Techniques for approximating a spatially varying Euler-Bernoulli model with a constant coefficient model

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam ∗

“…e books can provide a general overview about the Euler-Bernoulli beam theory, please see [1][2][3]. Some important studies related to beams modeled in the sense of classical beam theory are also summarized as follows, but not limited to [4][5][6][7][8][9][10][11][12][13][14][15]. e beam systems in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] have the integer order derivatives of the state function.…”

“…Some important studies related to beams modeled in the sense of classical beam theory are also summarized as follows, but not limited to [4][5][6][7][8][9][10][11][12][13][14][15]. e beam systems in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] have the integer order derivatives of the state function. In the beginning of 1930s, fractional derivative was introduced for describing the constitutive relation of some beam materials [16], and after 1980s, since fractional order equations have good memory and can be used to describe material properties more accurately with fewer parameters, they are considered to be good mathematical models for describing the dynamic mechanical behavior of materials [17].…”