A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beams

Abstract

The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.

Investigation of boundary flexibility on the performance of piezoelectric vibration energy harvesting beam systems by DTFM

“…The first method inputs each measured eigenfrequency from the test setup into an analytical frequency equation from which k t and k r are solved for (Ahmadian et al, 2001; Pabst and Hagedorn, 1995). The second method, called the sensitivity analysis, optimizes, an objective function which is the difference between the measured modal response from the test setup and the mathematically determined dynamic response to obtain the non-ideal boundary stiffness parameters (Ahmadian et al, 2014; Liu et al, 2019; Silva et al, 2015; Wang, 2014). Once the stiffness values are determined, the coefficients, p 1 , p 2 , and q 1 in equation (49), of the nonlinear fitting function can be computed or obtained from Figure 9 (which can be prepared a priori) shown here for efficiency range of 0.5%–99.5%.…”

“…Other approaches include modeling the non-ideal boundary as a linear combination of clamped and simply-supported boundary conditions using a weighting factor (Atci and Bagdatli, 2017; Bagdatli and Uslu, 2015; Heryudono and Lee, 2019; Hu and Adams, 2017; Lee, 2013), and as a deviation from the ideal boundary conditions (Eigoli and Ahmadian, 2011; Pakdemirli and Boyaci, 2001; Pakdemirli and Boyaci, 2002, 2003). Methods have also been proposed to identify the values of the support parameters, using mixed analytical and experimental methods (Ahmadian et al, 2001; Dehand et al, 2021; Liu et al, 2019; Pabst and Hagedorn, 1995; Rinaldi et al, 2008; Silva et al, 2015).…”

Variable Stiffness Composites: Optimal Design Studies

“…The optimization method used in the present work is an adaptive single objective method, which combines an optimal space-filling design of experiments, a kriging response surface, and mixed-integer sequential quadratic programming. This mathematical optimization method, based on a response surface, which enables in a lighter way the search for the global optimum, uses a minimum number of design points strictly necessary to allow building the kriging response surface [30,31].…”

“…This adaptive optimization technique can be described according to the present pseudocode, in a summarized form: This Algorithm 1 combines an optimal space-filling (OSF) design space, a kriging response surface and mixed-integer sequential quadratic programming (MISQP). Based on this hybrid approach the algorithm searches for the optimal solution based on the response surface obtained, which requires a minimum number of design points to build the kriging response surface [31]. This approach enables considering a reduced number of design points for the optimization process, which provides lower computation time requirements.…”

Identification of the viscoelastic boundary conditions of Euler‐Bernoulli beams using transmissibility

“…Ben‐Haim and Natke, Pabst and Hagedorn, and Aitbaeva and Akhtyamov determined the beam's boundary conditions from its natural frequencies by solving the characteristic equations. Silva et al utilized the differential evaluation optimization to identify the torsional stiffness of the elastic supports by taking the natural frequencies into the objective function. Another classical method used the static or dynamical responses of the Euler‐Bernoulli beam to identify the boundary conditions.…”