Buckling Electrothermal NEMS Actuators: Analytic Design for Very Slender Beams

Analytic approximations are presented for the response of buckling-mode electrothermal actuators with very slender beams with a width-to-length ratio of W/L≤0.001 of the type found in nanoelectromechanical systems (NEMS). The results are found as closed-form solutions to the Euler beam bending theory rather than by an iterative numerical solution or a time-consuming finite element analysis. Expressions for transverse deflections and stiffness are presented for actuators with the common raised cosine and chevron pre-buckled shapes. The approximations are valid when the effects of bending dominate over those of axial compression. A few higher-order approximations are also presented for less slender beams with 0.001≤W/L≤0.01.

The Cohesive Energy and Vibration Characteristics of Parallel Single-Walled Carbon Nanotubes

Based on the van der Waals (vdW) interaction between carbon atoms, the interface cohesive energy between parallel single-walled carbon nanotubes was studied using continuous mechanics theory, and the influence of the diameter of carbon nanotubes and the distance between them on the cohesive energy was analyzed. The results show that the size has little effect on the cohesive energy between carbon nanotubes when the length of carbon nanotubes is over 10 nm. At the same time, we analyzed the cohesive energy between parallel carbon nanotubes with the molecular dynamics simulation method. The results of the two methods were compared and found to be very consistent. Based on the vdW interaction between parallel carbon nanotubes, the vibration characteristics of the two parallel carbon nanotube system were analyzed based on the continuous mechanical Euler-beam model. The effects of the vdW force between carbon nanotubes, the diameter and length of carbon nanotubes on the vibration frequency of carbon nanotubes was studied. The obtained results are helpful in improving the understanding of the vibration characteristics of carbon nanotubes and provide an important theoretical basis for their application.

Damped outrigger semi-active control for seismic vibration mitigation

In earlier days, the only way to resist the lateral loads was to increase the lateral strength of the structure obtained by making larger cross sections and massive buildings. Structural control is one of the solutions and important topics in both points of view of security and comfort in recent years. To reduce the effect of seismic energy, one of the structural forms used is the outrigger. In recent years, supplementary devices are installed into the outrigger structure so that damping of the structure increases and helps in mitigating the vibration, this concept is called damped outrigger. In this study, a damped outrigger structure replicating St. Francis Shangri-La Place skyscraper is excited for the El-Centro earthquake, and the Kobe earthquake is numerically modeled with viscous dampers and Magneto-Rheological damper to compare its effectiveness. The finite element approach is used for the analysis of the structure using Bernoulli’s Euler beam theory in modeling the core of the structure as a beam element. The state-space approach is used in modeling the structure, dampers, and controller interface in MATLAB and Simulink, then results are obtained for the peak value of displacement, acceleration, and mean values of the response of the structure. The results are discussed, which shows the significant distinction between uncontrolled and controlled responses.

A New Class of Plane Curves with Arc Length Parametrization and Its Application to Linear Analysis of Curved Beams

The objective of this paper is to define one class of plane curves with arc-length parametrization. To accomplish this, we constructed a novel class of special polynomials and special functions. These functions form a basis of L2(R) space and some of their interesting properties are discussed. The developed curves are used for the linear static analysis of curved Bernoulli–Euler beam. Due to the parametrization with arc length, the exact analytical solution can be obtained. These closed-form solutions serve as the benchmark results for the development of numerical procedures. One such example is provided in this paper.

ANALYTICAL SOLUTION FOR NONLINEAR INTERACTION OF EULER BEAM RESTING ON A TENSIONLESS SOIL

The nonlinear interaction between an elastic Euler beam and a tensionless soil foundation is studied. Exact analytical solutions of the challenging problem are rather complicated. The basic obstacle is imposing compatibility conditions at lift-off points. These points are determined as a part of the solution although being needed to get the solution itself. In the current work, solutions are derived using the approximate Rayleigh-Ritz method. The principal of vanishing variation of potential energy is adopted. The solution is approximated using a set of suitable trial functions. Lift-off points are identified through an iterative procedure and compatibility conditions are satisfied implicitly. Results are presented for various cases, including clamped support and free end condition. Various distributed loading conditions are analyzed. Exact solutions are revised briefly. Accurate high order approximate analytical solutions are obtained using MAXIMA symbolic manipulator. The convergence of approximate solutions towards the exact solutions is verified. For each case detailed results of deflection, bending moment and shear are presented.

Watt Six-Bar Compliant Mechanism Analysis based on Kinematic and Dynamic Responses

In this study, a complete guide to kinematic and kinetic analyses of a Watt type six-bar compliant mechanism is conducted incorporating the flexible buckling of the initially straight element. In the analysis procedure, the hybrid utilization of the pseudo-rigid-body model (PRBM) and the nonlinear Elastic theory of beam buckling is presented. This partially compliant mechanism comprises three rigid links and two flexible links. The kinematic analyses of the mechanisms are done by using the vector loop closure equations, the PRBM of a large deflection cantilever beam, and derivation of nonlinear algebraic equations considering the quasi-static equilibrium and load-deflection curve of the flexible parts. Each of the elastic parts makes up a buckling pinned-pinned flexible Euler beam. The vector loop equations are combined with Newton-Euler dynamic formulations to provide the simultaneous constraint matrix. After these operations, the full mechanism is simulated to get both accelerations and forces for each time step. Finally, the design method is validated through experimental results. The findings derived from the combination of buckling Elastica solution and PRBM approach enable the analysis of Watt's six-bar compliant mechanism.