Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model

A simple noniterative method for recovering a space‐dependent load on the Euler‐Bernoulli beam equation

“…The only factor, which may cause a large amplification of the measured error, is the inversion of D, of which we plot the condition number of D with respect to m in Figure 1. It can be seen that the condition number is smaller than 50 000 even for m = 100, such that the matrix D is well-conditioned, which results in a stable solution of the expansion coefficients {a k , k = 1, … , m + 2}, and hence a stable solution of H(x) in Equation (14). We will give some examples to show the stability and accuracy of the new method.…”

“…Then, using Equation (14) for H(x), letting j = 1, … , n = m + 2 in Equation (15), and considering the orthogonality of…”

“…[3][4][5][6][7][8] The parameter identification issue is a subclass of inverse problems, which was studied as the inverse spectral problems. [9][10][11] Besides, some researchers studied different models of the Euler-Bernoulli nanobeams [12][13][14][15][16][17][18][19][20][21] in a microscopic scale.…”

Nanoscale mass nanosensor based on the vibration analysis of embedded magneto-electro-elastic nanoplate made of FGMs via nonlocal Mindlin plate theory

“…crack length, wavelength). However, the strain-driven integral constitutive nonlocal relation (5) proposed by Eringen (1983) is inapplicable to nonlocal elastic problems on bounded structural domains Barretta 2016, 2017a, b;Romano et al 2017a, b;Apuzzo et al 2017). In this paper we assume the following phenomenological differential constitutive law (consequent but not equivalent to Eq.…”

“…According to the suggested model of Eringen, the elastic strain is described by a Fredholm type integral equations in which the stress is result of a convolution between the local response to an elastic strain and a smoothing kernel dependent on a nonlocal parameter. But some researchers showed the constitutive boundary conditions and paradoxes of nonlocal integral model Barretta 2016, 2017a, b;Romano et al 2017a, b;Apuzzo et al 2017). They demonstrated that Eringen's nonlocal integral model admits no solution.…”