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[Purpose] Optimization of post-training muscle recovery is important in clinical rehabilitation and sports science. In this study, we investigated the effects of local vibration stimulation on post-training muscle recovery and hypertrophy in healthy adults, focusing on the upper extremities. [Participants and Methods] The study included 20 healthy students categorized into the control and vibration stimulation groups. Both groups underwent training, including elbow flexion. The vibration stimulation group received immediate post-training local vibration stimulation. Evaluation included measurement of upper arm circumference, muscle strength, muscle hardness, and ultrasonographic imaging. [Results] Our results showed that local vibration stimulation increased muscle luminosity but had no significant effect on muscle strength, hardness, or thickness. [Conclusion] Post-training vibration stimulation may promote muscle growth and recovery by stimulating blood flow and improving nutrient and oxygen supply to muscles.
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Double-row planetary gear set (PGS) is a common form of the PGS, which is relatively more complex than the regular PGSs. It consists of one sun gear, several long planets, several short planets, two ring gears, and one carrier. Due to the significantly wider tooth width of the long planet compared to the sun gear, the axial meshing position between the sun gear and the long planet can be adjusted. The vibrations of PGS should vary with different axial meshing positions. If the axial position of the sun gear is optimized, the vibrations of PGS can be reduced. This work establishes a dynamic model of a double-row PGS. The dynamic model considers the mesh forces of the gear pairs and the supporting forces of the bearing. The effect of the sun gear axial position on the sun gear and ring gear #2 vibrations are investigated. Finally, the recommended axial position for the sun gear is provided.
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Background: Considering the neuromuscular alterations in Achilles tendinopathy (AT), sensorimotor training (SMT) might be beneficial to restore the neuromuscular capacity of the muscle-tendon complex and thereby improve patients' functions and alleviate symptoms. However, there is still a lack of knowledge concerning the effects of SMT on improving functional (e.g., strength) and pain outcomes in this population. Thus, the purpose of this study was to synthesize current evidence to analyze the efficacy of SMT in people with AT. Methods: A systematic electronic search was performed in PubMed, Web of Science, and Cochrane Central Register of Controlled Trials from inception to December 2023. Studies applying SMT in people with AT investigating functional or clinical pain outcomes were considered. Protocols had to incorporate balance, stabilization, proprioception, or vibration training. Patients with insertional or mid-portion AT (≥18 years age) diagnosed with clinical or sonographic evaluation were included. Results: The search yielded 823 records. A total of three randomized controlled trials were considered eligible for the analysis. Each trial used a different SMT protocol: balance training, balance with stabilization training, or whole-body vibration training (WBVT) with other co-interventions. Most functional and pain parameters improved compared to baseline. The first study reported a decrease in pain and an increase in performance (i.e., countermovement jump height) and endurance (i.e., number of heel-raises) by 12-week use of a balance training in addition to isometric, concentric/eccentric, and eccentric exercises. The second study evaluated the four weeks effect of SMT (balance and stabilization training plus eccentric exercises) in addition to passive physiotherapy (deep frictions, ice, ultrasound), resulting in an increased plantarflexion peak torque and reduced pain levels. The third study investigating WBVT reported at 12 weeks an increase in flexibility and a decrease in tendon pain. Discussion: SMT in addition to other co-interventions (i.e., eccentric, isometric, concentric/eccentric training, physiotherapy) showed improvements in strength, performance, muscle flexibility, and alleviated clinical outcomes of pain. SMT might therefore be useful as part of a multimodal treatment strategy protocol in patients suffering from AT. However, due to the small number of studies included and the diversity of SMT protocols, the current evidence is weak; its additional effectiveness should be evaluated. Systematic Review Registration: https://www.crd.york.ac.uk/PROSPERO/display_record.php?RecordID=467698, Identifier CRD42023467698.
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Our aim was to explore possible relationships between serum levels of biomarkers in patients with hand-arm vibration injury in relation to the severity of the vascular, i.e., Raynaud's phenomenon (RP), and neurosensory manifestations, the current exposure level, and the duration of exposure. This study was of case series design and involved 92 patients diagnosed with hand-arm vibration injury. Jonckheere's trend test was used to assess any association between serum levels of biomarkers and RP as well as neurosensory manifestations, graded by the International Consensus Criteria. Generalized linear models with adjustment for possible confounders were also used for associations between serum levels of biomarkers and; (1) severity of RP recorded as the extent of finger blanching calculated with Griffin score, (2) vibration perception thresholds, (3) magnitude of current exposure as [A(8); (m/s2)] value, and (4) the duration of exposure in years. Serum levels of thrombomodulin, von Willebrand factor, calcitonin gene related peptide (CGRP), heat shock protein 27, and caspase-3 were positively associated with severity of RP. Serum levels of CGRP were positively associated with the neurosensory component. No associations with exposure were shown for these biomarkers. For Intercellular adhesion molecule 1 and monocyte chemoattractant protein 1, no associations were found with neither severity nor exposure. Levels of serum biomarkers associated with endothelial injury or dysfunction, inflammation, vasodilation, neuroprotection, and apoptosis were positively associated with the severity of hand-arm vibration injury.
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Biomarcadores , Síndrome da Vibração do Segmento Mão-Braço , Doença de Raynaud , Vibração , Humanos , Doença de Raynaud/sangue , Doença de Raynaud/diagnóstico , Biomarcadores/sangue , Masculino , Feminino , Pessoa de Meia-Idade , Vibração/efeitos adversos , Adulto , Síndrome da Vibração do Segmento Mão-Braço/sangue , Síndrome da Vibração do Segmento Mão-Braço/diagnóstico , Índice de Gravidade de Doença , Fator de von Willebrand/metabolismo , Fator de von Willebrand/análise , Peptídeo Relacionado com Gene de Calcitonina/sangue , IdosoRESUMO
Addressing the demand for high stability of beamline instruments at the SHINE facility, a high stability mirror regulating mechanism has been developed for mirror adjustments. Active mass damping was adopted to attenuate pitch angle vibrations of mirrors caused by structural vibrations. An internal absolute velocity feedback was used to reduce the negative impact of spillover effects and to improve performance. The experiment was conducted on a prototype structure of a mirror regulating mechanism, and results showed that the vibration RMS of the pitch angle was effectively attenuated from 47â nrad to 27â nrad above 1â Hz.
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Local vibration (LV) mainly stimulates primary afferents (Ia) and can induce a tonic vibration reflex (TVR) and an illusion of movement. This study aimed to evaluate the effect of these two phenomena on maximal voluntary isometric contraction (MVIC) capacity. LV (80 Hz) was applied to the wrist flexor muscles in two randomized experiments for 6 minutes. LV conditions were adjusted to promote either TVR (visual focus on the vibrated wrist) or ILLUSION (hand hidden, visual focus on electromyographic activity of the flexor carpi radialis muscle (FCR)). Mechanical and electromyographic (EMG) responses of the FCR and extensor carpi radialis muscles were recorded during MVIC in flexion and extension and during electrically evoked contractions at supramaximal intensity. Measurements were performed before (10 minutes and just before) and after (0 and 30 minutes) LV protocol. An increase in FCR EMG was observed during LV in the TVR condition (+340%) compared to the illusion condition (P=0.003). In contrast, the movement illusion was greater in the ILLUSION condition (assessed through subjective scales) (P=0.004). MVIC was reduced in flexion only after the TVR condition (≈ -7%, all P<0.034). Moreover, the decrease in force was correlated with the amount of TVR recorded on the FCR muscle (r=-0.64, P=0.005). Although potentiated doublets of each muscle did not evolve differently between conditions, a decrease was observed between the first and the last measure. In conclusion, when conducting research to assess maximal strength, it is necessary to have better control and reporting of the phenomena induced during LV.
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Copper indium selenide (CISe) is a prototype infrared semiconductor with low toxicity and unique optical characteristics. Its quantum dots (QDs) accommodate ample intrinsic point defects which may actively participate in their rather complex photophysical processes. We synthesize CISe QDs with similar sizes but with distinct highly stoichiometry-deviating atomic ratios. The synthesis condition employing Se-rich precursors yields the Cu-deficient CISe QDs with special photophysical properties. The photoluminescence exhibits monotonic red shift from 680 to 775 nm when the ratio of Cu's proportion to In's decreases. The luminescence is found to stem from the copper vacancy and antisite defects. The CISe QDs exhibit Raman activity at 5.6, 6.9, and 8.7 THz that is separately assigned to Cu-Se and In-Se optical phonon modes and surface mode.
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Vibration is an indispensable part of the tactile perception, which is encoded to oscillatory synaptic currents by receptors and transferred to neurons in the brain. The A2 and B1 neurons in the drosophila brain postsynaptic to the vibration receptors exhibit selective preferences for oscillatory synaptic currents with different frequencies, which is caused by the specific voltage-gated Na+ and K+ currents that both oppose the variations in membrane potential. To understand the peculiar role of the Na+ and K+ currents in shaping the filtering property of A2 and B1 neurons, we develop a linearized modeling framework that allows to systematically change the activation properties of these ionic channels. A data-driven conductance-based biophysical model is used to reproduce the frequency filtering of oscillatory synaptic inputs. Then, this data-driven model is linearized at the resting potential and its frequency response is calculated based on the transfer function, which is described by the magnitude-frequency curve. When we regulate the activation properties of the Na+ and K+ channels by changing the biophysical parameters, the dominant pole of the transfer function is found to be highly correlated with the fluctuation of the active current, which represents the strength of suppression of slow voltage variation. Meanwhile, the dominant pole also shapes the magnitude-frequency curve and further qualitatively determines the filtering property of the model. The transfer function provides a parsimonious description of how the biophysical parameters in Na+ and K+ channels change the inhibition of slow variations in membrane potential by Na+ and K+ currents, and further illustrates the relationship between the filtering properties and the activation properties of Na+ and K+ channels. This computational framework with the data-driven conductance-based biophysical model and its linearized model contributes to understanding the transmission and filtering of vibration stimulus in the tactile system.
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Ultrasonic scalpels (USs), as the preferred energy instruments, are facing a growing need to exhibit enhanced performance with the diversification of modern surgical challenges. Hence, we proposed an acoustic black hole ultrasonic scalpel (ABHUS) in longitudinal-bending coupled vibration for efficient surgical cutting. By incorporating an acoustic black hole profile, the local bending wave velocity is reduced and the amplitude is amplified cumulatively, thus creating a high-energy region near the blade tip to enhance the cutting performance of the ABHUS. The precise physical analysis model is established for systematic design of the ABHUS and quick estimation of its frequency characteristics. The vibration simulation and experiments demonstrate that compared with the conventional ultrasonic scalpel (CUS), the output amplitude of the ABHUS significantly increases, particularly a 425% increase in bending vibration displacement. The in-vitro cutting experiment confirms that ABHUS exhibits superior cutting performance. Our design presents vast possibilities and potential for the development of high-performance ultrasonic surgical instruments, serving as an innovative supplement with extraordinary significance for application of acoustic black holes.
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Polymer nanocomposites exhibiting remarkable mechanical properties are a focus of research for decades in structural applications. However, their practical application faces challenges due to poor interfacial load transfer, nanofiller dispersion, and processing limitations. These issues are critical in achieving stiff, strong, lightweight, and structurally integrated materials. Additionally, they often suffer from predetermined properties, which may not be effective under specific loading conditions. Addressing these challenges, the development of design strategies for mechano-responsive materials has advanced, enabling self-adaptive properties that respond to various mechanical stimuli. Drawing inspiration from natural systems, these approaches have been implemented in synthetic material systems, leveraging the design flexibility of nanocomposites as needed. Key focus areas include exploring mechanoradical reactions for dynamic mechano-responsiveness, as well as utilizing biomimetic mineralization and mechanical training for self-strengthening. This work also examines multistability, enabling on-demand deformation of materials and structures. Recent advancements in viscoelastic damping and nonreciprocal materials are discussed, highlighting their potential for directional energy absorption, transmission, and vibration control. Despite the need for significant improvements for real-world applications, mechano-responsive polymers and nanocomposites are expected to offer enormous opportunities not only in structural applications but also in other fields such as biomedical engineering, energy harvesting, and soft robotics.
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PURPOSE: The aim of this study was to examine the effect of vibration on motor unit (MU) firing behavior and physical performance of antagonist muscles in healthy young adult males. METHODS: Fourteen males (age = 24.3 ± 3.6 years) were included in this study. There were two conditions, one in which participants received 80 Hz vibration in the distal tendon of the hamstring for 30 s and the control condition (no vibration). High-density surface electromyography (HD-SEMG) signals and maximal voluntary contraction (MVC) of knee extensor muscles were evaluated before and after the respective conditions and recorded from the vastus lateralis muscle during submaximal ramp-up and sustained contractions at 30% MVC. Convolution blind source separation was used to decompose the HD-SEMG signals into individual MU firing behaviors. RESULTS: In total, 739 MUs were detected (control; 360 MUs and vibration; 379 MUs), and a total of 312 matched MUs were identified across both submaximal contraction conditions (control: 150 MUs; vibration: 162 MUs). Vibration significantly increased the discharge rate (p = 0.047) and decreased the recruitment threshold before and after intervention (p = 0.001) but not in the control condition. Furthermore, the recruitment threshold is a factor that influences discharge rate. Significant correlations were observed between the recruitment threshold and both the ∆ discharge rate and the ∆ recruitment threshold under the vibration condition (p < 0.001). CONCLUSION: Vibration increased in the discharge rate and decreased the recruitment threshold of the antagonist muscle. These findings suggested that vibration contributes to immediate changes in the neural control of antagonist muscles.
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PURPOSE: This study aimed to assess subclinical peripheral diabetic neuropathy (PDN) in adolescents with type 1 diabetes mellitus (T1DM). METHODS: Subjects included 53 T1DM patients (age (mean ± SE): 15.8 ± 0.54 years, disease duration: 6.0 ± 0.51 years and HbA1c: 7.9 ± 0.19%), and 37 healthy gender matched controls (age: 15.6 ± 0.52 years). PDN was assessed by vibration perception threshold (VPT) and by quantitative sensory testing (QST). In controls, 95% confidence intervals were calculated. RESULTS: Among patients, VPT prevalence of abnormality ranged from 60-73.4% on different sites. Higher VPT was found in patients on all examined sites (p < 0.01). In controls, VPT correlated with height (r = 0.48, p = 0.05). Regarding QST prevalence of abnormality, cold detection threshold (CDT) ranged 7.3-39.0%, cold pain threshold (CPT) ranged 22.22-29.63%, hot detection threshold (HDT) ranged 34.14-63.41%, and hot pain threshold (HPT) ranged 15.79-36.84%. In patients, CPT correlated with BMI (r = 0.42, p = 0.05) and diabetes duration, (r = 0.40, p = 0.05), HPT correlated with age (r = 0.36, p = 0.05) and height (r = 0.35, p = 0.05), while in controls with BMI (r = 0.51, p = 0.05). No correlation of VPT or QST with HbA1c was observed. CONCLUSION: Adolescents with T1DM in this study, although asymptomatic, showed a high prevalence of impaired indices of PDN, highlighting potential clinical implications of early identification of PDN.
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Background: Interventions using vibration stimulation have been recognized for their potential for increasing range of motion (ROM) without compromising muscle strength. Handheld vibration massagers can efficiently deliver vibration therapy to the shoulder joint and may be a potential treatment. Purpose: To evaluate the effects of vibration massage using a handheld device on the soft tissues of the posterior shoulder joint, particularly on internal rotation (IR) passive ROM and external rotation (ER) muscle strength. Study Design: Crossover study design. Methods: A crossover study with a 5-min vibration massage and passive control condition was conducted in healthy male volunteers (mean age 20.5 ± 1.7 years). Vibration massage was applied to the posterior shoulder soft tissues of the dominant arm, with no intervention under control conditions. IR-ROM (vertebral level and in abduction) and strength of the external rotators (isometric and isokinetic) were measured before and immediately after the intervention. Vertebral levels were calculated as a ratio of lengths (ratio decreases with increased mobility). IR-ROM in abduction, the angle was measured. Statistical analysis was performed with two-way repeated measures ANOVA and paired t-test (Bonferroni correction). Results: Vibration application decreased (improved) vertebral level IR ROM by -4.1% (p < 0.01, d = 0.445) and increased abduction position IR ROM by 11.4° (p < 0.01, d = 0.694). These changes exceeded the 95% confidence interval for the minimum detectable change. By contrast, the control condition produced no changes. IR-ROM (vertebral level and abduction) immediately after the intervention showed significant differences between the control and vibration conditions (p = 0.036, d = 0.273; p = 0.048, d = 0.483, respectively). Muscle strength did not show any interaction, time, or between-condition effects. Conclusions: A massage using a handheld vibration massager applied to the posterior shoulder soft tissues increased IR-ROM without negatively affecting muscle strength, suggesting its potential use as a means of warming up. Level of Evidence: Level 3.
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The acoustic black hole (ABH) structure exhibits remarkable energy focalization above a given cut-on frequency, offering potential for broadband vibration suppression in structures. However, its energy focusing properties diminish significantly below this cut-on frequency. Therefore, it is crucial to enhance the vibration attenuation capabilities of ABH structures within the low frequency range. This study presents a numerical investigation into the impact of thin-walled structures with embedded ABHs and distributed dynamic vibration absorbers (DVAs) on low frequency broadband vibration reduction. Initially, the focusing characteristics of the ABH thin-walled structure is analyzed, aiding in the attached position of DVAs. Furthermore, the influence of the design parameters and attached position of DVA on the broadband damping effect of the structure is explored. The findings indicate that DVAs designed for low frequencies can achieve significant vibration attenuation across the entire frequency spectrum, including low frequencies, when installed at specific focusing positions. When compared to the position with the maximum vibration response, while the attenuation of the low frequency common amplitude value is slightly reduced, greater vibration attenuation across the entire frequency band is achieved. This research offers valuable insights into optimizing the integration of DVAs with ABHs in thin-walled structures for enhanced broadband vibration attenuation.
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This paper presents a novel adaptation of the conventional approximate Bayesian computation sequential Monte Carlo (ABC-SMC) sampling algorithm for parameter estimation in the presence of uncertainties, coined combinatorial ABC-SMC. Inference of this type is used in situations where there does not exist a closed form of the associated likelihood function, which is replaced by a simulating model capable of producing artificial data. In the literature, conventional ABC-SMC is utilised to perform inference on continuous parameters. The novel scheme presented here has been developed to perform inference on parameters that are high-dimensional binary, rather than continuous. By altering the form of the proposal distribution from which to sample candidates in subsequent iterations (referred to as waves), high-dimensional binary variables may be targeted and inferred by the scheme. The efficacy of the proposed scheme is demonstrated through application to vibration data obtained in a structural dynamics experiment on a fibre-optic sensor simulated as a finite plate with uncertain boundary conditions at its edges. Results indicate that the method provides sound inference on the plate boundary conditions, which is validated through subsequent application of the method to multiple vibration datasets. Comparisons between appropriate forms of the metric function used in the scheme are also developed to highlight the effect of this element in the schemes convergence.
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Phantom limb pain, a common challenge for amputees, lacks effective treatment options. Vibration therapy is a promising non-pharmacologic intervention for reducing pain intensity, but its efficacy in alleviating phantom limb pain requires further investigation. This study focused on developing prosthesis liners with integrated vibration motors to administer vibration therapy for phantom limb pain. The prototypes developed for this study addressed previous issues with wiring the electronic components. Two transfemoral amputees participated in a four-week at-home trial, during which they used the vibration liner and rated their initial and final pain intensity on a numeric rating scale each time they had phantom pain. Semi-structured interviews were conducted to gather feedback following the at-home trial. Both participants described relaxing and soothing sensations in their residual limb and phantom limb while using vibration therapy. One participant reported a relaxation of his phantom limb sensations, while both participants noted a decrease in the intensity of their phantom limb pain. Participants said the vibration liners were comfortable but suggested that the vibration could be stronger and that aligning the contacts could be easier. The results of this study highlight the potential effectiveness of using vibration therapy to reduce the intensity of phantom limb pain and suggest a vibration liner may be a feasible mode of administering the therapy. Future research should address optimizing the performance of the vibration liners to maximize their therapeutic benefits.
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Amputados , Membro Fantasma , Robótica , Vibração , Humanos , Membro Fantasma/terapia , Vibração/uso terapêutico , Amputados/reabilitação , Masculino , Robótica/métodos , Robótica/instrumentação , Pessoa de Meia-Idade , Membros Artificiais , Adulto , FemininoRESUMO
Background/Objectives: Vibration therapy approaches are an effective and safe treatment option for musculoskeletal disorders. This study examines the effects of vibration therapy using a percussion massage gun (PMG) on joint position sense, range of motion, pain, functionality, and kinesiophobia in individuals with cervical disc herniation (CDH). Methods: This single-blind randomized controlled trial involved 44 CDH patients divided into a Vibration Group (VG) and a Conventional Group (CG). The CG underwent a standard physiotherapy treatment heat application, Transcutaneous Electrical Nerve Stimulation (TENS), and exercises for range of motion and strengthening. VG received conventional therapy augmented with vibration therapy (VT) via a PMG. Joint position sense (JPS) using the Laser Pointer Assisted Angle Repetition Test; pain intensity with the Visual Analog Scale, kinesiophobia with the Tampa Scale for Kinesiophobia, and cervical dysfunction with the Neck Disability Index were assessed. Results: Both groups showed statistically significant improvements in pain, kinesiophobia, disability, and proprioception after treatment (p < 0.05). When comparing the difference values between groups, the VG was found to be more effective than the CG in the parameters of VAS activity (p = 0.013). The CG had more improvement in JPS neck left rotation than the VG (p = 0.000). Conclusions: VT, when combined with conventional physiotherapy, is effective in improving pain, proprioception, and functionality in individuals with CDH. These findings support the inclusion of VT as a beneficial adjunct therapy. Further research with larger sample sizes and longer follow-ups is recommended to validate these results and explore the long-term effects of VT on CDH.
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This study focuses on the analysis of the displacements generated in 3D-printed acoustic guitar tops. Specifically, the influence of 3D printing direction parameters on the vibrational behavior of a guitar top designed for polylactic acid (PLA) by analyzing five points of the top surface at a reduced scale. For this purpose, finite element tests and laboratory experiments have been carried out to support the study. After analyzing the results, it can be affirmed that the vibrational response in reduced-scale top plates can be modified and controlled by varying the printing direction angle in additive manufacturing, providing relevant information about the displacement in the vibrational response of PLA acoustic guitars. Furthermore, this work shows that the behavior of a specific acoustic guitar design can be characterized according to a specific need.
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Vibration-fatigue failure occurs when a structure is dynamically excited within its natural frequency range. Unlike metals, which have constant fatigue parameters, polymers can exhibit frequency-dependent fatigue parameters, significantly affecting the vibration resilience of 3D-printed polymer structures. This manuscript presents a study utilizing a novel vibration-fatigue testing methodology to characterize the frequency dependence of polymer material fatigue parameters under constant temperature conditions. In this investigation, 3D-printed PLA samples with frequency-tunable geometry were experimentally tested on an electro-dynamical shaker with a random vibration profile. Using the validated numerical models, the estimation of vibration-fatigue life was obtained and compared to the experimental results. Performing the numerical minimization of estimated and actual fatigue lives, the frequency-dependent fatigue parameters were assessed. In particular, the results indicate that the tested samples exhibit varying fatigue parameters within the loading frequency range of 250-750 Hz. Specifically, as the loading frequency increases, the fatigue exponent increases and fatigue strength decreases. These findings confirm the frequency dependence of fatigue parameters for 3D-printed polymer structures, underscoring the necessity of experimental characterization to reliably estimate the vibration-fatigue life of 3D-printed polymer structures. The utilization of the introduced approach therefore enhances the vibration resilience of the 3D-printed polymer mechanical component.
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The study focuses on harnessing recycled materials to create sustainable and efficient composites, addressing both environmental issues related to waste management and industrial requirements for materials with improved vibration damping properties. The research involves the analysis of the physico-mechanical properties of the obtained composites and the evaluation of their performance in practical applications. Composite materials were tested in terms of their tensile strength and vibration damping capabilities, considering stress-strain diagrams, vibration amplitudes, frequency response functions (FRFs) and vibration modes. The research results have shown that by adding PVC and FA to the rubber-based matrix composition, the stiffness decreases and elasticity increases. The use of FA in the structure of composite materials causes an increase in the vibration damping possibilities due to the fact that it contributes to the chemical properties of the analyzed composite materials. Additionally, the use of PVC results in increased material elasticity, as evidenced by the higher damping factor compared to materials containing only rubber. Simultaneously, the addition of FA and PVC in specific proportions (60 phr) can lead to a decrease in stiffness and a greater increase in the damping factor. The incorporation of PVC and fly ash (FA) particles into rubber-based matrix composites reduces their stiffness and increases their elasticity. These effects are due to the fact that FA particles behave as extensions of chemical bonds during traction, which contributes to the increase in yield elongation. In addition, the use of flexible PVC increases the elasticity of the material, which is evidenced by the increase in the damping factor.