Nonlinear Vibrations in Homogeneous Non-Prismatic Timoshenko Cantilevers

Deep cantilever beams, modelled using Timoshenko beam kinematics, have numerous applications in engineering. This study deals with the nonlinear dynamic response in a non-prismatic Timoshenko beam characterized by considering the deformed configuration of the axis. The mathematical model is derived using the extended Hamilton's principle under the condition of finite deflections and angles of rotation. The discrete model of the beam motion is constructed based on the finite difference method (FDM), whose validity is examined by comparing the results for a special case with the corresponding data obtained by commercial finite element (FE) software ABAQUS 2019. The natural frequencies and vibration modes of the beam are computed. These results demonstrate decreasing eigenfrequency in the beam with increasing amplitudes of nonlinear oscillations. The numerical analyses of forced vibrations of the beam show that its points oscillate in different manners depending on their relative position along the beam. Points close to the free end of the beam are subject to almost harmonic oscillations, and the free end vibrates with a frequency equal to that of the external force. When a point approaches the clamped end of the beam, it oscillates in two-frequency mode and lags in phase from the oscillations of the free end. The analytical model allows for the study of the influence of each parameter on the eigenfrequency and the dynamic response. In all cases, a strong correlation exists between the results obtained by the analytical model and ABAQUS, nonetheless, the analytical model is computationally less expensive.

Model load in case of an internal explosion

Introduction. Presently, there are no model loads that describe the burst effect of an internal explosion. The goal of the article is to design a model load that characterizes an internal explosion with regard for the effect of inertial safety structures. The author provides relevant examples.Methods. The experiment and the numerical modeling identify the characteristics of an internal explosion, primarily, its destructive effect. First of all, these characteristics include the pressure value and rate in the process of the first peak formation. A drop follows the first peak. Another rise to the second peak is followed by the final pressure drop. The rise to the first peak is described by a cubic parabola. The constant value of pressure is equal to the highest value of the two peaks. It replaces the drop and rise between the peaks. The linear dependence describes the area of the final pressure drop, so that the deformation is completed at the end point. The time of the pressure rise is determined by breakup, and it takes account of the characteristics of safety structures. The time of the second peak is the time when the flame area is maximal.Results and discussion. The deformation that may occur before the first peak represents a solution to the equation, describing the beam motion. This equation is provided in the article. The deformation between the peaks is determined by the balance of energy. The deformation, that occurs when the pressure drops, is identified by the solution to the motion equation. The solution is subject to the deformation completion condition.Conclusions. The results show that the time between the peaks is important when the pressure is close to maximal. The analysis identifies the conditions under which deformation remains elastic. These results can be contributed to the assessment of the bearing capacity of buildings that accommodate explosive production facilities. This approach ensures conservative results.

Peculiarities of AD33 aluminum alloy hand laser welding

The comparative investigation results of AD33 aluminum alloy welded joint quality dependence upon changes in a laser beam motion rate for conditions of hand and automatic laser welding are shown. A micro-structure of a welded joint at the hand and automatic laser welding of the AD33 alloy is investigated.

Design and simulation of an out-of-plane electrothermal microactuator

Microactuators are one of the most important components in microelectromechanical systems (MEMS). Therefore, designing effective out-of-plane actuators has been in progress for the last decade. This paper presents a novel design of the microactuator with a double stepped beam structure for large out-of-plane deflection output applied to microvalves. The design and analysis of the out-of-plane microactuator are implemented by the finite element method. Silicon is selected as the material of the actuator and the beam motion is generated by the Joule heating effect. Compared to a single stepped beam design reported in the literature, the simulation results show that the proposed double-stepped beam structure can deliver a much larger out-of-plane deflection. Under an applied current of 15 mA, the maximum deflection of the double stepped beam is nearly seven times higher than that of the single stepped beam structure. In addition, the stress analysis indicates that the largest stress (1.46 GPa) induced in the beam is much smaller than the yield strength (7 GPa) of the selected silicon material.

Dynamic Modeling and Experimental Validation of an Impact-Driven Piezoelectric Energy Harvester in Magnetic Field

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.

CONTROL OF THE ELECTRON BEAM DEFLECTION SYSTEM OF AN ELECTRON BEAM INSTALLATION

This paper explores patterns of electronic beam movement by controlling the transverse axis of the bundle of the uniform magnetic field generated by the coils of the electronic gun. For electron beam processes, the type of process, the technological mode, the design dimensions of the electronic gun, and the shape of the machined parts determines beam motion. The free and precise movement on random trajectories determines the possible applications of the electron beam process in performing various scientific experiments on material processing.

ELECTRON BEAM DYNAMICS AT OUTPUT MAGNETRON GUN IN GRADIENT MAGNETIC FIELD

The results of numerical calculations based on the electron beam dynamics generated by a magnetron gun in the transport channel in a gradient magnetic field are presented. The dependence of the final transverse distribution on a target on the amplitude and gradient of the magnetic field was investigated. The possibility of controlling the transverse dimensions of the beam has been studied. It was found that the electron flux undergoes radial compression, the magnitude of which is determined by the form of the gradient magnetic field. The main dependences of the electron beam motion in a given magnetic field are modeled. The possibility of adjusting the beam diameter by varying the magnetic field is shown.

Nonlinear Dynamics of Temperature-Dependent FG-GRC Laminated Beams Resting on Visco-Pasternak Foundations

This paper studies the nonlinear dynamic responses of graphene-reinforced composite (GRC) beams in a thermal environment. It is assumed that a laminated beam rests on a Pasternak foundation with viscosity and consists of GRC layers with various volume fractions of graphene reinforcement to construct a functionally graded (FG) pattern along the transverse direction of the beam. An extended Halpin–Tsai model which is calibrated against the results from molecular dynamics (MD) simulations is used to evaluate the material properties of GRC layers. The mechanical model of the beam is on the establishment of a third-order shear deformation beam theory and includes the von-Kármán nonlinearity effect. The model also considers the foundation support and the temperature variation. The two-step perturbation technique is first applied to solve the beam motion equations and to derive the nonlinear dynamic load–deflection equation of the beam. Then a Runge–Kutta numerical method is applied and the solutions for this nonlinear equation are obtained. The influence of FG patterns, visco-elastic foundation, ambient temperature and applied load on transient response behaviors of simply supported FG-GRC laminated beams is revealed and examined in detail.