Modeling of electronic packages under vibrations is quite an interesting and important problem. The Finite element method (FEM) is the most common tool that is used in simulating the ...vibration-induced deformations and stresses of electronics. Therefore, this paper aims to present an equivalent static solution, instead of the dynamic solution, to simulate this mechanical problem. Towards this goal, the mathematical derivation of the equivalent static loading is thoroughly discussed. This analytical derived solution is then validated with the results of experimentally acquired data and with dynamic finite element analysis (FEA) simulations in terms of the board transverse deflections and solder array stresses. The validation study showed great agreement with all solutions. The validity of this approach is certified through a case study. Thus, the use of the equivalent static loading method is highly recommended as, unlike dynamic analysis, it allows for the crucial inclusion of the nonlinear mechanical properties of the solder interconnects in computationally effective simulations.
•An efficient methodology to use static solutions in simulating electronic packages under vibration is presented.•The theoretical basis of this methodology is fully introduced using simple vibrations principles.•The results of this method were validated with measurements and with FEA.•A case study is conducted to test efficiency of the use of this equivalent static analysis is presented.
•A method to directly obtain scaling laws from a sensitivity analysis is proposed.•First order sensitivities allow for geometrical scaling with factors from 0.5 to 3.5.•Global vibration responses of ...scaled structures in similitude are accurately predicted.•Material properties and local vibration responses can be scaled as well.
Scaling laws are used to scale-up calculation or measurement results from a prototype structure to those of an original structure or vice versa. The scaling laws of mechanical structures are usually obtained from their equations of motion or from a dimensional analysis. This paper proposes scaling laws that are represented by a power law. The power law is directly deduced from the Π-theorem of similitude theory and the coefficients of the power law are obtained from first order sensitivities (sensitivity-based scaling laws). Among existing similitude analysis methods such as dimensional analysis the sensitivity-based scaling laws can be directly obtained from a model without a priori knowledge of its scaling behavior, e.g., from a finite element (FE) model. The applicability of the sensitivity-based scaling laws is demonstrated in three case studies. A simply supported rectangular plate subject to mechanical vibrations is modeled by an analytical approach based on the Kirchhoff plate theory and by an FE model based on the Mindlin-Reissner theory. The plate’s dimensions are considered as design parameters for the sensitivity-based scaling laws. It is found in the first case study that the sensitivity-based scaling laws exactly predict the natural frequencies and the mean squared transfer admittances of scaled models from those of the original plate. This is in agreement with current literature and, thus, the method proposed in this paper can be considered verified. In the second case study the sensitivity-based scaling laws are directly obtained from the FE model. A good accuracy of the predicted vibration responses of the scaled models is found since (1) the scaled model and the original one are in similitude, i.e., the mode shape order and the damping are kept, and (2) the scaled plate can still be considered thin. The latter is assessed by the length (or width) to thickness ratios of the investigated plates and a lower bound is proposed. The third case study comprises a simplified car undercarriage to demonstrate the applicability of the method in practical design engineering. Besides the geometry parameters the material properties are incorporated in the sensitivity-based scaling laws as well. It is found that the natural frequencies as well as the vibration velocities at an arbitrarily chosen receiver point of the scaled models can be accurately predicted from those of the original one for complete similitude conditions.
This work presents an experimental study related to the mechanical performance of a special design spring fabricated with a superelastic shape memory alloy (SMA-SE). For the experimental testing, the ...spring was coupled in a rotor machine, aiming to attenuate the mechanical vibration when the system went through a natural frequency without any external power source. It was verified that the reduction in instabilities stemmed from the better distribution of vibration force in the proposed device, as well as the damping capacity of the spring material. These findings showed that the application of the M-Shape device of SMA-SE for three different cases could reduce vibration up to 23 dB when compared to the situations without, and with, 1.5 mm of preload. The M-Shape device was shown to be efficient in reducing the mechanical vibration in a rotor system. This was due to the damping capacity of the SMA-SE material, and because the application did not require any external source of energy to generate phase transformation.
Vibration and luminosity frequency analysis of the SuperKEKB collider Serluca, Maurizio; Balik, Gael; Brunetti, Laurent ...
Nuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment,
02/2022, Volume:
1025
Journal Article
Peer reviewed
Open access
The SuperKEKB collider has entered the physics production phase with the aim to reach its target luminosity of 6×1035 cm−2s−1. Vibrations of the accelerator elements, especially around the ...Interaction Point (IP), could limit the performance of the collider. Since 2018, a 24-hour monitoring system of vibrations has been put in place on both sides of the Belle II detector. Measurements and analyses of the spectral components of these vibrations and of the transfer function of the mechanical supports are presented, along with measurements of luminosity spectra from the LumiBelle2 detectors, showing good agreement in spectral peak frequencies for several of the vibration sources.
This work presents a novel development of the impact-based mechanism for piezoelectric vibration energy harvesters. More precisely, the effect of an impacting mass on a cantilever piezoelectric ...transducer is studied both in terms of the tip mass value attached to the cantilever and impact position to find an optimal condition for power extraction. At first, the study is carried out by means of parametric analyses at varying tip mass and impact position on a unimorph MEMS cantilever, and a suitable physical interpretation of the associated electromechanical response is given. The effect of multiple impacts is also considered. From the analysis, it emerges that the most effective configuration, in terms of power output, is an impact at the cantilever tip without a tip mass. By changing the value of the tip mass, a sub-optimal impact position along the beam axis can also be identified. Moreover, the effect of a tip mass is deleterious on the power performance, contrary to the well-known case of a resonant energy harvester. A mesoscale prototype with a bimorph transducer is fabricated and tested to validate the computational models. The comparison shows a good agreement between numerical models and the experiments. The proposed approach is promising in the field of consumer electronics, such as wearable devices, in which the impact-based device moves at the frequencies of human movement and is much lower than those of microsystems.
The response of a Long Period Grating Fibre Sensor embedded into polymer matrix of a smart composite material to applied mechanical vibrations is analysed by observing the spectral shifts, ...broadenings and splitting of the resonance absorption bands appearing into resulting transmission spectrum. The developed model aims to improve the engineering of smart composite material fabrication and the design of its applications in aeronautics, industry, medicine and defence. The Long Period Grating Fibre Sensor simulation model is developed considering the role of optical fibre micro-bending effects caused by mechanical vibrations applied to polymer matrix. The sensor is operated as the smart composite material feedback loop which provides the input signal for automation systems and/or for smart material monitoring. The results of the performed simulations are compared to experimental results reported in literature observing a good agreement.
Purpose:
Range verification in ion beam therapy relies to date on nuclear imaging techniques which require complex and costly detector systems. A different approach is the detection of thermoacoustic ...signals that are generated due to localized energy loss of ion beams in tissue (ionoacoustics). Aim of this work was to study experimentally the achievable position resolution of ionoacoustics under idealized conditions using high frequency ultrasonic transducers and a specifically selected probing beam.
Methods:
A water phantom was irradiated by a pulsed 20 MeV proton beam with varying pulse intensity and length. The acoustic signal of single proton pulses was measured by different PZT‐based ultrasound detectors (3.5 and 10 MHz central frequencies). The proton dose distribution in water was calculated by Geant4 and used as input for simulation of the generated acoustic wave by the matlab toolbox k‐WAVE.
Results:
In measurements from this study, a clear signal of the Bragg peak was observed for an energy deposition as low as 1012 eV. The signal amplitude showed a linear increase with particle number per pulse and thus, dose. Bragg peak position measurements were reproducible within ±30 μm and agreed with Geant4 simulations to better than 100 μm. The ionoacoustic signal pattern allowed for a detailed analysis of the Bragg peak and could be well reproduced by k‐WAVE simulations.
Conclusions:
The authors have studied the ionoacoustic signal of the Bragg peak in experiments using a 20 MeV proton beam with its correspondingly localized energy deposition, demonstrating submillimeter position resolution and providing a deep insight in the correlation between the acoustic signal and Bragg peak shape. These results, together with earlier experiments and new simulations (including the results in this study) at higher energies, suggest ionoacoustics as a technique for range verification in particle therapy at locations, where the tumor can be localized by ultrasound imaging. This acoustic range verification approach could offer the possibility of combining anatomical ultrasound and Bragg peak imaging, but further studies are required for translation of these findings to clinical application.
The scope of the study was the employment of an innovative method beneficial to evaluate the impact of various emulsifying salts (ES) addition on selected properties of processed cheese sauces (PCS). ...The ES applied were disodium hydrogenphosphate (DSP), tetrasodium disphosphate (TSPP), pentasodium triphosphate (PSTP), sodium salt of polyphosphate n ˜ 20 (POLY) and trisodium citrate (TSC). Moreover, the examined effect was observed in two groups of samples, (i) PCS with non-adjusted pH and in (ii) PCS with adjusted pH. The hardness of the samples was influenced by the type of the applied ES, pH, and storage period. The PCS produced with DSP:TSPP (1:1; without pH adjustment) exhibited the higher hardness which was also confirmed by the increasing samples viscosity and storage modulus. The results obtained by the mechanical vibrations damping analysis were analogous to rheological analysis. Generally, it was found that more viscous PCS exhibited “better” vibration damping properties, which was reflected by a shift of the first resonance frequency peak position to lower frequencies. In case of all investigated samples it was verified that the increasing storage period caused increasing stiffness and led to a shift of the first resonance frequency peak position to higher frequencies.
•Processed cheese sauces were manufactured with different emulsifying salts.•Hardest samples were produced with DSP:TSPP (1:1) and without pH adjustment.•The hardness of all samples increased with the prolonging of the storage time.•The first resonance frequency peak position depended on the storage time.
The authors evaluated the short-term neuromuscular effects on the assessment of mechanical hand—arm systems induced by vibrating tools to investigate the relationship between the force exerted and ...the vibration exposure. The motor task consisted of holding the instrumented handle with the dominant hand at predetermined grip force values. Five subjects took part in the tests. The tests were developed in the absence of vibration and in the presence of vibration at 5 m/s2, 7.5 m/s2 and 10 m/s2. The push and pull force values were calculated in the tests on the five subjects.
Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this ...paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.
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