Positive Solvability for Conjugate Fractional Differential Inclusion of (k,n-k) Type without Continuity and Compactness

The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the (k,n−k) conjugate fractional differential inclusion type with λ>0,1≤k≤n−1.

A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions

This article is dedicated to the existence results of solutions for boundary value problems of inclusion type. We suggest the infinite countable system to fractional differential inclusions written by D α ABC ν i t ∈ Y i t , ν i t i = 1 ∞ . The mappings y i t , ν i t i = 1 ∞ are proposed to be Lipschitz multivalued mappings. The results are explored according to boundary condition σ ν i 0 = γ ν i ρ , σ , γ ∈ ℝ . This type of condition is the generalization of periodic, almost, and antiperiodic types.

Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory

This paper deals with an optimization problem for a nonlinear integro-differential system that describes the unsteady plane motion of an incompressible viscoelastic fluid of Jeffreys–Oldroyd type within a fixed bounded region subject to the no-slip boundary condition. Control parameters are included in the initial condition. The objective of control is to match the velocity field at the final time with a prescribed target field. The control model under consideration is interpreted as a continuous evolution system in an infinite-dimensional Hilbert space. The existence of at least one optimal control is proved under inclusion-type constraints for admissible controls.

Analysis on the Dynamic Wave Attenuation Properties of Metaconcrete Considering a Quasi-Random Arrangement of Inclusions

The mitigation properties of metaconcrete cast with two types of resonant inclusions are assessed through wave transmission tests. Three cylindric metaconcrete specimens of regular size (20 cm height, 10 cm diameter), containing an equal number of different type of inclusions disposed in a semi-regular lattice, are tested in the longitudinal direction within the sonic range of frequencies. Inclusions, bi-material spheres consisting of a heavy core coated with a soft material, are characterized by a resonant behavior, evaluated numerically with a finite element modal analysis of a unit metaconcrete cell. Each metaconcrete specimen contains six layers consisting of six engineered aggregates of different type. Inclusions are disposed by rotating each layer with respect to the adjacent ones, as so as to create a pseudo-random arrangement. Specimens are excited by a sinusoidal signal of linearly growing frequency, sweeping a range centered at the translational eigenfrequency of the resonant inclusion. A standard plain concrete specimen is used as reference to define a transmissibility coefficient, that facilitates the quantification of the attenuation properties. With respect to plain concrete, all metaconcrete specimens show a marked (up to 80–90%) attenuation of the transmitted signal in proximity of the numerically estimated eigenfrequency of the inclusion. The intensity of the attenuation is weakly dependent on the type of the inclusion, while the frequency where the attenuation is observed depends markedly on the inclusion type. As a very positive quality in the view of practical applications, experimental results confirm that the attenuation effectiveness of metaconcrete is not related to the ordered microstructural arrangement.

Оценка реальной чувствительности приемочного ультразвукового контроля рельсов

In this article, the analysis of the acoustic path during the ultrasonic pulse echo testing of the rail head in production is carried out. The influence of the parameters of the applied piezoelectric transducers on the distribution of sensitivity for the sounding scheme used in the existing installations is estimated and the real sensitivity of detecting defects of the «non-metallic inclusion» type is estimated.

Experimental Validation of the Attenuation Properties in the Sonic Range of Metaconcrete Containing Two Types of Resonant Inclusions

Background Metaconcrete is a new concept of concrete, showing marked attenuation properties under impact and blast loading, where traditional aggregates are partially replaced by resonant bi-material inclusions. In a departure from conventional mechanical metamaterials, the inclusions are dispersed randomly as cast in the material. The behavior of metaconcrete at supersonic frequencies has been investigated theoretically and numerically and confirmed experimentally. Objective The feasibility of metaconcrete to achieve wave attenuation at low frequencies demands further experimental validation. The present study is directed at characterizing dynamically, in the range of the low sonic frequencies, the—possibly synergistic—effect of combinations of different types of inclusions on the attenuation properties of metaconcrete. Methods Dynamic tests are conducted on cylindrical metaconcrete specimens cast with two types of spherical inclusions, made of a steel core and a polymeric coating. The two inclusions differ in terms of size and coating material: type 1 inclusions are 22 mm diameter with 1.35 mm PDMS coating; type 2 inclusions are 24 mm diameter with 2 mm layer natural rubber coating. Linear frequency sweeps in the low sonic range (< 10 kHz), tuned to numerically estimated inclusion eigenfrequencies, are applied to the specimens through a mechanical actuator. The transmitted waves are recorded by transducers and Fast-Fourier transformed (FFT) to bring the attenuation spectrum of the material into full display. Results Amplitude reductions of transmitted signals are markedly visible for any metaconcrete specimens in the range of the inclusion resonant frequencies, namely, 3,400-3,500 Hz for the PDMS coating inclusions and near 3,200 Hz for the natural rubber coating inclusions. Specimens with mixed inclusions provide a rather uniform attenuation in a limited range of frequencies, independently of the inclusion density, while specimens with a single inclusion type are effective over larger frequency ranges. With respect to conventional concrete, metaconcrete reduces up to 90% the amplitude of the transmitted signal within the attenuation bands. Conclusions Relative to conventional concrete, metaconcrete strongly attenuates waves over frequency bands determined by the resonant frequencies of the inclusions. The present dynamical tests conducted in the sonic range of frequencies quantify the attenuation properties of the metaconcrete cast with two types inclusions, providing location, range and intensity of the attenuation bands, which are dependent on the physical-geometric features of the inclusions.

Hip preservation

Classical indications for hip preserving surgery are: femoro-acetabular impingement (FAI) (intra- and extra-articular), hip dysplasia, slipped capital femoral epiphysis, residual deformities after Perthes disease, avascular necrosis of the femoral head. Pre-operative evaluation of the pathomorphology is crucial for surgical planning including radiographs as the basic modality and magnetic resonance imaging (MRI) and/or computed tomography (CT) to evaluate further intra-articular lesions and osseous deformities. Two main mechanisms of intra-articular impingement have been described: (1) Inclusion type FAI (‘cam type’). (2) Impaction type FAI (‘pincer type’). Either arthroscopic or open treatment can be performed depending on the severity of deformity. Slipped capital femoral epiphysis often results in a cam-like deformity of the hip. In acute cases a subcapital re-alignment (modified Dunn procedure) of the femoral epiphysis is an effective therapy. Perthes disease can lead to complex femoro-acetabular deformity which predisposes to impingement with/without joint incongruency and requires a comprehensive diagnostic workup for surgical planning. Developmental dysplasia of the hip results in a static overload of the acetabular rim and early osteoarthritis. Surgical correction by means of periacetabular osteotomy offers good long-term results. Cite this article: EFORT Open Rev 2020;5:630-640. DOI: 10.1302/2058-5241.5.190074

A dynamic thermo-mechanical actuator system with contact and Barber's heat exchange boundary conditions

This work, motivated by the rapid developments in Micro-Electro-Mechanical Systems (MEMS) structures, especially actuators and grippers, analyses the dynamics of a thermo-mechanical system consisting of a horizontal beam joined at one end to a vertical rod. As a result of thermal expansion or vibration of the rod, the other end may come into contact with another part of the MEMS device and that closes an electrical circuit, which is the actuating or switching function of such a beam–rod system. The interaction between the rod's contacting end and the supporting device is described by a normal compliance contact law for the displacements and by an inclusion-type Barber's heat exchange condition for the temperature. The heat-exchange coefficient is a multi-function taking into account the air resistance in the gap when there is no contact and the contact pressure when contact occurs. The model consists of a nonlinear variational inclusion for the temperature coupled with a nonlinear variational equation for the displacements. The existence of a weak solution to the problem is proved by using the Galerkin method, a regularization of Barber's condition with the Yosida approximation of a maximal monotone operator, and a priori estimates.