Numerical Study of the Vibrations of Beams with Variable Stiffness under Impulsive or Harmonic Loading

The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.

THE GENERAL SOLUTION FOR DYNAMIC RESPONSE OF NONHOMOGENEOUS BEAM WITH VARIABLECROSSSECTION

In this paper by means of the exact analytic method [1], the general solution fordynamic response of nonhomogeneous beam with variable cross section is obtained un-der arbitrary resonant load and boundary conditions. The problem is reduced to solvea non-positive differential equation. Generally, it is not solved by variational method.By the present method, the general solution for this problem may be written as an ana-lytic form. Hence, it is convenient for structure optimizing problem. In this paper, itsconvergence is proved. Numerical examples are given at the end of the paper. which in-dicates satisfactory results can be obtained.

EXACT SOLUTION FOR FINITE DEFORMATION PROBLEMS OF CANTILEVER BEAM WITH VARIABLE SECTION UNDER THE ACTION OF ARBITRARY TRANSVERSE LOADS

This paper deals with finite deformation problems of cantilever beam with variable sec- tion under the action of arbitrary transverse loads.By the use of a method of variable replacement, the nonlinear differential equation with varied coefficient for the problem can be transformed into an equation with variable separable.The exact solution can be obtained by the integration method. Some examples are given in the paper,and the results of these examples show that this exact solution includes the existing solutions in references as special cases.

Mobility-Aware Adaptive Beam Tracking for Vehicles in Mm Wave Communication Networks

The millimeter wave(mm Wave)is a potential solution for high data rate communication due to its availability of large bandwidth.However,it is challenging to perform beam tracking in vehicular mm Wave communication systems due to high mobility and narrow beams.In this paper,an adaptive beam tracking algorithm is proposed to improve the network throughput performance while reducing the training signal overhead.In particular,based on the mobility prediction at base station(BS),a novel frame structure with dynamic bundled timeslot is designed.Moreover,an actor-critic reinforcement learning based algorithm is proposed to obtain the joint optimization of both beam width and the number of bundled timeslots,which makes the beam tracking adapt to the changing environment.Simulation results demonstrate that,compared with the traditional full scan and Kalman filter based beam tracking algorithms,our proposed algorithm can improve the time-averaged throughput by 11.34%and 24.86%respectively.With the newly designed frame structure,it also outperforms beam tracking with conventional frame structure,especially in scenarios with large range of vehicle speeds.

Design and dynamic analysis of integrated architecture for vibration energy harvesting including piezoelectric frame and mechanical amplifier

Vibration energy harvesters(VEHs) can transform ambient vibration energy to electricity and have been widely investigated as promising self-powered devices for wireless sensor networks, wearable sensors, and applications of a micro-electro-mechanical system(MEMS). However, the ambient vibration is always too weak to hinder the high energy conversion efficiency. In this paper, the integrated frame composed of piezoelectric beams and mechanical amplifiers is proposed to improve the energy conversion efficiency of a VEH. First, the initial structures of a piezoelectric frame(PF) and an amplification frame(AF) are designed. The dynamic model is then established to analyze the influence of key structural parameters on the mechanical amplification factor. Finite element simulation is conducted to study the energy harvesting performance, where the stiffness characteristics and power output in the cases of series and parallel load resistance are discussed in detail. Furthermore, piezoelectric beams with variable cross-sections are introduced to optimize and improve the energy harvesting efficiency. Advantages of the PF with the AF are illustrated by comparison with conventional piezoelectric cantilever beams. The results show that the proposed integrated VEH has a good mechanical amplification capability and is more suitable for low-frequency vibration conditions.