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In this paper, an analytical solution for vibration in cantilevered functionally graded (FG) sandwich beams based on the refined zigzag theory (RZT) is presented. In RZT, the zigzag term in the kinematics of axial displacements is considered by introducing a zigzag function that is related to the shear modulus of each layer in the sandwich beam. The face layers with FGM are modeled by infinite sublayers, and the RZT formulations can be applied to the FG sandwich beam. The natural frequency equations, mode shapes, orthogonal relations, and frequency responses are presented in exact forms. In the modal analysis, the differences of the first two natural frequencies between RZT and FEM are less than 2.81%. For the third vibration mode, the shear deformations are more severe than for the first two modes and the differences of natural frequencies between RZT and FEM are slightly increased to 6.95%. For the mode shape and frequency response comparisons, the RZT results also agree well with the FEM results. It is concluded that the RZT is quite applicable to calculate the natural frequencies, mode shapes, and frequency responses of on FG sandwich beams.

In this paper, a press-button-type piezoelectric energy harvester (PEH) is presented. The proposed device is composed of a piezoelectric bender, four magnets, a button, and a reverted spring. The proposed structure is triggered by an impact driven by magnetic force, so this novel trigger mechanism enhances its optimal power output. Based on the piezoelectricity, beam theory, and the vibration theory, a complete numerical model was developed to simulate and predict the output voltage. A prototype was fabricated for verification, and the characterization of the energy harvester was measured. The harvested power and energy by a single impact was recorded as ${\text{20 mW}}$ and ${\text{190}\,\mu \text{J}}$ , respectively, at an optimum resistive load of ${\text{30 k}\Omega }$ . The measured data agreed with the results of numerical model. Finally, the piezoelectric energy charger extractor (PECE) was used to store the harvested energy. The energy stored in a capacitor of ${\text{1}\,\mu \text{F}}$ was ${\text{42.1}}\,{\mu \text{J}}$ .

In this paper, the assessments of structural health monitoring (SHM) for metallic structures are presented. Tests were conducted on three specimens for fatigue crack testing and damage inde...

In this study, an impact-driven piezoelectric energy harvester (PEH) in magnetic field is presented. The PEH consists of a piezoelectric cantilever beam and plural magnets. At its initial status, the beam tip magnet is attracted by a second magnet. The second magnet is moved away by hand and then the beam tip magnet moves to a third magnet by the guidance of the magnetic fields. The impact occurs when the beam motion is stopped by the third magnet. The impact between magnets produces an impact energy and causes a transient beam vibration. The electric energy is generated by the piezoelectric effect. Based on the energy principle, a multi-DOF (multi-degree of freedom) mathematical model was developed to calculate the displacements, velocities, and voltage outputs of the PEH. A prototype of the PEH was fabricated. The voltages outputs of the beam were monitored by an oscilloscope. The maximum generated energy was about 0.4045 mJ for a single impact. A comparison between numerical and experimental results was presented in detail. It showed that the predictions based on the model agree with the experimental measurements. The PEH was connected to a diode bridge rectifier and a storage capacitor. The charges generated by the piezoelectric beam were stored in the capacitor by ten impacts. The experiments showed that the energy stored in the capacitor can light up the LED.

This paper presents an analytical approach to determine the singular stress fields near sharp corners in anisotropic notched plate subjected to bending. The first-order shear deformation plate theory (FSDPT) is used and the material anisotropy is modeled by the Stroh formalism. Based on the Mellin transform method, the stress singularity orders as well as the stress intensities are determined analytically. The results presented in this paper give us the singular behaviors for various plate angle α, material orientation angles ϕ and the anisotropic parameters e. These new findings are helpful in reducing or even eliminating the singularities near the sharp corner.

In this paper, the bending singularity at the apex of V-notch in an anisotropic thick plate is investigated. The Stroh-like formalism is used to model the anisotropy of the material. Based on the Ressiner-Mindlin plate theory and the eigenfunction expansion method, the characteristic equation for bending singularity order is derived and the order can be determined numerically. The numerical results show that the singularity orders strongly depend on the plate angle a. In addition, the singularity orders also depend on the principal orientation of the anisotropic material. The singularity orders for the case of are stronger than for that of. In the case of, to reduce the anisotropy is helpful to release the singularity at the notch tip. For the other case of, it is preferable to increase the anisotropy to reduce the singularity. The disappearance conditions of the bending singularity can be found based on the numerical results.

In this paper, the wave propagation in phononic crystal composed of auxetic star-shaped honeycomb matrix with negative Poisson&rsquo, s ratio is presented. Two types of inclusions with circular and rectangular cross sections are considered and the band structures of the phononic crystals are also obtained by the finite element method. The band structure of the phononic crystal is affected significantly by the auxeticity of the star-shaped honeycomb. Some other interesting findings are also presented, such as the negative refraction and the self-collimation. The present study demonstrates the potential applications of the star-shaped honeycomb in phononic crystals, such as vibration isolation and the elastic waveguide.

This paper aims at the stress singularities in a sectorial plate based on Reissner–Mindlin plate theory. The Mellin transform is applied to solve the governing equations of the plate. Both the bending stress singularities due to concentrated moments at boundaries and transverse shear stress singularities due to concentrated transverse shear forces at boundaries are investigated. The application of inverse Mellin transform gives the exact forms of singular stress fields near the corner, including the stress singularity orders and the generalized stress intensity factors. For various plate angles and loading conditions, the singular stress parameters are computed by finite element models and the results are compared to the analytical solutions. The comparisons reveal that the stresses obtained by the analytical procedure proposed in this paper are correct.

In this paper, the mode II strain energy release rates (SERR) of a cracked sandwich beam (CSB) subjected to a three-point loading are investigated. Due to the stiff face sheets and soft core, the displacements in the sandwich beam have the zigzag distribution through the thickness. A literature survey reveals that SERR of the CSB can be determined by the first-order shear deformation theory (FSDT). However, the accuracy of the results in FSDT is limited due to the lack of zigzag phenomenon. In this paper, we re-solve the CSB based on the refined zigzag theory (RZT), in which the kinematics of the displacements are assumed to have zigzag characteristic. The kinematic variables of the displacements can be determined from solving the governing equations of RZT in conjunction with the boundary conditions and continuity conditions of the CSB, and then SERR can be calculated by the compliance method. We show that for sandwich beams with slender aspect ratio (large L/h) or with thin face sheet (large rh), the FSDT can provide a satisfactory results due to the insignificant zigzag displacements. Otherwise for small L/h or small rh, the RZT should be used to take the significant zigzag displacements into consideration. For a given crack length, the FSDT give a result that the SERR is independent of the beam length. By using the RZT, it is found that the SERR depends on the beam length for a given crack length, especially for long crack length that a/L is ranged from 0.4 to 0.5. The material properties of the core materials on SERR are also investigated. By comparing with the finite element method (FEM), the deflections, compliances and SERRs in the CSB obtained by RZT are more accurate than those by FSDT. It is found that, for the cases of the core with very small shear modulus, the RZT gives correct results that are validated by FEM. For such cases, the FSDT gives incorrect calculations for SERR due to the lack of the zigzag model. The results arose in this study show the superior advantages of the use of the RZT in the SERR calculation of CSB specimen.

In this paper, the electro-elastic fields in a functionally gradient piezoelectric strip with an internal semi-infinite electrode are analyzed by using Fourier transform and Wiener-Hopf technique. The exact forms of asymptotic solutions and intensity factor and energy are obtained. The energy density criterion is proposed to study the fracture behavior near the electrode tip. The fracture initiation angle depends on the fracture resistance of the piezoelectric ceramic, bonding strength between piezoelectric and electrode, and the direction of least energy density factor S inside the piezoceramic.

The objective of this study is to develop and analyze a nonlinear suspended energy harvester (NSEH) that can be mounted on a rotating wheel. The device comprises a permanent magnet as a mass in the kinetic system, two springs, and two coil sets. The mass vibrates along the transverse direction because of the variations in gravitational force. This research establishes nonlinear vibration equations based on the resonance frequency variation of the energy harvester, these equations are used for analyzing the power generation and vibration of the harvester. The kinetic behaviors can be determined according to the stiffness in the two directions of the two suspended springs. Electromagnetic damping is examined to estimate the power output and effect of the kinematic behaviors on NSEH. The power output of the NSEH with a 52 Ω resistor connected in series ranged from approximately 30 to 4200 μW at wheel speeds that ranged from nearly 200 to 900 rpm.

In this paper, the wrist braces for the wrist fracture patients are developed. Geometry of the patient’s wrist surface anatomy was digitalized and recorded by an optical 3D scanner. An expert software was developed to generate the brace model, on which several holes are distributed to increase the air permeability. Finally, the brace is fabricated by commercial FDM 3D printer. For ensuring the strength of the wrist brace, the tensile test and impact test were conducted to measure the elastic modulus, yielding strength and fracture strength. A finite element model was established to investigate the stresses and deformations when the wrist brace is subjected to a static load. The mechanical properties measured in the tensile tests are as input parameters in the model. The static analysis showed that, for four considered movements of the wrist, the maximum von-Mises stress is less than the yielding strength. An impact analysis was also conducted to simulate brace impacted by a moving rigid ball with a mass of 0.3768[Formula: see text]kg. The results showed that the deformation at the impact point remains in the elastic range when the impact speed is 3[Formula: see text]m/s. The finite element calculations give us rules to design the number of holes and the thickness of the brace.