Design and Amplitude Dependence of Resonance Frequency of Origami-Inspired Vibration Isolators With Quasi-Zero-Stiffness Characteristic

This study aims to design two types of vibration isolators, with different spring mechanisms, using a foldable structure that is based on a cylinder torsional buckling pattern, and evaluate the vibration isolation performance of each design. Vibration isolation is achieved through nonlinear spring characteristics of the isolators, which have zero spring stiffness, achieved by attaching a linear spring to the foldable isolator structure. The two vibration isolators differ in the mechanical elements that constitute the foldable structure, which undergo tensile forces as the structure folds. For the first isolator, the mechanical elements are represented only by tension springs, which appropriately undergo tension. For the second isolator, the mechanical elements are designed so that embedded compression springs within the elements compress under tension, thus enabling the elements to work as tension springs. The excitation experiment results revealed that the different spring mechanisms produced equivalent resonance frequencies but different damping effects at the resonance and higher frequencies. When oscillations with multiple amplitudes were input, larger input amplitudes were found to correspond to lower resonance frequencies for both isolators. This trend contradicts that described in the nonlinear vibration theory modeled by the Duffing equation, and was determined to be caused by hysteresis of the spring phenomena in the vibration isolators.

Anechoic Stubs As a Means for Damping Frame Vibrations: Analysis Using an Exact Wave-Based Approach

This paper explores the addition of small stubs with anechoic terminations (termed herein ‘anechoic stubs’) as means for damping and/or removing vibration modes from planar frame structures. Due to the difficulties associated with representing anechoic boundary conditions in more traditional analysis approaches (e.g., analytical, finite element, finite difference, finite volume, etc.), the paper employs an exact wave-based approach, incorporating Timoshenko beams, in which an anechoic boundary is simply represented by a zero reflection matrix. Several numerically-evaluated examples are presented documenting novel effects anechoic stubs have on the vibration modes of a two-story frame, such as eliminated, inserted and exchanged mode shapes. Modal damping ratios are also computed as a function of the location and number of anechoic stubs, illustrating optimal locations as a function of mode number. Forced vibration studies are then carried-out, demonstrating reduced, eliminated, and inserted resonance response.

Computing Natural Frequencies and Mode Shapes of an Axially Moving Non-Uniform Beam

The partial differential equation of motion of an axially moving beam with spatially varying geometric, mass and material properties has been derived. Using the theory of linear time-varying systems, a general algorithm has been developed to compute natural frequencies, mode shapes, and the critical speed for stability. Numerical results from the new method are presented for beams with spatially varying rectangular cross sections with sinusoidal variation in thickness and sine-squared variation in width. They are also compared to those from the Galerkin method. It has been found that critical speed of the beam can be significantly reduced by non-uniformity in a beam’s cross section.

Experimental Forced Response Analysis of Two-Degree-of-Freedom Piecewise-Linear Systems With a Gap

In this paper, an experimental forced response analysis for a two degree of freedom piecewise-linear oscillator is discussed. First, a mathematical model of the piecewise linear oscillator is presented. Second, the experimental setup developed for the forced response study is presented. The experimental setup is capable of investigating a two degree of freedom piecewise linear oscillator model. The piecewise linearity is achieved by attaching mechanical stops between two masses that move along common shafts. Forced response tests have been conducted, and the results are presented. Discussion of characteristics of the oscillators are provided based on frequency response, spectrogram, time histories, phase portraits, and Poincaré sections. Period doubling bifurcation has been observed when the excitation frequency changes from a frequency with multiple contacts between the masses to a frequency with single contact between the masses occurs.

Extracting Maximum Power in the Presence of Internal Inductance of Electromagnetic Energy Harvesting Systems

In this paper, the effect of internal inductance of electromagnetic generators in the field of energy harvesting is discussed. Electromagnetic energy harvesters are typically operated at low frequencies. This results in the generator internal inductor impedance being significantly less than the generator internal resistance. However, at high frequencies, this inductance can no longer be ignored. Therefore, to maximize the harvested power, the internal inductance must be considered while designing the power electronics. This paper presents two methods to tackle this issue. The first method involves making use of a discrete capacitor which is able to reduce the inductance effect not just at resonant frequency but for the entire operating frequency range. The second method makes use of a concept similar to synchronized switching harvesting on inductors (SSHI) in piezoelectric energy harvesting. A capacitor and switch are added in the electromagnetic energy harvesting circuit to reduce the generator internal inductance effect. This method not only provides the benefit of performing well in the entire operating frequency range but also eliminates the need for precise maximum power tracking techniques, which further helps in reducing the circuit losses. Simulation results show a maximum power output increase of 56%.

Parametric Stiffness in Large-Scale Wind-Turbine Blades and the Effects on Resonance and Speed Locking

This paper is on parametric effect in large scale horizontal-axis wind-turbine blades and speed locking phenomenon for a simplified model of the in-plane blade-hub dynamics. The relative strength of the parametric stiffness is evaluated for actual and scaled-length blades. Fixed-position natural frequencies are found at different rotation angles to show the significance of the gravity’s parametric effect. The ratio of the parametric and elastic modal stiffness is then estimated for the scaled versions of the NREL’s blades for four models to present the relation between the blade size and the parametric effects. The parametric effect on blade tip placements are investigated for superharmonic resonances at orders two and three for blades of various lengths. An analysis of speed-locking is presented, and interpreted for the various blades.

Deformable Blade Element and Unsteady Vortex Lattice Fluid-Structure Interaction Modeling of a 2D Flapping Wing

Flapping insect wings experience appreciable deformation due to aerodynamic and inertial forces. This deformation is believed to benefit the insect’s aerodynamic force production as well as energetic efficiency. However, the fluid-structure interaction (FSI) models used to estimate wing deformations are often computationally demanding and are therefore challenged by parametric studies. Here, we develop a simple FSI model of a flapping wing idealized as a two-dimensional pitching-plunging airfoil. Using the Lagrangian formulation, we derive the reduced-order structural framework governing wing’s elastic deformation. We consider two fluid models: quasi-steady Deformable Blade Element Theory (DBET) and Unsteady Vortex Lattice Method (UVLM). DBET is computationally economical but does not provide insight into the flow structure surrounding the wing, whereas UVLM approximates flows but requires more time to solve. For simple flapping kinematics, DBET and UVLM produce similar estimates of the aerodynamic force normal to the surface of a rigid wing. More importantly, when the wing is permitted to deform, DBET and UVLM agree well in predicting wingtip deflection and aerodynamic normal force. The most notable difference between the model predictions is a roughly 20° phase difference in normal force. DBET estimates wing deformation and force production approximately 15 times faster than UVLM for the parameters considered, and both models solve in under a minute when considering 15 flapping periods. Moving forward, we will benchmark both low-order models with respect to high fidelity computational fluid dynamics coupled to finite element analysis, and assess the agreement between DBET and UVLM over a broader range of flapping kinematics.

Effects of Correlated Noise on the Performance of Persistence Based Dynamic State Detection Methods

The ability to characterize the state of dynamic systems has been a pertinent task in the time series analysis community. Traditional measures such as Lyapunov exponents are often times difficult to recover from noisy data, especially if the dimensionality of the system is not known. More recent binary and network based testing methods have delivered promising results for unknown deterministic systems, however noise injected into a periodic signal leads to false positives. Recently, we showed the advantage of using persistent homology as a tool for achieving dynamic state detection for systems with no known model and showed its robustness to white Gaussian noise. In this work, we explore the robustness of the persistence based methods to the influence of colored noise and show that colored noise processes of the form 1/ f α lead to false positive diagnostic at lower signal to noise ratios for α < 0.

Broadband and Enhanced Energy Harvesting Using Inerter Pendulum Vibration Absorber

Inerter-based vibration energy harvesters (VEHs) have been widely studied to harvest energy from large-scale structural vibrations. Recently, there have been efforts to increase the operation frequency bandwidth of VEHs by introducing a variety of stiffness and inertia nonlinearity. This paper proposes a new inerter-based VEH comprising an epicyclic-gearing inerter and a pendulum vibration absorber. The centrifugal force of the pendulum introduces a new type of inertia nonlinearity that broadens the frequency bandwidth. This inerter-pendulum VEH (IPVEH) is incorporated in a single-degree-of-freedom structure to demonstrate its performance and the equations of motion of the system are derived. The method of multiple scales is applied to derive the amplitude–frequency response relationship of the harvested power in the primary resonance. The harvested power is optimized through tuning the harvester’s electrical damping and the optimum power is benchmarked with that of conventional linear inerter-based VEHs. The results show that the IPVEH has larger bandwidth and harvested power and the improvement is correlated with the strength of its inertia nonlinearity.

Computational Modal Analysis of Half Scale Generic Business Jet Substructures

The primary objective of this work was to determine the modal parameters of two substructures of a half scale generic business jet model with pre-stressed skin panels. The effect that pre-stiffened skin panels has on the modal parameters of an aircraft fuselage subsection is not well documented in the literature. First, bending pre-stress on stiffened plates was empirically determined to increase stiffness without changing mode shapes. Second, preliminary finite element models of the substructures determined that the effect of skin pre-stress was significant in one of the two substructures. Finally, an updating technique to account for stiffening effects was proposed and validated to be effectively used in the substructure, improving computational results across all metrics. It is recommended that the model updating procedure developed in this work be used to model skin pre-stress for aircraft fuselage substructures. The improved accuracy of the updated computational model should be of significant interest to the aerospace industry. Future work can be performed to further develop the model updating technique introduced in this work to allow for widespread application.