rotation bandages induced a significant increase in internal hip rotation and foot progression angle towards internal without affecting pelvic rotation. The peak hip internal rotator moment during loading response and the peak hip external rotator moment during the first half of stance phase increased significantly and the peak hip internal rotator moment during the second half of stance phase decreased significantly. Anterior pelvic tilt, hip flexion, knee flexion and ankle dorsiflexion increased significantly. The first peak of the frontal hip moment decreased, and the second increased significantly. The second peak of the frontal knee moment decreased significantly, while the first didn’t change significantly. SignificanceThe data suggest, that the bilaterally increased dynamic internal hip rotation itself has a relevant impact on frontal hip moments. The increased anterior pelvic tilt, hip and knee flexion may be either induced by the pull of the rotation bandage or a secondary gait deviation.

Biomechanical Comparison between Down-the-Line and Cross-Court Topspin Backhand in Competitive Table Tennis

The aim of this study was to compare the kinematic and kinetic differences of the racket arm when balls were hit cross-court (CC) and down the line (DL) by topspin backhand. Eight elite female players participated and were instructed to hit the ball down the line and cross-court using a topspin backhand. Kinematic and kinetic data were collected. The results show that at the impact, participants had a greater wrist flexion angle in DL than CC (p = 0.017). The angular velocity of shoulder flexion (p = 0.038), shoulder abduction (p = 0.006) and thorax–pelvis internal rotation (p = 0.017) was faster when participants impacted the ball DL than CC. As for the joint kinetics, the shoulder external rotation moment was greater in CC than DL (p = 0.043). For a high-quality DL technique, it is important to exhibit a greater wrist flexion and have faster adduction and flexion in the shoulder, as well as faster internal rotation in thorax–pelvis, while having a smaller wrist flexion and more external rotation power in the shoulder are important to perform a CC at the impact. If these key and different factors of hitting CC and DL are ignored, it may lead to failure to complete a high-quality shot.

Biomechanical asymmetries differ between autograft types during unplanned change of direction after ACL reconstruction.

Nine months after anterior cruciate ligament (ACL) reconstruction, athletes who undergo surgery using a bone-patellar-tendon-bone (BPTB) autograft demonstrate higher loading asymmetries during vertical jumping than those with a hamstring tendon (HT) autograft. These asymmetries may transfer into sporting movements with a greater ACL injury risk. The aim of this study was to compare between-limb asymmetries in knee mechanics and task performance during an unplanned 90° change-of-direction (CoD) task in male field sport athletes reconstructed with BPTB or HT autografts. Seventy-eight male multidirectional field sport athletes with either a BPTB (n=39) or HT (n=39) autograft completed maximal unplanned CoD trials in a three-dimensional motion capture laboratory at approximately 9months post-surgery. A mixed-model 2x2 ANOVA (autograft type x limb) was used to compare variables related to ACL injury risk (e.g., internal knee moments) and performance (e.g., completion time) between autografts and limbs. Statistical parametric mapping was used for a waveform comparison throughout stance, supplemented with a discrete point analyses of peak knee moments and performance variables. Interaction effects were found at the knee joint, with BPTB demonstrating greater asymmetries than HT in knee extension moment (p<0.001); resultant ground reaction force (p<0.001); peak knee external rotation moment (p=0.04); and knee adduction (p=0.05), medial rotation (p<0.001), and flexion (p<0.001) angles. No differences were found between autografts for any performance variable. BPTB demonstrated greater lower-limb biomechanical asymmetries than HT during CoD, which may influence knee loading and longer-term outcomes and should thus be targeted during rehabilitation prior to return to play.

Development of the center of pressure velocity in the healing process after intra-articular calcaneus fractures

BackgroundCalcaneal fractures are among the most common foot injuries and sometimes develop manifold post-surgical complications. Restricted foot movement is one of the main functional limitations which often persists during long-term rehabilitation. Therefore, it is important to quantitatively monitor the biomechanical foot mobility after calcaneal fracture from an early stage in order to achieve an optimal therapeutic treatment. Research questionEvaluation of the Center of Pressure velocity (vCOP) in patients after intrarticular calcaneal fractures during the healing progress from three to 24 months after surgery. MethodsA total of 20 patients with unilateral calcaneal fracture were investigated by means of pedobarography and marker-based gait analysis at three, six, 12 and 24 months after surgery. Data for vCOP [m/s], maximum external dorsal extension moments during stance (DEmomentstance) and tibiotalar range of motion during mid stance (MS) and terminal stance (TS) were obtained. Functional evaluation was performed using clinical examination (e.g. calf circumference measurements) and patient-reported outcome measures (SF-36). ResultsWhen compared to the healthy side, vCOP of the injured side showed a significant reduction during MS (3 months: 48%, p < 0.001; 6 months: 13%; p = 0.040) and an significant increase during TS (3 months: 110%, p < 0.001; 6 months: 43%, p < 0.001; 12 months: 17%, p = 0.012). DEmomentstance of the fractured foot, showed a significant increase of 80% (p < 0.001) from three to 24 months after surgery, which correlated with vCOP at three and six months after surgery (p < 0.05; vCOP MS: 3 months: r = 0.876, 6 months: r = 0.685; vCOP TS: 3 months: r = −0.554, 6 months r = −0.626). SignificancevCOP might serve as an indicator for foot mobility and function during the early healing phase after calcaneal fractures. As vCOP can be obtained by pedobarography it is more readily accessible an less costly compared to foot function obtained by marker based gait analysis.

Modulation of internal tissue stresses of the knee via control of variable-stiffness properties in a 3D-printed footwear: A combined experimental and finite element analysis

Aims: Therapeutic footwear with variable-stiffness properties has been shown to be effective in reducing the external knee adduction moment. However, the exact changes of internal tissue stresses following intervention with variable-stiffness footwear remains unknown. The objective of this study is to construct a finite element model of the foot-ankle-knee complex to investigate the therapeutic efficacy of the variable-stiffness footwear in modulating internal knee joint stress distributions. Methods: Footwear with lateral-to-medial stiffness ratio of 1.00, 1.33, 1.49 and 1.77 were designed and 3D-printed as lattice structures at different porosity levels. A three-dimensional finite element model of the foot-ankle-knee complex was constructed with cartilage-meniscus structures characterized by magnetic resonance imaging. Ground reaction forces and muscular loads estimated from gait experiments with 3D-printed variable-stiffness footwear were used to drive the model, and effects of footwear intervention with four stiffness ratios on tibiofemoral joint loads were evaluated during the simulated instant in gait. Results: Compared with the constant-stiffness design, the variable-stiffness footwear reached a maximum reduction of the first peak knee adduction moment up to 17.1%. As the lateral-to-medial stiffness ratio increases, the peak stresses at the meniscus in the medial compartment of the knee were reduced by 5.0%, 7.9%, and 16.4%, respectively. The stress-modifying effects were less pronounced for the lateral compartment of the knee. Conclusion: The variable-stiffness footwear design produced stress relieving to the cartilage and meniscus structures, and the fact that lower stiffness ratio had reached significantly less effects, suggesting a favourable stress-relief effect should consider footwear with a higher lateral-to-medial stiffness ratio.

Coordinated Control of Path Following and Yaw Stability for Distributed Drive Autonomous Vehicle

Abstract This paper researches a coordinated control approach of path following and yaw motion stability for distributed drive autonomous electric vehicle. In the upper-level controller, a linear time-varying model predictive control algorithm is used to obtain the front wheel steering angle to guarantee the vehicle to drive along the planned path. Meanwhile, the sliding mode control theory is aimed to calculate the external yaw moment to ensure the vehicle yaw stability. In the low-level controller, this research proposes the particle swarm optimization algorithm to execute the torque distribution control. The Matlab/Simulink simulation results indicate that the coordinated control strategy can not only effectively improve the accuracy of path following, but also guarantee yaw motion stability of the autonomous vehicles.

Analysis of Lower Limb Joint Kinetics With Increasing Running Speed

Purpose: Due to the paucity of information regarding the lower limb biomechanics in running at slow speed, as well as the concentration of most previous studies on a single movement plane, this study aimed to investigate lower limb joint kinetics with increasing running speed. Methods: Twenty-eight runners were asked to stay on the treadmill at a bent velocity which was incrementally increased to 2.5 m/s, 3.5 m/s, and 4.5 m/s speeds. The three-dimensional joint moment and sagittal mechanical muscle power of the lower limb were calculated during the stance phase of running. Repeated measures analysis of variance (ANOVA) with Bonferroni post hoc test was used to examine the variables during running at various speeds. Results: The results showed that at the hip joint in the frontal plane, an adduction moment developed in the middle of the stance phase, and the highest peak adduction moment was obvious at the highest speed condition (4.5 m/s). Also, the time elapsed to peak in the highest speed condition was less than the others. In the transverse plane, although the 3.5 m/s-speed condition experienced the maximum external rotation peak moment, the 4.5 m/s-condition speed reached the internal status earlier than the two other speeds. In the sagittal plane, the highest speed condition showed the highest extension and flexion moments. Conclusion: Increasing running speed in runners leads to more kinetic output and mechanical power gradient.

Optimal detumbling strategy for a non-cooperative target with unknown inertial parameters using a space manipulator

Capturing tumbling target is considered as one of the greatest challenges in on-orbit service missions due to tumbling motion and parameter uncertainty of the space non-cooperative target. The tumbling motion of the target should be attenuated as quickly as possible before grasping to avoid the unexpected collisions and possible damages to the space manipulator or the target, which means the shortest-time detumbling trajectory is necessary. In many studies about the optimal detumbling trajectory planning the inertial parameters of the target have been assumed to be accurately known, which is usually difficult for a non-cooperative target so that parameter identification is needed before planning a optimal detumbling trajectory. In this paper, a novel strategy for parameter identification and detumbling of a tumbling target by a space manipulator is proposed. The strategy includes two phases. First, unknown inertial parameters of the target are identified in finite-time by a new estimation method with the assumption of interval excitation (IE), which relaxes the strict persistent excitation (PE) condition required in most prior studies. Second, the shortest-time detumbling trajectory of the tumbling target is generated by formulating a time-optimal control problem (OCP) in which the target attitude bounds and the limitations of the contact force as well as the relative velocity between the space manipulator and the target are represented as extended dynamical sub-systems and saturation functions. Then, the Calculus of Variations method is used to solve the OCP to obtain a high accuracy solution. During two phases, the contact force between the space manipulator and the target is utilized to generate external moment for identifying the inertia parameters of the target and detumbling the target. Meanwhile, a unified hybrid impedance control framework is applied to the space robot to track the desired contact force and motion trajectory. The whole strategy is verified by a space manipulator capturing a tumbling target, and numerical simulations demonstrate the effectiveness of the proposed methods.

Walking-related knee contact forces and associations with knee pain across people with mild, moderate and severe radiographic knee osteoarthritis: a cross-sectional study

To investigate knee contact forces (KCFs), and their relationships with knee pain, across grades of radiographic knee osteoarthritis (OA) severity. Cross-sectional exploratory analysis of 164 participants with medial knee OA. Radiographic severity was classified as mild (grade 2), moderate (grade 3) or severe (grade 4) using the Kellgren & Lawrence (KL) scale. Walking knee pain was assessed using an 11-point numerical rating scale. External knee adduction moment (external KAM) and internal muscle forces were used to calculate medial, lateral and total KCFs using a musculoskeletal computational model. Force-time series across stance phase of gait were compared across KL grades using Statistical Parametric Mapping. Associations between KCFs and pain across KL grades were assessed using linear models. Medial KCFs during early and middle stance were higher in participants with KL3 and KL4 compared to those with KL2. In contrast, lateral KCFs were higher in those with KL2 compared to KL3 and KL4 in middle to late stance. The external loading component (i.e., KAM) of the medial KCF during middle to late stance was also greater in participants with KL3 and KL4 compared to those with KL2, whereas the internal (i.e., muscle) component was greater in those with KL3 and KL4 compared to KL3 during early stance. There were no associations between medial KCF and knee pain in any KL grade. Medial and lateral KCFs differ between mild, moderate and severe radiographic knee OA but are not associated with knee pain severity for any radiographic OA grade.

Elastic Foundation and Timoshenko Beam Theory Solution for Face/Core Sandwich Debonds

This paper presents closed-form expressions for the energy release rate and mode partitioning of face/core debonds in sandwich composites with orthotropic faces and core, by use of an elastic foundation analysis. The elastic foundation analysis used here is comprehensive and includes the deformation of the substrate part (core and the bottom face) and is done for generally asymmetric sandwich construction. To capture the transverse shear effects, the Timoshenko beam theory is used, which introduces an additional degree of freedom. A finite length sandwich is treated as having a debonded section, where the debonded top face and the substrate are free, and a bonded section, where an elastic foundation is used between the face and the substrate. The interaction between the face and the substrate in the bonded section is modeled using both normal and shear spring distributions. A double-cantilever beam specimen with applied external moments and shearing forces is chosen to demonstrate the procedure. The energy release rate is obtained by use of the J-integral. A mode partitioning measure in terms of the crack flank opening and shearing displacements is used. The results are compared with finite element results and show very good agreement.

Ground reaction forces and external hip joint moments predict in vivo hip contact forces during gait

Younger patients increasingly receive total hip arthroplasty (THA) as therapy for end-stage osteoarthritis. To maintain the long-term success of THA in such patients, avoiding extremely high hip loads, i.e., in vivo hip contact force (HCF), is considered essential. However, in vivo HCFs are difficult to determine and their direct measurement is limited to instrumented joint implants. It remains unclear whether external measurements of ground reaction forces (GRFs), a non-invasive, markerless and clinic-friendly measure can estimate in vivo HCFs. Using data from eight patients with instrumented hip implants, this study determined whether GRF time series data, alone or combined with other scalar variables such as hip joint moments (HJMs) and lean muscle volume (LMV), could predict the resultant HCF (rHCF) impulse using a functional linear modeling approach. Overall, single GRF time series data did not predict in vivo rHCF impulses. However, when GRF time series data were combined with LMV of the gluteus medius or sagittal HJM using a functional linear modeling approach, the in vivo rHCF impulse could be predicted from external measures only. Accordingly, this approach can predict in vivo rHCF impulses, and thus provide patients with useful insight regarding their gait behavior to avoid hip joint overloading.

The angular dependence of magnetization dynamics induced by a GHz range strain pulse

The dynamics of magnetization is important in spintronics, where the coupling between phonon and magnon attracts much attention. In this work, we study the angular dependence of the coupling between longitudinal-wave phonon and magnon. We investigated the magnetization dynamics using the time-resolved magneto-optical Kerr effect, which allows measuring spin-wave resonances and the magnetic echo signal. The frequency, mode number, and amplitude of the spin-wave resonance change with the out-of-plane angle of the external magnetic field. The amplitude of the magnetic echo signal caused by the strain pulse also changes with the angle. We calculate these angular dependences based on the Landau–Lifshitz–Gilbert equation and find that the angles of the external field and magnetic moment are important factors for the phonon–magnon coupling when phonon propagates in the thickness direction under the out-of-plane magnetic field.

Deep reinforcement learning based active safety control for distributed drive electric vehicles

Distributed drive electric vehicles are regarded as the promising transportation due to the advanced power flow architecture. Optimizing the yaw motion to enhance vehicle safety is a challenging job. Besides, the nonlinear features in vehicles affect the control accuracy of the yaw motion controllers. To this end, a deep reinforcement learning (DRL) based direct yaw moment control (DYC) strategy is put forward here. Vehicle dynamics can be approximated with the DRL algorithm, which reduces the complex nonlinear solving process. Concretely, the DYC problem is formulated as Markov Decision Process in which the observed signals and external yaw moment are incorporated as the state and action sets. Thereupon, actor-critic network is exhibited to approximate action-value function and policy function for better control performance. Furthermore, to guarantee the continuous solution of external yaw moment, the deep deterministic policy gradient algorithm is employed, in which target and online network parameters are simultaneously trained to maintain learning process stability. The proposed DRL based DYC strategy is verified using the Carsim/Simulink platform under the typical lane change manoeuvres. Numerical test results demonstrate that the proposed DYC strategy outperforms the linear approaches on taking full advantage of understeer features and enhancing the lateral stability, especially under the critical steering manoeuvres.

The relationship between muscle capacity utilization during gait and pain in people with symptomatic knee osteoarthritis

BackgroundMuscle capacity utilization reflects the percentage of maximal knee extensor strength required to complete physical activities. Research questionIs pain associated with muscle capacity utilization during walking in older adults with knee osteoarthritis? Secondarily, is muscle capacity utilization in older adults with knee osteoarthritis sex-specific? MethodsTwenty-three participants (15 females) with symptomatic knee OA completed this study [age 67 ( ± 8) years, body mass index 29.7 ( ± 3.9) kg/m2, gait speed during the Six Minute Walk test 1.25 ( ± 0.25) m/s]. Pain was measured using the Knee injury and Osteoarthritis Outcome Score. Muscle capacity utilization was quantified as the peak external knee flexor moment during level walking normalized to knee extensor maximum voluntary isometric contraction. The knee flexor moment was calculated from kinematic and kinetic data during barefoot level walking at a self-selected speed and at 1.1 m/s. Knee extensor maximum voluntary isometric contraction was measured on a dynamometer. Multiple linear regressions were used to determine the relationship between pain and muscle capacity utilization after adjusting for age, sex, body mass index, and gait speed. Independent sample t-tests examined sex differences. ResultsPain was not associated with muscle capacity utilization during self-selected and standardized walking speeds (p = 0.38 and p = 0.36, respectively). Females did not require a greater muscle capacity utilization than males to complete gait at self-selected and standardized speeds (p = 0.28, and p = 0.40, respectively). SignificanceMuscle capacity utilization was not associated with pain during walking in people with knee osteoarthritis. Future work should explore more challenging activities of daily living in knee OA.

A geometrically exact discrete elastic rod model based on improved discrete curvature

This paper presents a discrete, geometrically exact elastic rod model based on improved discrete curvature. The model is an extension of finite difference type discretization of Kirchhoff–Love rod from Discrete Differential Geometry, with 4 unknowns, including translational displacements of the axis and the axial cross-sectional rotation. The orthogonality of the rod axis and cross-section is guaranteed by parallel transport in pseudotime. A newly defined unified discrete curvature with five weighting function schemes is presented. Three of them are proposed by reducing the max nonlinear term of the Taylor expansion of the rotation vector. Theory and numerical tests show that these three methods can increase the accuracy of the model compared to the traditional method. Scheme 5 performs the best out of the recommended schemes. A transformation of freedoms to the translational displacements and end rotations is introduced to the Discrete Differential Geometry model. By using this technique, rigid connections between rod segments, rotational boundaries and external ending moments can be realized conveniently and naturally. Important properties such as convergence, objectivity and insensitivity to the slenderness ratio are also verified and investigated with several suitable numerical examples. Furthermore, results show the use of discrete curvature has better performance for the stiff bar system with flexible connections than the continuous beam.

Effects of Dual Task Interference on Biomechanics of The Entire Lower Extremity During the Drop Vertical Jump.

The dual task is an important factor affecting knee biomechanics during jump-landing tasks. Athletes often have trouble in performing two tasks concurrently and a dual task can deteriorate landing performance. However, it is still unknown whether a dual task will affect the entire lower extremity. The purpose of this study was to clarify the effects of cognitive task interference on biomechanics of hip and ankle joints as well as the knee joint during the drop vertical jump (DVJ). A total of 20 female collegiate athletes participated in the study. Athletes performed a DVJ with or without a cognitive task. The DVJ was captured using a motion analysis system. Mental arithmetic of 2-digit addition was used as a cognitive task. Maximum vertical ground reaction force (vGRF), joint angles at initial contact (IC), joint moments within 40 milliseconds (ms) after IC, and joint angles and moments at peak vGRF were assessed. The data were statistically compared between with and without a cognitive task condition using a two-tailed paired t-test or the Wilcoxon singed rank test. The peak external knee abduction moment on both limbs within 40 ms after IC during the DVJ was significantly larger in the dual task than in the single task with less knee and hip flexion at initial contact. In addition, all moments of hip and ankle joints within 40 ms after IC were significantly larger in the dual task than in the single task accompanied with greater vGRF, except for the hip internal rotation moment. Cognitive tasks during a DVJ will result in biomechanical changes of the entire lower extremity in female athletes.

Influence of Compliance and Aging of Artificial Turf Surfaces on Lower Extremity Joint Loading

Background: Artificial turf (AT) has been related to increased injury rates when compared to natural grass (NG). One potential reason for the differences in injury rates is the difference in mechanical characteristics of the surfaces. Over the course of a season on artificial turf, due to heavy use and environmental factors, properties of the surface (such as compliance) may be altered. The purpose was to compare the effects of newly installed versus aged AT on injury risks at the metatarsophalangeal, ankle, and knee joint during soccer-specific movements. Methods: Eleven male soccer players performed three movements on newly installed and ‘aged’ AT. Kinematics and kinetics were collected for the different surfaces. Results: Knee adduction moments were increased during the v-cut (119 Nm vs. 164 Nm, p = 0.02), and knee external rotation joint moments were increased during the circle run (23 Nm vs. 28 Nm, p = 0.04) with the aged surface. No surface effects were seen during the jog-sprint transition. Conclusions: For movements associated with a high risk for non-contact injuries, the age of the AT resulted in greater risk factors for injury potential at the knee joint. Further research comparing injury rates associated with AT should consider mechanical features, specifically surface compliance.

Modification of SDOF model for reinforced concrete beams under close-in explosion

In this paper, a modified single-degree-of-freedom (SDOF) model of reinforced concrete (RC) beams under close-in explosion is proposed by developing the specific impulse equivalent method and flexural resistance calculation method. The equivalent uniform specific impulse was obtained based on the local conservation of momentum and global conservation of kinetic energy. Additionally, the influence of load uniformity, boundary condition and complex material behaviors (e.g. strain rate effect, hardening/softening and hoop-confined effect) was considered in the resistance calculation process by establishing a novel relationship between external force, bending moment, curvature and deflection successively. The accuracy of the proposed model was verified by carrying out field explosion tests on four RC beams with the scaled distances of 0.5 m/kg1/3 and 0.75 m/kg1/3. The test data in other literatures were also used for validation. As a result, the equivalent load implies that the blast load near the mid-span of beams would contribute more to the maximum displacement, which was also observed in the tests. Moreover, both the resistance model and test results declare that when the blast load becomes more concentrated, the ultimate resistance would become lower, and the compressive concrete would be more prone to softening and crushing. Finally, based on the modified SDOF model, the calculated maximum displacements agreed well with the test data in this paper and other literatures. This work fully proves the rationality of the modified SDOF method, which will contribute to a more accurate damage assessment of RC structures under close-in explosion.