Nonlinear Harmonic Vibration Analysis of a Fully Clamped Micro-Beam

Nonlinear harmonic vibration analysis of a clamped-clamped micro-beam is studied in this paper. Nonlinear forced vibration of a special kind of micro-actuators is examined for the first time. Galerkin method is employed to derive the equation of motion of the micro-beam with two symmetric potential wells. An electric force composed of DC and AC components is applied to the structure. Multiple Scales method (MSM) is used to solve the nonlinear equation of motion. Primary and secondary resonances are taken into account and steady-state response of the microbeam is obtained. A parametric study is then carried out to investigate the effects of different parameters on the amplitude-frequency curves. Finally, phase plot and Poincare map have been taken into consideration to investigate the influence of the amplitude of the harmonic excitation on stability of the microelectromechanical system.

The Development of a Human Gait Model With Predictive Capability and the Simulation of Able-Bodied Gait

The development of current prostheses and orthoses typically follows a trial and error approach where the devices are designed based on experience, tried on human subjects and then redesigned iteratively. This design approach is costly, risky and time consuming. A predictive human gait model is desired such that prostheses can be virtually tested so that their performance can be predicted qualitatively, the cost can be reduced, and the risks can be minimized. The development of such a model is explained in this paper. The developed model includes two parts: a plant model which represents the forward dynamics of human gait and a controller which represents the central nervous system (CNS). The development of the plant model is explained in a different paper. This paper focuses on the control algorithm development and able-bodied gait simulation. The controller proposed in this paper utilizes model predictive control (MPC). MPC uses an internal model to predict the output in advance, compare the predicted output to the reference, and optimize control input so that the error between them is minimal. The developed predictive human gait model was validated by simulating able-bodied human gait. The simulation results showed that the controller is able to simulate the kinematic output close to experimental data.

Self-Excited Lateral Vibrations of Rolling Tires

In this study, a low degree-of-freedom mechanical model of a rolling tire is constructed, in which the lateral deformation of the contact patch and tire carcass is considered. The so-called delayed contact patch model is implemented and combined with a simple tire carcass model. The interaction between the contact patch and the carcass together with the lateral mode of the attached suspension system is modeled by means of minimum number of relevant parameters in a simplified way in order to construct analytical results. Critical parameter ranges of self-excited vibrations are determined against the longitudinal speed of the tire. The intricate shapes of the corresponding tire deformations are presented by means of numerical simulations.

Finding Periodic Solutions of Forced Systems With Local Nonlinearities: A Mixed Shooting Harmonic Balance Method

Several numerical approaches have been developed to capture nonlinear effects of dynamical systems. In this paper we present a mixed shooting-harmonic balance method to solve large mechanical systems with local nonlinearities efficiently. The Harmonic Balance Method as well as the shooting method have both their pros and cons. The proposed mixed shooting-HBM approach combines the efficiency of HBM and the accuracy of the shooting method and has therefore advantages of both.

Prediction of Isolated Resonance Curves Using Nonlinear Normal Modes

Isolated resonance curves are separate from the main nonlinear forced-response branch, so they can easily be missed by a continuation algorithm and the resonant response might be underpredicted. The present work explores the connection between these isolated resonances and the nonlinear normal modes of the system and adapts an energy balance criterion to connect the two. This approach provides new insights into the occurrence of isolated resonances as well as a method to find an initial guess to compute the isolated resonance curve using numerical continuation. The concepts are illustrated on a finite element model of a cantilever beam with a nonlinear spring at its tip. This system presents jumps in both frequency and amplitude in its response to a swept sinusoidal excitation. The jumps are found to be the result of a modal interaction that creates an isolated resonance curve that eventually merges with the main resonance branch as the excitation force increases. Excellent insight into the observed dynamics is provided with the NNM theory, which supports that NNMs can also be a useful tool for predicting isolated resonance curves and other behaviors in the damped, forced response.

Energy Harvesting Using the Rattleback: Theoretical Analysis and Simulations of Spin Resonance

This paper investigates the spin resonance of a rattleback subjected to base oscillations. The phenomenon of Spin resonance can transduce vibrations to rotations. The rattleback is an ellipsoidal top with a preferred direction of spin. If rotated anti to it, longitudinal vibrations are set up and spin direction is reversed. Simulations and results are presented which show that the rattleback has a mono-peak spin resonance with respect to base vibrations. Two frequencies that appear in the response are identified — the Coupled and Uncoupled frequencies. Spin resonance, it is deduced, occurs when the base frequency is twice the coupled frequency of the rattleback. A linearized model is developed and a closed form expression for the Resonant frequency in terms of the inertia parameters of the rattleback is derived. Novel ideas for applications in Energy harvesting and Vibration sensing that utilize the phenomenon of spin resonance are also included.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

Nonlinear Vibration Absorber Design: An Asymptotic Approach

The one-to-one internal resonance occurring in a two-degree-of-freedom (2DOF) system composed by a damped non-linear primary structure coupled with a nonlinear vibration absorber is studied via the method of multiple scales up to higher order (i.e., the first nonlinear order beyond the internal/external resonances). The periodic response predicted by the asymptotic approach is in good agreement with the numerical results obtained via continuation of the periodic solution of the equations of motion. The asymptotic procedure lends itself to manageable sensitivity analyses and thus to versatile optimization by which different optimal tuning criteria for the vibration absorber can possibly be found in semi-closed form.

Influence of the Hip Joint Modeling Approaches on the Kinematics of Human Gait

The influence of the hip joint formulation on the kinematic response of the model of human gait is investigated throughout this work. To accomplish this goal, the fundamental issues of the modeling process of a planar hip joint under the framework of multibody systems are revisited. In particular, the formulations for the ideal, dry, and lubricated revolute joints are described and utilized for the interaction of femur head inside acetabulum or the hip bone. In this process, the main kinematic and dynamic aspects of hip joints are analyzed. In a simple manner, the forces that are generated during human gait, for both dry and lubricated hip joint models, are computed in terms of the system’s state variables and subsequently introduced into the dynamics equations of motion of the multibody system as external generalized forces. Moreover, a human multibody model is considered, which incorporates the different approaches for the hip articulation, namely ideal joint, dry, and lubricated models. Finally, several computational simulations based on different approaches are performed and the main results presented and compared to identify differences among the methodologies and procedures adopted in this work. In addition some experimental data are presented and analyzed.

A Geometric Derivation of the Equations of Motion for Mechanical Systems With Scleronomic Constraints

A new set of equations of motion is presented for a class of mechanical systems subjected to equality motion constraints. Specifically, the systems examined satisfy a set of holonomic and/or nonholonomic scleronomic constraints. The main idea is to consider the equations describing the action of the constraints as an integral part of the overall process leading to the equations of motion. The constraints are incorporated one by one, in a process analogous to that used for setting up the equations of motion. This proves to be equivalent to assigning appropriate inertia, damping and stiffness properties to each constraint equation and leads to a system of second order ordinary differential equations for both the coordinates and the Lagrange multipliers associated to the motion constraints automatically. This brings considerable advantages, avoiding problems related to systems of differential-algebraic equations or penalty formulations. Apart from its theoretical value, this set of equations is well-suited for developing new robust and accurate numerical methods.