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1. Spectral analysis of Euler–Bernoulli beam model with distributed damping and fully non-conservative boundary feedback matrix

   https://doi.org/10.3233/ASY-211722  

   Shubov, Marianna A. (August 2021, Asymptotic Analysis)

   null (Ed.)

   The distribution of natural frequencies of the Euler–Bernoulli beam resting on elastic foundation and subject to an axial force in the presence of several damping mechanisms is investigated. The damping mechanisms are: ( i ) an external or viscous damping with damping coefficient ( − a 0 ( x )), ( ii ) a damping proportional to the bending rate with the damping coefficient a 1 ( x ). The beam is clamped at the left end and equipped with a four-parameter (α, β, κ 1 , κ 2 ) linear boundary feedback law at the right end. The 2 × 2 boundary feedback matrix relates the control input (a vector of velocity and its spacial derivative at the right end) to the output (a vector of shear and moment at the right end). The initial boundary value problem describing the dynamics of the beam has been reduced to the first order in time evolution equation in the state Hilbert space of the system. The dynamics generator has a purely discrete spectrum (the vibrational modes). Explicit asymptotic formula for the eigenvalues as the number of an eigenvalue tends to infinity have been obtained. It is shown that the boundary control parameters and the distributed damping play different roles in the asymptotical formulas for the eigenvalues of the dynamics generator. Namely, the damping coefficient a 1 and the boundary controls κ 1 and κ 2 enter the leading asymptotical term explicitly, while damping coefficient a 0 appears in the lower order terms. 

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2. Electrode pattern definition in ultrasound power transfer systems

   https://doi.org/10.1063/5.0139866  

   Sayed Ahmed, Moustafa; Shahab, Shima (March 2023, Applied Physics Letters)

   We use a high pattern-fidelity technique on piezoelectric electrodes to selectively excite high-order vibration modes, while isolating other modes, in multi-layered through-wall ultrasound power transfer (TWUPT) systems. Physical mechanisms, such as direct and inverse piezoelectric effects at transmitting and receiving piezoelectric elements, as well as wave propagation across an elastic barrier and coupling layers, all contribute to TWUPT. High-order radial modes in a TWUPT system feature strain nodes, where the dynamic strain distribution changes sign in the direction of disks' radii. This study explains theoretically and empirically how covering the strain nodes of vibration modes with continuous electrodes results in substantial cancelations of the electrical outputs. A detailed analysis is given for predicting the locations of the strain nodes. The electrode patterning for creating the transmitter and receiver shapes is determined by the regions where local force and charge cancelation do not occur, i.e., the two modal principal stress components have the same sign. Patterning for creating the electrode shapes is performed by high-fidelity numerical modeling supported by experiments. Using differential excitation on the transmitter side while monitoring transmitted power and efficiency on the reception side at various vibration modes is made possible by the unique nature of TWUPT systems. Due to an improvement in system quality and power factors, it is determined that employing the proposed electrode pattern designs enhances overall device efficiency and active power. The suppression of other modes makes up a filter feature that is paired with the enhancement at the mode under consideration. 

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3. Identification‐ and singularity‐robust inference for moment condition models

   https://doi.org/10.3982/QE1219  

   Andrews, Donald W.; Guggenberger, Patrik (January 2019, Quantitative Economics)

   This paper introduces a new identification‐ and singularity‐robust conditional quasi‐likelihood ratio (SR‐CQLR) test and a new identification‐ and singularity‐robust Anderson and Rubin (1949) (SR‐AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 +  γ bounded moments for some γ  > 0. No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification (for all k  ≥  p , where k and p are the numbers of moment conditions and parameters, respectively). The SR‐CQLR test reduces asymptotically to Moreira's CLR test when p  = 1 in the homoskedastic linear IV model. The same is true for p  ≥ 2 in most, but not all, identification scenarios. We also introduce versions of the SR‐CQLR and SR‐AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification. 

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4. Multiple-Scale Analysis of a Tunable Bi-Stable Piezoelectric Energy Harvester

   https://doi.org/10.1115/1.4046961  

   Qian, Feng; Abaid, Nicole; Zuo, Lei (April 2021, ASME Letters in Dynamic Systems and Control)

   null (Ed.)

   Abstract This paper presents the theoretical modeling and multiple-scale analysis of a novel piezoelectric energy harvester composed of a metal cantilever beam, piezoelectric films, and an axial preload spring at the moveable end. The harvester experiences mono- and bi-stable regimes as the stiffness of preload spring increases. The governing equations are derived with two high-order coupling terms induced by the axial motion. The literature shows that these high-order coupling terms lead to tedious calculations in the stability analysis of solutions. This work introduces an analytical strategy and the implementation of the multiple-scale method for the harvester in either the mono- or bi-stable status. Numerical simulations are performed to verify the analytical solutions. The influence of the electrical resistance, excitation level, and the spring pre-deformation on the voltage outputs and dynamics are investigated. The spring pre-deformation has a slight influence on the energy harvesting performance of the mono-stable system, but a large effect on that of the bi-stable system. 

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5. Franck–Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: A branch-cut free, numerically stable derivation

   https://doi.org/10.1063/5.0112217  

   Changala, P Bryan; Genossar, Nadav; Baraban, Joshua H (September 2022, The Journal of Chemical Physics)

   Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulas. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck–Condon approximation for the lowest-order anharmonic and Herzberg–Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F2, HOCl, CH2NH, and NO2. 

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