Terms Of Kinematics Research Articles

The impaired diaphragmatic function after bilateral lung transplantation: A multifactorial longitudinal study

Lung transplantation is a complex but effective treatment of end-stage pulmonary disease. Among the post-operative complications, phrenic nerve injury, and consequent diaphragmatic dysfunction are known to occur but are hitherto poorly described. We aimed to investigate the effect of lung transplantation on diaphragmatic function with a multimodal approach. A total of 30 patients were studied at 4 time points: pre-operatively, at discharge after surgery, and after approximately 6 and subsequently 12 months post surgery. The diaphragmatic function was studied in terms of geometry (assessed by the radius of the diaphragmatic curvature delineated on chest X-ray), weakness (considering changes in forced vital capacity when the patient shifted from upright to supine position), force (maximal pressure during sniff), mobility (excursion of the dome of the diaphragm delineated by ultrasound), contractility (thickening fraction assessed by ultrasound), electrical activity (latency and area of compound muscle action potential during electrical stimulation of phrenic nerve), and kinematics (relative contribution of the abdominal compartment to tidal volume). Despite good clinical recovery (indicated by spirometry and 6minutes walking test), a reduction of the diaphragmatic function was detected at discharge; it persisted 6 months later to recover fully 1 year after transplantation. Diaphragmatic dysfunction was demonstrated in terms of force, weakness, electrical activity, and kinematics. Our data suggest that the dysfunction was caused by phrenic nerve neurapraxia or moderate axonotmesis, potentially as a consequence of the surgical procedure (i.e., the use of ice and pericardium manipulation). The occurrence of diaphragmatic dysfunction in patients with a good clinical recovery indicates that the evaluation of diaphragmatic function should be included in the post-operative assessment after lung transplantation.

Lorentz violation effects in 2νββ decay

Observable effects for the Lorentz invariance violation (LIV) at a low energy scale can also be investigated in double beta decay. For example, by comparing the theoretical predictions with a precise analysis of the summed energy spectra of electrons in 2νββ decay, one can constrain the coefficient that governs the time-like component of the Lorentz invariance violating operator that appears in the Standard Model extension theory. In this work, we perform calculations of the phase space factors (PSF) and summed energy spectra of electrons as well as of their deviations due to LIV necessary in such experimental investigations. The Fermi functions needed in the calculation are built up with exact electron wave functions obtained by numerically solving the Dirac equation in a realistic Coulomb-type potential with the inclusion of the finite nuclear size and screening effects. We compared our results with those used in previous LIV investigations that were obtained with approximate (analytical) Fermi functions and found differences of up to 30% for heavier nuclei. Our work includes eight experimentally interesting nuclei. Next, we estimate and discuss the uncertainties of our calculations associated with uncertainties in Q-values measurements and the differences raised from the inclusion of the kinematic terms in the formalism. Finally, we provide the ratio between the standard PSF and their LIV deviations and the energies where the LIV effects are expected to be maximal. We expect our study to be useful in the current LIV investigations in 2νββ decay and to lead to improved constraints on the coefficient.

Evolution of the electric field along null rays for arbitrary observers and spacetimes

We derive, in a manifestly covariant and electromagnetic gauge independent way, the evolution law of the electric field $E^\alpha = Ee^\alpha\ (e^\alpha e_\alpha=1)$, relative to an arbitrary set of instantaneous observers along a null geodesic ray, for an arbitrary Lorentzian spacetime, in the geometrical optics limit of Maxwell's equations in vacuum. We show that, in general, neither the magnitude $E$ nor the direction $e^\alpha$ of the electric field (here interpreted as the observed polarization of light) are parallel transported along the ray. For an extended reference frame around the given light ray, we express the evolution of the direction $e^\alpha$ in terms of the frame's kinematics, proving thereby that its expansion never spoils parallel transport, which bears on the unbiased inference of intrinsic properties of cosmological sources, such as, for instance, the polarization field of the cosmic microwave background (CMB). As an application of the newly derived laws, we consider a simple setup for a gravitational wave (GW) interferometer, showing that, despite the (kinematic) shear induced by the GW, the change in the final interference pattern is negligible since it turns out to be of the order of the ratio of the GW and laser frequencies.

Custom made total knee arthroplasty : Review of current literature

Custom-designed total knee replacement has become astandard procedure in some orthopaedic centres worldwide. Due to the lack of literature, the discussion about the hypothetical advantages has remained controversial. It was the aim of this study to focus on the current literature on custom-made total knee arthroplasty. We can demonstrate that custom-made total knee arthroplasty is areproducible strategy with good clinical results in terms of leg-axis reconstruction, natural kinematics, patient-related outcomes and cost effectiveness. This has led to the fact that the Orthopaedic Data Evaluation Panel (ODEP) of the National Health Service in Great Britain rated the Conformis custom-designed knee replacement in 2017 with a3D rating.

Physics-Based Simulations to Predict the Differential Effects of Motor Control and Musculoskeletal Deficits on Gait Dysfunction in Cerebral Palsy: A Retrospective Case Study.

Physics-based simulations of walking have the theoretical potential to support clinical decision-making by predicting the functional outcome of treatments in terms of walking performance. Yet before using such simulations in clinical practice, their ability to identify the main treatment targets in specific patients needs to be demonstrated. In this study, we generated predictive simulations of walking with a medical imaging based neuro-musculoskeletal model of a child with cerebral palsy presenting crouch gait. We explored the influence of altered muscle-tendon properties, reduced neuromuscular control complexity, and spasticity on gait dysfunction in terms of joint kinematics, kinetics, muscle activity, and metabolic cost of transport. We modeled altered muscle-tendon properties by personalizing Hill-type muscle-tendon parameters based on data collected during functional movements, simpler neuromuscular control by reducing the number of independent muscle synergies, and spasticity through delayed muscle activity feedback from muscle force and force rate. Our simulations revealed that, in the presence of aberrant musculoskeletal geometries, altered muscle-tendon properties rather than reduced neuromuscular control complexity and spasticity were the primary cause of the crouch gait pattern observed for this child, which is in agreement with the clinical examination. These results suggest that muscle-tendon properties should be the primary target of interventions aiming to restore an upright gait pattern for this child. This suggestion is in line with the gait analysis following muscle-tendon property and bone deformity corrections. Future work should extend this single case analysis to more patients in order to validate the ability of our physics-based simulations to capture the gait patterns of individual patients pre- and post-treatment. Such validation would open the door for identifying targeted treatment strategies with the aim of designing optimized interventions for neuro-musculoskeletal disorders.

Observer-Agent Kinematic Similarity Facilitates Action Intention Decoding

It is well known that the kinematics of an action is modulated by the underlying motor intention. In turn, kinematics serves as a cue also during action observation, providing hints about the intention of the observed action. However, an open question is whether decoding others’ intentions on the basis of their kinematics depends solely on how much the kinematics varies across different actions, or rather it is also influenced by its similarity with the observer motor repertoire. The execution of reach-to-grasp and place actions, differing for target size and context, was recorded in terms of upper-limb kinematics in 21 volunteers and in an actor. Volunteers had later to observe the sole reach-to-grasp phase of the actor’s actions, and predict the underlying intention. The potential benefit of the kinematic actor-participant similarity for recognition accuracy was evaluated. In execution, both target size and context modulated specific kinematic parameters. More importantly, although participants performed above chance in intention recognition, the similarity of motor patterns positively correlated with recognition accuracy. Overall, these data indicate that kinematic similarity exerts a facilitative role in intention recognition, providing further support to the view of action intention recognition as a visuo-motor process grounded in motor resonance.

A Geometric Algebra Based Higher Dimensional Approximation Method for Statics and Kinematics of Robotic Manipulators

Evaluation of a robotic (serial or parallel) manipulator’s static and kinematics performance requires the solution of closed and complicated non-closed form systems of equations for both the forward and inverse problem types. In this work, a robotic system or manipulator is represented as a network whose motion generating kinematic pairs are represented as the network’s inter-connected nodes. Within this network theoretic context, we develop a formulation employing higher dimensional multivectors defined in Clifford Algebra that approximates the computational outcomes of such complicated systems of equations, for both inverse and forward problem types. The statics and kinematics performance of these mechanical networks (serial and parallel robots) are rapidly evaluated without the need to solve their respective traditional systems of equations using what we call ‘screw hypervolumes’, which capture the algebro-geometric structures generated by a robot’s physical design parameters and end-effector position in terms of kinematics and statics. These dimensionless hypervolume functions enable the specialist to produce a very computationally efficient function/index that approximates the kinematic and static output spaces of robots. We find that this formulation inadvertently presents a curious mathematical analogue to these systems of equations. A 6R serial robot, the Delta robot and the 3-RRR manipulator are analysed using the hypervolume methods for the case studies. This approach can be adapted and applied to other multi-agent physical systems displaying non-commutative interactions as well.

Unraveling the complex deformation pattern at Yellowstone plateau through seismicity and fracture analysis

The intense unrest of the Yellowstone volcanic plateau is manifested through diffuse seismic activity, earthquake swarms, and episodes of complex surficial deformation that have been related to magmatic fluid transfer in the upper crust over the past several decades. While past studies have focused on modeling contemporary geophysical data, there has not been a fully-integrated evaluation of seismicity, fault kinematics, and stress field. Here we analyze a catalog of 10,201 relocated earthquakes recorded between 2010 and 2016 and determine 224 well-constrained double-couple focal mechanisms. The majority of the focal mechanisms (65%) are associated with the 2010 Madison Plateau seismic swarm. The focal mechanisms are predominantly strike-slip with subordinate normal faulting mechanisms. Possible causes of this predominance and of the concurrence of both kinematics are here discussed, in order to unravel the influence of magmatic processes such as past sill intrusions. The earthquake catalog has been analyzed in terms of location, time, and kinematics according to the phases of surficial deformation documented by GPS data in order to identify systematic patterns of deformation and has been compared to the 1988–2009 seismicity. The continuous downwarping of the overburden from 2010 to 2016 was accomodated by structural adjustment of the shallow crust through strike-slip motions on a multitude of scattered small fault planes. Furthermore, the predominance of strike-slip faulting during seismic swarms occurs when the fluid overpressure induces horizontal propagation of vertical fractures with strike-slip motions, followed by horizontal fluid flow.

Design of an experiment for the biomechanical and thermal analysis of athletes during prolonged running exercise

Biomechanics and thermoregulation of human running are key aspects playing an important role in the training of professional athletes. In the case of a prolonged exercise, as occurs during the marathon race, the intensity and duration of the exercise (in concert with environmental conditions) can affect the thermoregulatory response and the running mechanics. The aim of this study is the design of a novel experiment able to simultaneously capture information concerning the biomechanics of lower limbs and the surface temperature map of the whole body during a prolonged running exercise on treadmill. Kinematics quantities, such as linear and angular displacement, velocity and acceleration of relevant body markers are recorded by a video system, while surface temperature evolution on time is detected by an infrared thermal camera. A group of five amateur athletes, with long experience in long-distance running competitions, was involved in this study. Results for the sample group, in terms of kinematic (displacements and angles) and thermal (local and total-body skin temperatures) quantities, revealed features related to individual response to the effort. Even though the relatively little number of athletes does not permit to infer general conclusions, the combined mechanical and thermal experiment is deemed to be a useful tool for the investigation of endurance running characteristics.

Improving Passive Ankle Foot Orthosis System Using Estimated Ankle Velocity Reference

This study aims to investigate an appropriate ankle velocity reference (ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ref</sub> ), which is the average ankle velocity of a certain healthy subject when walking with a certain walking speed. The goal is to improve a Passive Controllable Ankle Foot Orthosis (PICAFO) by implementing the ankle velocity reference. Firstly, the function to estimate ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ref</sub> , based on walking speed and body mass index (BMI), is obtained from 16 able-bodied subjects walking gait data. The effect of controlled stiffness (based on wref) to the user's ankle kinematics and muscle activity was evaluated by comparing it to other settings, such as walking barefooted and various constant damping stiffness (0%, 30%, 60%, and 100% of the maximum damping stiffness). Two able-bodied subjects (normal and overweight) participated in the evaluation, where they had to walk at two different walking speeds (1 and 2 km/h). The result showed that ankle kinematics and muscle activity were improved when w was controlled during walking speed of 1 km/h for both subjects. In terms of ankle kinematics, the toe clearance occurred, and walking stability increased. In terms of muscle activity, the average muscle activity had reduced by ~29% for the normal subject and by ~57% for an overweight subject, which shows that PICAFO provides necessary damping stiffness to replace the muscle works partially. In the future, by using the ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ref</sub> based on walking speed and BMI, the therapists can skip the trial and error process of finding an appropriate PICAFO prescription for a post-stroke patient.

A Computational Biomechanics Human Body Model Coupling Finite Element and Multibody Segments for Assessment of Head/Brain Injuries in Car-To-Pedestrian Collisions.

It has been challenging to efficiently and accurately reproduce pedestrian head/brain injury, which is one of the most important causes of pedestrian deaths in road traffic accidents, due to the limitations of existing pedestrian computational models, and the complexity of accidents. In this paper, a new coupled pedestrian computational biomechanics model (CPCBM) for head safety study is established via coupling two existing commercial pedestrian models. The head–neck complex of the CPCBM is from the Total Human Model for Safety (THUMS, Toyota Central R&D Laboratories, Nagakute, Japan) (Version 4.01) finite element model and the rest of the parts of the body are from the Netherlands Organisation for Applied Scientific Research (TNO, The Hague, The Netherlands) (Version 7.5) multibody model. The CPCBM was validated in terms of head kinematics and injury by reproducing three cadaveric tests published in the literature, and a correlation and analysis (CORA) objective rating tool was applied to evaluate the correlation of the related signals between the predictions using the CPCBM and the test results. The results show that the CPCBM head center of gravity (COG) trajectories in the impact direction (YOZ plane) strongly agree with the experimental results (CORA ratings: Y = 0.99 ± 0.01; Z = 0.98 ± 0.01); the head COG velocity with respect to the test vehicle correlates well with the test data (CORA ratings: 0.85 ± 0.05); however, the correlation of the acceleration is less strong (CORA ratings: 0.77 ± 0.06). No significant differences in the behavior in predicting the head kinematics and injuries of the tested subjects were observed between the TNO model and CPCBM. Furthermore, the application of the CPCBM leads to substantial reduction of the computation time cost in reproducing the pedestrian head tissue level injuries, compared to the full-scale finite element model, which suggests that the CPCBM could present an efficient tool for pedestrian brain-injury research.

Chemical enrichment and host galaxies of extremely strong intervening DLAs towards quasars

We present the results from VLT/X-shooter spectroscopic observations of 11 extremely strong intervening damped Lyman-α absorbers (ESDLAs) that were initially selected as high N(H I) (i.e. ≥5 × 1021 cm−2) candidates from the Sloan Digital Sky Survey (SDSS). We confirm the high H I column densities, which we measure to be in the range log N(H I) = 21.6 − 22.4. Molecular hydrogen is detected with high column densities (N(H2)≥1018 cm−2) in 5 out of 11 systems, 3 of which are reported here for the first time, and we obtain conservative upper limits on N(H2) for the remaining 6 systems. We also measure the column density of various metal species (Zn II, Fe II, Si II, Cr II, and C I), quantify the absorption-line kinematics (Δv90), and estimate the extinction of the background quasar light (AV) by dust in the absorbing gas. We compare the chemical properties of this sample of ESDLAs, supplemented with literature measurements, to that of DLAs located at the redshift of long-duration γ-ray bursts (GRB-DLAs). We confirm that the two populations are almost indistinguishable in terms of chemical enrichment and gas kinematics. In addition, we find no marked differences in the incidence of H2. All this suggests that ESDLAs and GRB-DLAs probe similar galactic environments. We search for the galaxy counterparts of ESDLAs and find associated emission lines in 3 out of 11 systems, 2 of which are reported here for the first time (at zabs = 2.304 and 2.323 towards the quasars SDSS J002503.03+114547.80 and SDSS J114347.21+142021.60, respectively). The measured separations between the quasar sightlines and the emission associated with the ESDLA galaxy (for a total of five sightlines) are all very small (ρ &lt; 3 kpc). Because our observations are complete up to ρ ∼ 7 kpc, we argue that the emission counterparts of the remaining systems are more likely below the detection limit than outside the search area. While the small impact parameters are similar to what is observed for GRB-DLAs, the associated star formation rates are on average lower than for GRB host galaxies. This is explained by long-duration GRBs being associated with the death of massive stars and therefore pinpointing regions of active star formation in the GRB host galaxies. Our observations support the suggestion from the literature that ESDLAs could act as blind analogues of GRB-DLAs, probing neutral gas with high column density in the heart of high-redshift galaxies, without any prior on the instantaneous star formation rate.

Eburnean deformation pattern of Burkina Faso and the tectonic significance of shear zones in the West African craton

Shear zones of the Paleoproterozoic Eburnean accretionary Orogen (West African craton) are investigated by means of large-scale structural mapping. Regional scale (10-100 km) mapping was based on the aeromagnetic survey of Burkina Faso and craton-scale (1000 km) mapping on a compilation of fabric data. At both scales, shear zones are arranged as an anastomosed transpressional network that accommodated distributed shortening and lateral flow of the orogenic lithosphere between the converging Kénéma-Man and Congo Archean provinces. Structural interference patterns at both scales were due to three-dimensional partitioning of progressive transpressional deformation and interactions among shear zones that absorbed heterogeneities in the regional flow patterns while maintaining the connectivity of the shear zone network. Such orogen-scale kinematic patterns call for caution in using the deformation phase approach without considering the “bigger structural picture” and interpreting displacement history of individual shear zones in terms of plate kinematics. The West African shear zone pattern is linked to that of the Guiana shield through a new transatlantic correlation to produce an integrated kinematic model of the Eburnean-Transamazonian orogen.

Numerical analysis of passenger kinematics and injury risks during a railway vehicle collision: The effect of safety belts

The aim of this paper is to contribute to investigation of passive safety of passengers in railway vehicles using numerical simulations. At first, a typical interior of a railway vehicle is created in the Virtual Performance Solution software. It includes finite element models of seats. Their mechanical properties have been determined experimentally. Particular attention is paid to the table in the backseat as a potentially harmful element. In numerical simulations, both folded and unfolded states of the table are considered. The passenger is represented with the virtual human body model Virthuman. Its structure is composed of rigid bodies and deformable segments to account for deformability of soft tissues. It allows for the prediction of injury risk. The numerical simulations aim to investigate the potential benefit of standard seat belts in a railway vehicle. Therefore, the passenger is seated considering three configurations: seating with no constraints, belted with a two-point belt and a three-point belt. The interior is loaded with a crash-pulse prescribed by the GM/RT2100 regulation. The results are discussed in terms of passenger kinematics and injury risk.

Gait and postural control patterns and rehabilitation in Down syndrome: a systematic review.

[Purpose] To describe (1) the current knowledge on gait and postural control in individuals with Down syndrome in terms of spatiotemporal, kinematics and kinetics, and (2) relevant rehabilitation strategies. [Methods] Randomized and non-randomized clinical trials published between January 1997 and October 2019 were selected by searching four scientific databases. We included studies on patients with Down syndrome involving gait analysis or postural control. A custom data-extraction and appraisal form was developed to collect the key features of each article. The PEDro Scale was used to evaluate the methodological quality of the studies. [Results] A total of 37 out of 146 cross-sectional and longitudinal studies were included in the review. The main abnormalities included: reduction of gait velocity and step length, poor static balance with increased anteroposterior and mediolateral oscillations and a larger step width. [Conclusion] A number of compensatory patterns during movement was observed, with a direct influence on improvements in stability and postural control throughout daily life. Intensive gait training at an early age appears to produce long-term improvements in this population. Future research should focus on the interaction between the motor and cognitive function, and on the functional effects due to the exposure to an enriched environment.

Design of Multiple Wearable Robotic Extra Fingers for Human Hand Augmentation

Augmenting the human hand with robotic extra fingers is a cutting-edge research topic and has many potential applications, in particular as a compensatory and rehabilitation tool for patients with upper limb impairments. Devices composed of two extra fingers are preferred with respect to single finger devices when reliable grasps, resistance to external disturbances, and higher payloads are required. Underactuation and compliance are design choices that can reduce the device complexity and weight, maintaining the adaptability to different grasped objects. When only one motor is adopted to actuate multiple fingers, a differential mechanism is necessary to decouple finger movements and distribute forces. In this paper, the main features of a wearable device composed of two robotic extra fingers are described and analyzed in terms of kinematics, statics, and mechanical resistance. Each finger is composed of modular phalanges and is actuated with a single tendon. Interphalangeal joints include a passive elastic element that allows restoring the initial reference configuration when the tendon is released. The stiffness of each passive element can be customized in the manufacturing process and can be chosen according to a desired closure movement of the fingers. Another key aspect of the device is the differential system connecting the actuator to the fingers.

Advancing drops on curved and flat surfaces

The paper is concerned with the dynamics of advancing liquid blobs of fluid on curved and flat solid surfaces, such as cycloids and inclined planes. We investigate the kinematics of such blobs on hydrophobic surfaces with emphasis on the shape of the interface as the fluid advances. A theoretical model is proposed that captures the shape of the interface at early times. Also, the trajectory of the fluid, as it detaches from the cycloid, is investigated and compared with theoretical predictions. We find a good qualitative agreement between predictions and experimental data. As an extension of the present findings, we also investigate the shape and the dynamics of advancing drops on cycloids, placed in a viscous outer immiscible liquid. We find both similarities, in terms of kinematics, and specific differences in the shape of the advancing drop.

Gait strategy and body composition in patients with Prader-Willi syndrome.

Individuals with Prader-Willi syndrome (PWS) exhibit reduced lean body mass and increased fat-lean mass ratio when compared with individuals of normal weight and obese ones. Thus, research on the association of functional limitations during gait and body composition may be of great importance from a rehabilitative viewpoint. In particular, the aim of this study was to compare the gait profile of persons with PWS to that of unaffected individuals and to see if a relationship exists between gait profile and body composition in individuals with PWS. Eighteen individuals with PWS and 20 unaffected individuals (Healthy Group: HG) were assessed. Their gait pattern was quantified with 3D-Gait Analysis (3D-GA). Overall body weight, lean and fat masses were measured by dual-energy X-ray absorptiometry. Individuals with PWS were found to be characterized by a significantly different (p < 0.05) gait pattern with respect to healthy controls in terms of both kinematic and kinetic parameters. No correlations were found between kinematic parameters and overall mass and lean/fat mass, while some parameters associated with ground reaction force were found to be significantly correlated with overall mass, lean mass and fat mass. Significant regression models were obtained, including impact and propulsive force and loading rate. Our data suggest that in individuals with PWS, gait is influenced by the overall and lean body mass. Thus, therapeutic strategies should target both weight reduction and lean mass increase to optimize gait, minimize articular stress, and reduce the risk of repetitive strain on the lower limbs. Level III: Case-control analytic study.

EMG-based vibro-tactile biofeedback training: effective learning accelerator for children and adolescents with dystonia? A pilot crossover trial

BackgroundThis study is aimed at better understanding the role of a wearable and silent ElectroMyoGraphy-based biofeedback on motor learning in children and adolescents with primary and secondary dystonia.MethodsA crossover study with a wash-out period of at least 1 week was designed; the device provides the patient with a vibration proportional to the activation of an impaired target muscle. The protocol consisted of two 5-day blocks during which subjects were trained and tested on a figure-8 writing task: their performances (at different levels of difficulty) were evaluated in terms of both kinematics and muscular activations on day 1 and day 5, while the other 3 days were purely used as training sessions. The training was performed with and without using the biofeedback device: the week of use was randomized. Data were collected on 14 subjects with primary and secondary (acquired) dystonia (age: 6–19 years).ResultsResults comparing kinematic-based and EMG-based outcome measures pre- and post-training showed learning due to practice for both subjects with primary and secondary dystonia. On top of said learning, an improvement in terms of inter-joint coordination and muscular pattern functionality was recorded only for secondary dystonia subjects, when trained with the aid of the EMG-based biofeedback device.ConclusionsOur results support the hypothesis that children and adolescents with primary dystonia in which there is intact sensory processing do not benefit from feedback augmentation, whereas children with secondary dystonia, in which sensory deficits are often present, exhibit a higher learning capacity when augmented movement-related sensory information is provided. This study represents a fundamental investigation to address the scarcity of noninvasive therapeutic interventions for young subjects with dystonia.

Analytical and finite element solutions of free and forced vibration of unrestrained and braced thin-walled beams

In this article, vibration of thin-walled beams with arbitrary open cross-section shape is investigated. Based on the beam element model accounting for warping and flexural–torsional coupling, analytical solutions for different boundary conditions are derived for higher free vibration modes in bending, torsion and flexural–torsional coupled modes. In the model, the effects of rotational inertial kinematic terms are considered. The finite element approach of the model is also investigated. Three-dimensional beams with seven degrees of freedom per node are adopted in the mesh process. Free vibration and forced vibration analyses are possible. In forced vibration, the behaviour of the beams is studied in the frequency domain using the steady-state method (modal analysis). Damping is considered using the Rayleigh model. The model is validated by comparing the results to benchmark solutions found in the literature and to other recent numerical and experimental results. Additional finite element simulations are performed by means of commercial softwares (Abaqus and Adina). In slender unrestrained beams, the vibration behaviour is predominated by torsion and lateral bending modes. In design, recourse to braces is a good compromise. This solution is discussed, and improvement of the vibration behaviour in the presence of intermediate braces is confirmed. Application of higher vibration modes in building and bridge design is outlined. The effects of the number and distribution of the intermediate braces to improve structural stability against vibration behaviour is outlined.