Purpose <p>In this paper, a numerical solution approach is proposed for the free vibration analysis of joined laminated composite conical-cylindrical-spherical shell (CCSS) structures with the application of the Walsh series method (WSM).</p> Methods <p>Identical laminated composite materials construct the individual shells of the joined structure, and each shell is elastically joined by the artificial spring technique. The displacements at any point of the joined laminated composite CCSS are derived based on the first-order shear deformation theory (FSDT). The differential equations of motion of joined shell structures are transformed into the algebraic equation discretized by the Walsh series and it can be treated as a standard linear eigenvalue problem. Similar to the boundary conditions, the artificial spring technique is also applied to the coupling conditions, thus it is possible to find out the natural frequencies of joined shells with arbitrary boundary conditions and connection conditions. The Walsh series method using the new orthogonal basis function, the Walsh function, is an effective numerical approach with high computational efficiency due to its simplicity and fast convergence. Therefore, in this paper, the Walsh series method is applied to the free vibration analysis of joined laminated composite CCSS for the first time. In order to verify the convergence and accuracy of the proposed approach, a comparison of the results obtained by the proposed approach with the ones in published literature and the ones of the ABAQUS software by finite element method (FEM) is carried out.</p> Results <p>The final results indicate that the proposed WSM converges stably at very fast rate and they are brought in line with previous literature data and finite element method (FEM) results. In the parametric study, the variations of the free vibration characteristics of the joined shell with respect to the orientation angle of the laminate, the number of layers, the elastic modulus ratio and the thickness variation are investigated. At the end of the parametric study, the characteristics of the variation of the frequency parameter with respect to the change of the connecting spring stiffness between shells, which has not been mentioned in the previous literature, are considered under various boundary conditions. In the parametric study, the variations of the frequency parameter with respect to the changes in the orientation angle and elastic modulus ratio() of the laminate composite material, the ones of the laminated material thickness and elastic modulus ratio and the variations of the frequency parameter with respect to changes in the orientation angle of every layer that consists the 3-layred laminated composite material are studied respectively. In addition, the whole progress demonstrates the numeric results of the frequency parameter in relation with the changes in the properties and geometric dimensions of the material. In this paper, a numerical solution approach is proposed for the free vibration analysis of joined laminated composite conical-cylindrical-spherical shell (CCSS) structures with the application of the Walsh series method (WSM). Identical laminated composite materials construct the individual shells of the joined structure, and each shell is elastically joined by the artificial spring technique. The displacements at any point of the joined laminated composite CCSS are derived based on the first-order shear deformation theory (FSDT). The differential equations of motion of joined shell structures are transformed into the algebraic equation discretized by the Walsh series and it can be treated as a standard linear eigenvalue problem. Similar to the boundary conditions, the artificial spring technique is also applied to the coupling conditions, thus it is possible to find out the natural frequencies of joined shells with arbitrary boundary conditions and connection conditions. The Walsh series method using the new orthogonal basis function, the Walsh function, is an effective numerical approach with high computational efficiency due to its simplicity and fast convergence. Therefore, in this paper, the Walsh series method is applied to the free vibration analysis of joined laminated composite CCSS for the first time. In order to verify the convergence and accuracy of the proposed approach, a comparison of the results obtained by the proposed approach with the ones in published literature and the ones of the ABAQUS software by finite element method (FEM) is carried out. The final results indicate that the proposed WSM converges stably at very fast rate and they are brought in line with previous literature data and finite element method (FEM) results. In the parametric study, the variations of the free vibration characteristics of the joined shell with respect to the orientation angle of the laminate, the number of layers, the elastic modulus ratio and the thickness variation are investigated. At the end of the parametric study, the characteristics of the variation of the frequency parameter with respect to the change of the connecting spring stiffness between shells, which has not been mentioned in the previous literature, are considered under various boundary conditions. In the parametric study, the variations of the frequency parameter with respect to the changes in the orientation angle and elastic modulus ratio() of the laminate composite material, the ones of the laminated material thickness and elastic modulus ratio and the variations of the frequency parameter with respect to changes in the orientation angle of every layer that consists the 3-layred laminated composite material are studied respectively. In addition, the whole progress demonstrates the numeric results of the frequency parameter in relation with the changes in the properties and geometric dimensions of the material.</p>