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The purpose of this paper is to present some modifications in the spline‐based differential quadrature method (DQM), in order to accelerate the convergence of the method. The improvements are explained and examined by the examples of the free vibration of conical shells. The composite laminated shell, as well as isotropic one, are taken under consideration.

To determine weighting coefficients for the DQM, the spline interpolation with non‐standard definitions of the end conditions is used. One of these definitions combines natural and not‐a‐knot end conditions, while the other one uses the boundary conditions for considered problem as the end conditions. The weighting coefficients can be determined by solving set of equations arising from spline interpolation.

It is shown that the proposed modifications significantly improve the convergence of the method, especially when the boundary conditions are introduced at the stage of the computation of the weighting coefficients. Unfortunately, the use of this approach is limited to some types of boundary conditions.

The paper describes development of the modified spline interpolation dedicated to DQM and examines the possibility of building boundary conditions into the weighting coefficients at the stage of the computation of these coefficients.