Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Dynamic Response of Stepped Beams Under Impulsive Loading

Aim To analyze dynamic failure of aerospace strutures subjected lateral impulsive loading. Methods Structures were modeled as rigid-perfectly plastic free-free stepped beams. Basic equations of motion un set up for analysis. Results Final pat deformation and rigid motion solutions were determined for a uniform impulsive loading. The critical rupture conditions for a space shuttle and a missile were obtained. Conclusion Failure is possible for aerospace structures under a uniform impulsive loading, but it is mere difficult in space.

On the Innovation,Design,Construction,and Experiments of OMEGA-Based SSPS Prototype:The Sun-Chasing Project

This study systematically introduces the development of the world’s first full-link and full-system ground demonstration and verification system for the OMEGA space solar power satellite(SSPS).First,the OMEGA 2.0 innovation design was proposed.Second,field-coupling theoretical models of sunlight concentration,photoelectric conversion,and transmitting antennas were established,and a systematic optimization design method was proposed.Third,a beam waveform optimization methodology considering both a high beam collection efficiency and a circular stepped beam shape was proposed.Fourth,a control strategy was developed to control the condenser pointing toward the sun while maintaining the transmitting antenna toward the rectenna.Fifth,a high-efficiency heat radiator design method based on bionics and topology optimization was proposed.Sixth,a method for improving the rectenna array’s reception,rectification,and direct current(DC)power synthesis efficiencies is presented.Seventh,high-precision measurement technology for high-accuracy beam-pointing control was developed.Eighth,a smart mechanical structure was designed and developed.Finally,the developed SSPS ground demonstration and verification system has the capacity for sun tracking,a high concentration ratio,photoelectric conversion,microwave conversion and emission,microwave reception,and rectification,and thus satisfactory results were obtained.

Three-to-one internal resonance in multiple stepped beam systems

In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales （a perturbation technique）. The modulation equations of the amplitudes and the phases are derived for two modes. These equations are utilized to determine steady state solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and .frequency- response curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots.

Sensitivity analysis of pull-in voltage for RF MEMS switch based on modified couple stress theory

An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency （RF） micro electro-mechanical system （MEMS） switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.