Thermal/structural dynamic analysis via approximate analytical approach

The present paper uses a classical Galerkin weighted residual formulation to obtain the approximate analytical solution of a thermally loaded beam executing free flexural vibrations. The approach used is one where the time variable is considered in the same manner as the spatial variable, and is included in the basis functions. The basis functions used in the approach are polynomials obtained from the terms of a power series, with the condition of nullity on the boundary. This choice simplifies the algebraic manipulations considerably and yields close form expressions for components of the system matrix. The latter also simplifies the numerical computation of coefficients of the approximating polynomial. The approach provides benefits in terms of increased accuracy and lower computational costs.