scholarly journals Natural Frequency Method: estimating the preferred walking speed of Tyrannosaurus rex based on tail natural frequency

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Pasha A. van Bijlert ◽  
A. J. ‘Knoek’ van Soest ◽  
Anne S. Schulp
Keyword(s):  
Energy Storage ◽  
Natural Frequency ◽  
Elastic Energy ◽  
Walking Speed ◽  
Natural Frequencies ◽  
Body Parts ◽  
Step Frequency ◽  
Frequency Method ◽  
Cost Of Transport ◽  
Moment Arms

Locomotor energetics are an important determinant of an animal's ecological niche. It is commonly assumed that animals minimize locomotor energy expenditure by selecting gait kinematics tuned to the natural frequencies of relevant body parts. We demonstrate that this allows estimation of the preferred step frequency and walking speed of Tyrannosaurus rex , using an approach we introduce as the Natural Frequency Method. Although the tail of bipedal dinosaurs was actively involved in walking, it was suspended passively by the caudal interspinous ligaments. These allowed for elastic energy storage, thereby reducing the metabolic cost of transport. In order for elastic energy storage to be high, step and natural frequencies would have to be matched. Using a 3D morphological reconstruction and a spring-suspended biomechanical model, we determined the tail natural frequency of T. rex (0.66 s −1 , range 0.41–0.84), and the corresponding walking speed (1.28 m s −1 , range 0.80–1.64), which we argue to be a good indicator of preferred walking speed (PWS). The walking speeds found here are lower than earlier estimations for large theropods, but agree quite closely with PWS of a diverse group of extant animals. The results are most sensitive to uncertainties regarding ligament moment arms, vertebral kinematics and ligament composition. However, our model formulation and method for estimation of walking speed are unaffected by assumptions regarding muscularity, and therefore offer an independent line of evidence within the field of dinosaur locomotion.

scholarly journals Correction to ‘Natural Frequency Method: estimating the preferred walking speed of Tyrannosaurus rex based on tail natural frequency’

2021 ◽  
Vol 8 (7) ◽  
pp. 211139
Author(s):  
Pasha A. van Bijlert ◽  
A. J. ‘Knoek’ van Soest ◽  
Anne S. Schulp
Keyword(s):  
Natural Frequency ◽  
Walking Speed ◽  
Frequency Method

scholarly journals Shorter heels are linked with greater elastic energy storage in the Achilles tendon

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
A. D. Foster ◽  
B. Block ◽  
F. Capobianco ◽  
J. T. Peabody ◽  
N. A. Puleo ◽  
...  
Keyword(s):  
Energy Storage ◽  
Achilles Tendon ◽  
Elastic Energy ◽  
Mechanical Energy ◽  
Running Economy ◽  
Triceps Surae ◽  
Morphological Data ◽  
Energetic Cost ◽  
Moment Arm ◽  
Moment Arms

AbstractPrevious research suggests that the moment arm of the m. triceps surae tendon (i.e., Achilles tendon), is positively correlated with the energetic cost of running. This relationship is derived from a model which predicts that shorter ankle moment arms place larger loads on the Achilles tendon, which should result in a greater amount of elastic energy storage and return. However, previous research has not empirically tested this assumed relationship. We test this hypothesis using an inverse dynamics approach in human subjects (n = 24) at speeds ranging from walking to sprinting. The spring function of the Achilles tendon was evaluated using specific net work, a metric of mechanical energy production versus absorption at a limb joint. We also combined kinematic and morphological data to directly estimate tendon stress and elastic energy storage. We find that moment arm length significantly determines the spring-like behavior of the Achilles tendon, as well as estimates of mass-specific tendon stress and elastic energy storage at running and sprinting speeds. Our results provide support for the relationship between short Achilles tendon moment arms and increased elastic energy storage, providing an empirical mechanical rationale for previous studies demonstrating a relationship between calcaneal length and running economy. We also demonstrate that speed and kinematics moderate tendon performance, suggesting a complex relationship between lower limb geometry and foot strike pattern.

Jumping, Climbing and Suspensory Locomotion

2018 ◽  
Keyword(s):  
Energy Storage ◽  
Elastic Energy ◽  
The Core ◽  
Power Amplification ◽  
Core Concepts

Jumping, climbing and suspensory locomotion are specialized locomotor mechanisms used on land and in the air. Jumping is used for rapid launches from substrates. Climbing and suspensory movements enable locomotion up, under and through vertically-structured habitats, such as forests. Elastic energy storage is particularly important for jumping and catapult systems and we address the core concepts of power amplification that are exemplified in nature’s extreme jumpers. We examine the diverse mechanisms of attachment that characterize animals that can grasp and adhere to a diversity of structures. We conclude the chapter by examining the integration of biological capabilities with engineering innovations in these systems.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

scholarly journals A Vibration-Based Structural Health Monitoring System for Transmission Line Towers

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 515 ◽  
Author(s):  
Long Zhao ◽  
Xinbo Huang ◽  
Ye Zhang ◽  
Yi Tian ◽  
Yu Zhao
Keyword(s):  
Structural Health Monitoring ◽  
Transmission Line ◽  
Natural Frequency ◽  
Health Monitoring ◽  
Structural Changes ◽  
Natural Frequencies ◽  
Transmission Tower ◽  
Health Monitoring System ◽  
Wind Speeds ◽  
Before And After

In this paper, we present a vibration-based transmission tower structural health monitoring system consisting of two parts that identifies structural changes in towers. An accelerometer group realizes vibration response acquisition at different positions and reduces the risk of data loss by data compression technology. A solar cell provides the power supply. An analyser receives the data from the acceleration sensor group and calculates the transmission tower natural frequencies, and the change in the structure is determined based on natural frequencies. Then, the data are sent to the monitoring center. Furthermore, analysis of the vibration signal and the calculation method of natural frequencies are proposed. The response and natural frequencies of vibration at different wind speeds are analysed by time-domain signal, power spectral density (PSD), root mean square (RMS) and short-time Fouier transform (STFT). The natural frequency identification of the overall structure by the stochastic subspace identification (SSI) method reveals that the number of natural frequencies that can be calculated at different wind speeds is different, but the 2nd, 3rd and 4th natural frequencies can be excited. Finally, the system was tested on a 110 kV experimental transmission line. After 18 h of experimentation, the natural frequency of the overall structure of the transmission tower was determined before and after the tower leg was lifted. The results show that before and after the tower leg is lifted, the natural frequencies of each order exhibit obvious changes, and the differences in the average values can be used as the basis for judging the structural changes of the tower.

scholarly journals Evidence for a vertebrate catapult: elastic energy storage in the plantaris tendon during frog jumping

2011 ◽  
Vol 8 (3) ◽  
pp. 386-389 ◽  
Author(s):  
Henry C. Astley ◽  
Thomas J. Roberts
Keyword(s):  
Energy Storage ◽  
Elastic Energy ◽  
High Speed ◽  
Angular Acceleration ◽  
Whole Body ◽  
Joint Motion ◽  
Joint Movement ◽  
Fascicle Length ◽  
Muscle Fascicle ◽  
Muscle Shortening

Anuran jumping is one of the most powerful accelerations in vertebrate locomotion. Several species are hypothesized to use a catapult-like mechanism to store and rapidly release elastic energy, producing power outputs far beyond the capability of muscle. Most evidence for this mechanism comes from measurements of whole-body power output; the decoupling of joint motion and muscle shortening expected in a catapult-like mechanism has not been demonstrated. We used high-speed marker-based biplanar X-ray cinefluoroscopy to quantify plantaris muscle fascicle strain and ankle joint motion in frogs in order to test for two hallmarks of a catapult mechanism: (i) shortening of fascicles prior to joint movement (during tendon stretch), and (ii) rapid joint movement during the jump without rapid muscle-shortening (during tendon recoil). During all jumps, muscle fascicles shortened by an average of 7.8 per cent (54% of total strain) prior to joint movement, stretching the tendon. The subsequent period of initial joint movement and high joint angular acceleration occurred with minimal muscle fascicle length change, consistent with the recoil of the elastic tendon. These data support the plantaris longus tendon as a site of elastic energy storage during frog jumping, and demonstrate that catapult mechanisms may be employed even in sub-maximal jumps.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

scholarly journals Associations Between Foot Placement Asymmetries and Metabolic Cost of Transport in Hemiparetic Gait

2016 ◽  
Vol 31 (2) ◽  
pp. 168-177 ◽  
Author(s):  
James M. Finley ◽  
Amy J. Bastian
Keyword(s):  
Walking Speed ◽  
Metabolic Cost ◽  
Positive Association ◽  
Stroke Survivor ◽  
Gas Analysis ◽  
Stroke Survivors ◽  
Cost Of Transport ◽  
Foot Placement ◽  
Hemiparetic Gait ◽  
All Speeds

Stroke survivors often have a slow, asymmetric walking pattern. They also walk with a higher metabolic cost than healthy, age-matched controls. It is often assumed that spatial-temporal asymmetries contribute to the increased metabolic cost of walking poststroke. However, elucidating this relationship is made challenging because of the interdependence between spatial-temporal asymmetries, walking speed, and metabolic cost. Here, we address these potential confounds by measuring speed-dependent changes in metabolic cost and implementing a recently developed approach to dissociate spatial versus temporal contributions to asymmetry in a sample of stroke survivors. We used expired gas analysis to compute the metabolic cost of transport (CoT) for each participant at 4 different walking speeds: self-selected speed, 80% and 120% of their self-selected speed, and their fastest comfortable speed. We also computed CoT for a sample of age- and gender-matched control participants who walked at the same speeds as their matched stroke survivor. Kinematic data were used to compute the magnitude of a number of variables characterizing spatial-temporal asymmetries. Across all speeds, stroke survivors had a higher CoT than controls. We also found that our sample of stroke survivors did not choose a self-selected speed that minimized CoT, contrary to typical observations in healthy controls. Multiple regression analyses revealed negative associations between speed and CoT and a positive association between asymmetries in foot placement relative to the trunk and CoT. These findings suggest that interventions designed to increase self-selected walking speed and reduce foot-placement asymmetries may be ideal for improving walking economy poststroke.

PNEUMATIC VIBROISOLATION SYSTEM OF THE BASE DESK WITH NATURAL FREQUENCY REGULATION

2021 ◽  
Vol 113 ◽  
pp. 91-100
Author(s):  
Radka JÍROVÁ ◽  
Lubomír PEŠÍK
Keyword(s):  
Natural Frequency ◽  
Automotive Industry ◽  
Natural Frequencies ◽  
Dynamical Behaviour ◽  
Operating Conditions ◽  
Frequency Regulation ◽  
The Stability ◽  
Short Time

Vibroisolation systems of base desks for machine and testing facilities usually cannot effect efficient changing of their own frequencies according to operating conditions. Especially in the case of the automotive industry, the possibility of changing natural frequencies is very desirable. During varying operating conditions, the vibroisolation system needs to be regulated easily and quickly regarding the minimisation of dynamical forces transmitted to the ground and to ensure the stability of the testing process. This paper describes one of the options of tuning the base desk at a relatively short time and by sufficient change of own frequencies, which decides the dynamical behaviour of the whole system.

scholarly journals Identification of Corrosion on a Hollow Tube Using Vibration

2014 ◽  
Vol 564 ◽  
pp. 176-181
Author(s):  
S.T. Cheng ◽  
Nawal Aswan Abdul Jalil ◽  
Zamir A. Zulkefli
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Impact Loading ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Localized Corrosion ◽  
Free Boundary Conditions ◽  
The Impact ◽  
Impact Vibration

Vibration based technique have so far been focused on the identification of structural damage. However, not many studies have been conducted on the corrosion identification on pipes. The objective of this paper is to identify corrosion on pipes from vibration measurements. A hollow pipe, 500 mm in length with 63.5 mm in diameter was subjected to impact loading using an impact hammer to identify the natural frequency of the tube in two conditions i) without any corrosion and ii) with an induced localized 40 mm by 40 mm corrosion at the middle of the pipe. The shift of natural frequencies of the structures under free boundary conditions was examined for each node of excitation. The results showed that there is a shift in natural frequency of the pipe, between 3 and 4 Hz near to the corrosion area. It can suggested that that the impact vibration is capable of identifying of localized corrosion on a hollow tube.

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