Double-Versus Triple-Potential Well Energy Harvesters: Dynamics and Power Output.

The basic types of multi-stable energy harvesters are bistable energy harvesting systems (BEH) and tristable energy harvesting systems (TEH). The present investigations focus on the analysis of BEH and TEH systems, where the corresponding depth of the potential well and the width of their characteristics are the same. The efficiency of energy harvesting for TEH and BEH systems assuming similar potential parameters is provided. Providing such parameters allows for reliable formulation of conclusions about the efficiency in both types of systems. These energy harvesting systems are based on permanent magnets and a cantilever beam designed to obtain energy from vibrations. Starting from the bond graphs, we derived the nonlinear equations of motion. Then, we followed the bifurcations along the increasing frequency for both configurations. To identify the character of particular solutions, we estimated their corresponding phase portraits, Poincare sections, and Lyapunov exponents. The selected solutions are associated with their voltage output. The results in this numerical study clearly show that the bistable potential is more efficient for energy harvesting provided the corresponding excitation amplitude is large enough. However, the tristable potential could work better in the limits of low-level and low-frequency excitations.

Energy Harvesting System Whose Potential Is Mapped with the Modified Fibonacci Function.

In this paper, we compare three energy harvesting systems in which we introduce additional bumpers whose mathematical model is mapped with a non-linear characteristic based on the hyperbolic sine Fibonacci function. For the analysis, we construct non-linear two-well, three-well and four-well systems with a cantilever beam and permanent magnets. In order to compare the effectiveness of the systems, we assume comparable distances between local minima of external wells and the maximum heights of potential barriers. Based on the derived dimensionless models of the systems, we perform simulations of non-linear dynamics in a wide spectrum of frequencies to search for chaotic and periodic motion zones of the systems. We present the issue of the occurrence of transient chaos in the analyzed systems. In the second part of this work, we determine and compare the effectiveness of the tested structures depending on the characteristics of the bumpers and an external excitation whose dynamics are described by the harmonic function, and find the best solutions from the point view of energy harvesting. The most effective impact of the use of bumpers can be observed when dealing with systems described by potential with deep external wells. In addition, the use of the Fibonacci hyperbolic sine is a simple and effective numerical tool for mapping non-linear properties of such motion limiters in energy harvesting systems.

Nonlinear Dynamics of a Star-Shaped Structure and Variable Configuration of Elastic Elements for Energy Harvesting Applications.

The subject of the model research contained in this paper is a new design solution of the energy harvesting system with a star-shaped structure of elastic elements and variable configuration. Numerical experiments focused mainly on the assessment of the configuration of elastic elements in the context of energy harvesting efficiency. The results of computer simulations were limited to zero initial conditions as it is the natural position of the static equilibrium. The article compares the energy efficiency for the selected range of the dimensionless excitation frequency. For this purpose, four cases of elastic element configurations were compared. The results are visualized based on the diagram of RMS voltage induced on piezoelectric electrodes, bifurcation diagrams, Lyapunov exponents, and Poincaré maps, showing the impact of individual solutions on the efficiency of energy harvesting. The results of the simulations show that the harvester's efficiency ranges from 4 V to 20 V depending on the configuration and the frequency range of the excitation, but the design allows for a smooth adjustment to the given conditions.

On Theoretical and Numerical Aspects of Bifurcations and Hysteresis Effects in Kinetic Energy Harvesters.

The piezoelectric energy-harvesting system with double-well characteristics and hysteresis in the restoring force is studied. The proposed system consists of a bistable oscillator based on a cantilever beam structure. The elastic force potential is modified by magnets. The hysteresis is an additional effect of the composite beam considered in this system, and it effects the modal solution with specific mass distribution. Consequently, the modal response is a compromise between two overlapping, competing shapes. The simulation results show evolution in the single potential well solution, and bifurcations into double-well solutions with the hysteretic effect. The maximal Lyapunov exponent indicated the appearance of chaotic solutions. Inclusion of the shape branch overlap parameter reduces the distance between the external potential barriers and leads to a large-amplitude solution and simultaneously higher voltage output with smaller excitation force. The overlap parameter works in the other direction: the larger the overlap value, the smaller the voltage output. Presumably, the successful jump though the potential barrier is accompanied by an additional switch between the corresponding shapes.

Energy Harvesting in a System with a Two-Stage Flexible Cantilever Beam.

The subject of the research contained in this paper is a new design solution for an energy harvesting system resulting from the combination of a quasi-zero-stiffness energy harvester and a two-stage flexible cantilever beam. Numerical tests were divided into two main parts-analysis of the dynamics of the system due to periodic, quasiperiodic, and chaotic solutions and the efficiency of energy generation. The results of numerical simulations were limited to zero initial conditions as they are the natural position of the static equilibrium. The article compares the energy efficiency for the selected range of the dimensionless excitation frequency. For this purpose, three cases of piezoelectric mounting were analyzed-only on the first stage of the beam, on the second and both stages. The analysis has been carried out with the use of diagrams showing difference of the effective values of the voltage induced on the piezoelectric electrodes. The results indicate that for effective energy harvesting, it is advisable to attach piezoelectric energy transducers to each step of the beam despite possible asynchronous vibrations.

Association between Anatomical Features of Petrotympanic Fissure and Tinnitus in Patients with Temporomandibular Joint Disorder Using CBCT Imaging: An Exploratory Study.

Mandible displacement is known to correlate with otological conditions such as pain in the ear canal, hearing loss, or tinnitus. The present work aimed to determine the association between the displacement of the condyle in a temporomandibular joint, the structure and position of the petrotympanic fissure (PTF), and comorbid tinnitus in patients affected by temporomandibular joint and muscle disorder (TMD). We enrolled 331 subjects with TMD (268 women and 63 men). The average age of women was 40.8 ± 16.8 years (range 13-88), whereas the average age of the examined men was 38 ± 14 years (range 13-74). We performed imaging studies of the facial part of the skull in the sagittal plane using a volumetric imaging method and a large imaging field (FOV) of 17 cm × 23 cm. The habitual position of the mandible was determined and used as a reference. Based on the imaging results, we developed a classification for the topography and the structure of the petrotympanic fissure. Thirty-three TMD patients (about 10% of the sample) reported having tinnitus. These patients had PTF configurations characterized by a rear (36.59%) or intracranial-cranial (63.41%) condylar displacement of the temporomandibular joint. Our findings imply that the TMJ- and tinnitus-positive group of patients possibly represents a distinct phenotype of tinnitus. We concluded that for such patients, the therapeutic approach for tinnitus should include TMD treatment.

Identification of Biomechanical Properties of Temporomandibular Discs.

Material: Experimental and model tests were conducted on ten fresh porcine temporomandibular joint discs. The average thickness of disc tissue was, accordingly, 2.77 mm for the anterior zone, 3.98 mm for the posterior, and 1.54 mm for the intermediate. The selection of research material in the form of porcine discs was due to the similarity to human discs. Methods: Discs were loaded in cycles, a temporary course with the amplitude 3 N and frequency 0.07 Hz, and growth in the load was 1 N/s. The selection of load frequency was due to real conditions of temporomandibular joint functioning during mastication. The necessary experimental research was conducted on a testing machine with a measurement range of 2.5 kN. Results: The obtained numeric calculation results indicate that the number of load cycles has a decisive impact on the limitation of energy dispersion capacity through disc tissue. This phenomenon was observed in all the studies on the disc areas. Along with the growth in load cycles, discs are stiffened, and the most significant stiffness was observed in the intermediate area. Conclusions: Based on the conducted research, it should be concluded that excessive load affecting temporomandibular joints caused by the act of mastication and occlusal forces generated during parafunction and in people with defined long-term bruxism has crucial importance on biomechanical disc properties and hence the course of temporomandibular joint conditions.

Evaluation of articular disc loading in the temporomandibular joints after prosthetic and pharmacological treatment in model studies.

BACKGROUND: Temporomandibular joint dysfunction is often related to excessive load in the stomatognathic system. OBJECTIVES: The objective of the model tests, using numeric calculations, was to assess the articular disc loads in the temporomandibular joints after prosthetic and pharmacological treatment of functional disorders of the masticatory organ. MATERIAL AND METHODS: The study involved 10 patients, aged 21-48 years, of both sexes, randomly selected from a group of 120 patients treated with relaxation occlusal splints (60 patients, group I) and intramuscular injection of botulinum toxin type A (60 patients, group II), suffering from temporomandibular joint dysfunction with the dominant muscle component. In all subjects, a specialized functional examination was carried out. Treatment groups: occlusal splint therapy (group I) and intramuscular injection of botulinum toxin type A (group II). An assessment of the loads of 4 disc zones of the temporomandibular joints was carried out based on the results of clinical studies (phase I of the study), and numeric model tests (phase II). In the representatives of the study groups (5 patients in each group), measurements of occlusal forces and an evaluation of tension of the masseter and temporalis muscle were performed. RESULTS: The results of the average load values for all evaluated zones of the right and left articular disc differ in a statistically significant way in favor of group II, with the exception of the external mid part of the discs. In the case of the anterior of the right disc, the load was lower in patients belonging to group I than in those obtained in group II. CONCLUSIONS: Botulinum toxin type A significantly reduces the loads within the temporomandibular joints, generated by masseter muscle hypertonia.

Model identification of stomatognathic muscle system activity during mastication.

The present study aimed to determine the numeric projection of the function of the mandible and muscle system during mastication. An experimental study was conducted on a healthy 47 year-old subject. On clinical examination no functional disorders were observed. To evaluate the activity of mastication during muscle functioning, bread cubes and hazelnuts were selected (2 cm2 and 1.2/1.3 cm in diameter, respectively) for condyloid processing. An assessment of the activity of mastication during muscle functioning was determined on the basis of numeric calculations conducted with a novel software programme, Kinematics 3D, designed specifically for this study. The efficacy of the model was verified by ensuring the experimentally recorded trajectories were concordant with those calculated numerically. Experimental measurements of the characteristic points of the mandible trajectory were recorded six times. Using the configuration coordinates that were calculated, the dominant componential harmonics of the amplitude-frequency spectrum were identified. The average value of the dominant frequency during mastication of the bread cubes was ~1.16±0.06 Hz, whereas in the case of the hazelnut, this value was nearly two-fold higher at 1.84±0.07 Hz. The most asymmetrical action during mastication was demonstrated to be carried out by the lateral pterygoid muscles, provided that their functioning was not influenced by food consistency. The consistency of the food products had a decisive impact on the frequency of mastication and the number of cycles necessary to grind the food. Model tests on the function of the masticatory organ serve as effective tools since they provide qualitative and quantitative novel information on the functioning of the human masticatory organ.

Identification of mastication organ muscle forces in the biocybernetic perspective.

UNLABELLED: PURPOSE OF THE PAPER: This paper is an attempt to mathematically describe the mastication organ muscle functioning, taking into consideration the impact of the central nervous system. MATERIAL: To conduct model tests, three types of craniums were prepared: short, normal, and long. The necessary numeric data, required to prepare the final calculation models of different craniofacial types, were used to identify muscle and occlusion forces generated by muscles in the area of incisors and molars. The mandible in model tests was treated as a nondeformable stiff form. METHODS: The formal basis for the formulated research problem was reached using the laws and principles of mechanics and control theory. The proposed method treats muscles as "black boxes," whose properties automatically adapt to the nature of the occlusion load. The identified values of occlusion forces referred to measurements made in clinical conditions. RESULTS: The conducted verification demonstrated a very good consistency of model and clinical tests' results. The proposed method is an alternative approach to the so far applied methods of muscle force identification. Identification of muscle forces without taking into account the impact of the nervous system does not fully reflect the conditions of mastication organ muscle functioning.

Assessment of the TMJ Dysfunction Using the Computerized Facebow Analysis of Selected Parameters.

THE PURPOSE OF THE PAPER: Qualitative and quantitative analysis of selected parameters of mandible movements, electronically registered in patients with temporomandibular joint dysfunction and healthy ones. MATERIAL: Function test of the mandible movements was conducted in 175 patients. Gender distribution was 143 women and 32 men, aged 9 to 84. METHODS: The studied population, after accurate clinical examination, was divided into age groups with the range of five years. All the patients had Zebris JMA computerized facebow examination done, according to the generally accepted principles and procedures. RESULTS: Mean values of mouth opening calculated to 45.6 mm in healthy group and 37.6 mm in TMJ dysfunction group. Mean length of condylar path amounted to 39 ± 7% of the maximum value of mouth opening in the group of healthy people, 44 ± 11% in the case of muscle-based disorders, and 35 ± 11% with joint-based. The mean value of the condylar path inclination oscillated in the range of 25° to 45°. CONCLUSIONS: The ratio of length of the condylar path to the size of mouth opening may be a significant value characterising the type and degree of intensification of the TMJ dysfunctions.