Numerical Analysis Of Viscoelastic Euler-Bernoulli Beams

Based on the constitutive relation of viscoelastic mechanics,the constitutive equations of viscoelastic Euler-Bernoulli beams are constructed,and the dynamic behavior of viscoelastic Euler-Bernoulli beams is numerically analyzed.The main work of the thesis is as follows:First,the constitutive equations of viscoelastic Euler-Bernoulli beams are established.The differential structure model and the integral structure model are studied,and several commonly used differential structure models,Maxwell model,Kelvin model,and standard linear model are given.The advantages and disadvantages of the differential structure model and the integral structure model are compared.Based on this,the constitutive equation of the viscoelastic Euler-Bernoulli beam is established.Secondly,the constitutive equations of the fractional viscoelastic Euler-Bernoulli beam is solved by the method of the Legendre polynomial,and the algorithm is analyzed.The constitutive equation of the Euler Bernoulli beam is transformed into the matrix equation by subtly using the quasi-Legendre polynomial in the time domain.Can greatly simplify the solution process.The matrix equation is then discretized and solved to obtain a numerical solution.Finally,the kinetic analysis of two different fractional viscoelastic materials was carried out by numerical experiments,and the influence of time on displacement was considered for the first time.With the change of time and position,the displacement of polybutadiene beam and butyl B252 beam under different external forces was obtained,and the variation of displacement was obtained.In addition,the performance of the two materials was compared and analyzed...