A convolution type semi-analytical approach is proposed for structural dynamic response.With convolution original governing equation is transformed into a complete initial-value problem with initial conditions.The equation is mathematically equivalent to Gutrin's variational principle while it involves no functional and complicated calculation in variational principle.The new governing equation is solved by differential quadrature method in space domain and analytical series in time domain to obtain dynamic response.Dynamic response of a beam is studied.It is shown that the proposed method is accurate and efficient.

A method is proposed for controlling partial differential equation directly to beam.It takes differential quadrature method in space domain and series in time domain,and yields equations of determining all parameters for the displacement field by adding time points.The response displacement field can be obtained by solving linear equations.

A computational method is proposed on the basis of controling partial differential equation of thin circular plate.It takes differential quadrature method in space domain and series in time domain,adopts DQ linear equations for solving all parameters of the displacement field by adding time points.

The Semi-analytical method is derived based on convolution-type varicational principles to solve the 2-D transient heat transfer problems,which takes finite element discretization in space domain and analytic function in time domain.

A semi-analytical method is derived on the basis of Gurtin variational principle for solving one dimension initial-value problems of dynamics under alternating forces. This method takes finite element discretization in space domain and series in time domain.