On the nonlinear dynamics of a piezoresistive based mass switch based on catastrophic bifurcation.

This research investigates the feasibility of mass sensing in piezoresistive MEMS devices based on catastrophic bifurcation and sensitivity enhancement due to the orientation adjustment of the device with respect to the crystallographic orientation of the silicon wafer. The model studied is a cantilever microbeam at the end of which an electrostatically actuated tip mass is attached. The piezoresistive layers are bonded to the vicinity of the clamped end of the cantilever and the device is set to operate in the resonance regime by means of harmonic electrostatic excitation. The nonlinearities due to curvature, shortening and electrostatic excitation have been considered in the modelling process. It is shown that once the mass is deposited on the tip mass, the system undergoes a cyclic fold bifurcation in the frequency domain, which yields a sudden jump in the output voltage of the piezoresistive layers; this bifurcation is attributed to the nonlinearities governing the dynamics of the response. The partial differential equations of the motion are derived and discretized to give a finite degree of freedom model based on the Galerkin method, and the limit cycles are captured in the frequency domain by using the shooting method. The effect of the orientation of the device with respect to the crystallographic coordinates of the silicon and the effect of the orientation of the piezoresistive layers with respect to the microbeam length on the sensitivity of the device is also investigated. Thanks to the nonlinearity and the orientation adjustment of the device and piezoresistive layers, a twofold sensitivity enhancement due to the added mass was achieved. This achievement is due to the combined amplification of the sensitivity in the vicinity of the bifurcation point, which is attributed to the nonlinearity and maximizing the sensitivity by orientation adjustment of the anisotropic piezoresistive coefficients.

Explainable Artificial Intelligence to Investigate the Contribution of Design Variables to the Static Characteristics of Bistable Composite Laminates.

Material properties, geometrical dimensions, and environmental conditions can greatly influence the characteristics of bistable composite laminates. In the current work, to understand how each input feature contributes to the curvatures of the stable equilibrium shapes of bistable laminates and the snap-through force to change these configurations, the correlation between these inputs and outputs is studied using a novel explainable artificial intelligence (XAI) approach called SHapley Additive exPlanations (SHAP). SHAP is employed to explain the contribution and importance of the features influencing the curvatures and the snap-through force since XAI models change the data into a form that is more convenient for users to understand and interpret. The principle of minimum energy and the Rayleigh-Ritz method is applied to obtain the responses of the bistable laminates used as the input datasets in SHAP. SHAP effectively evaluates the importance of the input variables to the parameters. The results show that the transverse thermal expansion coefficient and moisture variation have the most impact on the model's output for the transverse curvatures and snap-through force. The eXtreme Gradient Boosting (XGBoost) and Finite Element (FM) methods are also employed to identify the feature importance and validate the theoretical approach, respectively.

Comparative study on free vibration analysis of rotating bi-directional functionally graded beams using multiple beam theories with uncertainty considerations.

The present study investigates the free vibration behavior of rotating beams made of functionally graded materials (FGMs) with a tapered geometry. The material properties of the beams are characterized by an exponential distribution model. The stiffness and mass matrices of the beams are derived using the principle of virtual energy. These matrices are then evaluated using three different beam theories: Bernoulli-Euler (BE) or Classical Beam Theory (CBT), Timoshenko (T) or First-order Shear Deformation Theory (FSDT), and Reddy (R) or Third-order Shear Deformation Theory (TSDT). Additionally, the study incorporates uncertainties in the model parameters, including rotational velocity, beam material properties, and material distribution. The mean-centered second-order perturbation method is employed to account for the randomness of these properties. To ensure the robustness and accuracy of the probabilistic framework, numerical examples are presented, and the results are compared with those obtained through the Monte Carlo simulation technique. The investigation explores the impact of critical parameters, including material distribution, taper ratios, aspect ratio, hub radius, and rotational speed, on the natural frequencies of the beams is explored within the scope of this investigation. The outcomes are compared not only with previously published research findings but also with the results of 3-Dimensional Finite Element (3D-FE) simulations conducted using ANSYS to validate the model's effectiveness. The comparisons demonstrate a strong agreement across all evaluations. Specifically, it is observed that for thick beams, the results obtained from FSDT and TSDT exhibit a greater agreement with the 3D-FE simulations compared to CBT. It is shown that the coefficient of variation (C.O.V.) of first mode eigenvalue of TSDT, FSDT and CBT are approximately identical for random rotational velocity and discernible deviations are noted in CBT compared to FSDT and TSDT in the case of random material properties. The findings suggest that TSDT outperforms FSDT by eliminating the need for a shear correction coefficient, thereby establishing its superiority in accurately predicting the natural frequencies of rotating, tapered beams composed of FGMs.

Robust topological designs for extreme metamaterial micro-structures.

We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical properties of metamaterials. The algorithm is based on the bi-directional evolutionary topology optimization and energy-based homogenization approach. To simulate additive manufacturing uncertainty, combinations of spatial variation of the elastic modulus and/or, parametric variation of the Poisson's ratio at the unit cell level are considered. Computationally parallel Monte Carlo simulations are performed to quantify the effect of input material uncertainty to the mechanical properties of interest. Results are shown for four configurations of extreme mechanical properties: (1) maximum bulk modulus (2) maximum shear modulus (3) minimum negative Poisson's ratio (auxetic metamaterial) and (4) maximum equivalent elastic modulus. The study illustrates the importance of considering uncertainty for topology optimization of metamaterials with extreme mechanical performance. The results reveal that robust design leads to improvement in terms of (1) optimal mean performance (2) least sensitive design, and (3) elastic properties of the metamaterials compared to the corresponding deterministic design. Many interesting topological patterns have been obtained for guiding the extreme material robust design.

Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis.

The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed Ω of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes. Focusing on the cases of 2 : 1 and 3 : 2 resonances, detailed numerical results for small rotor damping reveal that stable bouncing periodic orbits, which coexist with non-contacting motion, arise just beyond the resonance speed Ω p:q . The theory of discontinuity maps is used to analyse the problem as a codimension-two degenerate grazing bifurcation in the limit of zero rotor damping and Ω = Ω p:q . An analytic unfolding of the map explains all the features of the bouncing orbits locally. In particular, for non-zero damping ζ, stable bouncing motion bifurcates in the direction of increasing Ω speed in a smooth fold bifurcation point that is at rotor speed O ( ζ ) beyond Ω p:q . The results provide the first analytic explanation of partial-contact bouncing orbits and has implications for prediction and avoidance of unwanted machine vibrations in a number of different industrial settings.

Excess baggage for birds: inappropriate placement of tags on gannets changes flight patterns.

Devices attached to flying birds can hugely enhance our understanding of their behavioural ecology for periods when they cannot be observed directly. For this, scientists routinely attach units to either birds' backs or their tails. However, inappropriate payload distribution is critical in aircraft and, since birds and planes are subject to the same laws of physics during flight, we considered aircraft aerodynamic constraints to explain flight patterns displayed by northern gannets Sula bassana equipped with (small ca. 14 g) tail- and back-mounted accelerometers and (larger ca. 30 g) tail-mounted GPS units. Tail-mounted GPS-fitted birds showed significantly higher cumulative numbers of flap-glide cycles and a higher pitch angle of the tail than accelerometer-equipped birds, indicating problems with balancing inappropriately placed weights with knock-on consequences relating to energy expenditure. These problems can be addressed by carefully choosing where to place tags on birds according to the mass of the tags and the lifestyle of the subject species.

Experimental and analytical parametric study of single-crystal unimorph beams for vibration energy harvesting.

This research presents an experimental and theoretical energy harvesting characterization of beam-like, uniform cross-section, unimorph structures employing single-crystal piezoelectrics. Different piezoelectric materials, substrates, and configurations are examined to identify the best design configuration for lightweight energy harvesting devices for low-power applications. Three types of piezoelectrics (singlecrystal PMN-PZT, polycrystalline PZT-5A, and PZT-5H-type monolithic ceramics) are evaluated in a unimorph cantilevered beam configuration. The devices have been excited by harmonic base acceleration. All of the experimental characteristics have been used to validate an exact electromechanical model of the harvester. The study shows the optimum choice of substrate material for single-crystal piezoelectric energy harvesting. Comparison of energy scavengers with stainless steel substrates reveals that single-crystal harvesters produce superior power compared with polycrystalline devices. To further optimize the power harvesting, we study the relation between the thickness of the substrate and the power output for different substrate materials. The relation between power and substrate thickness profoundly varies among different substrate materials. The variation is understood by examining the change of mechanical transmissibility and the variations of the coupling figure of merit of the harvesters with thickness ratio. The investigation identifies the optimal thickness of the substrate for different substrate materials. The study also shows that the densities of the substrates and their mechanical damping coefficients have significant effects on the power output.

Damage identification using inverse methods.

This paper gives an overview of the use of inverse methods in damage detection and location, using measured vibration data. Inverse problems require the use of a model and the identification of uncertain parameters of this model. Damage is often local in nature and although the effect of the loss of stiffness may require only a small number of parameters, the lack of knowledge of the location means that a large number of candidate parameters must be included. This paper discusses a number of problems that exist with this approach to health monitoring, including modelling error, environmental effects, damage localization and regularization.