| An approximation technique is developed to compute the natural frequencies and mode shapes of coupled shear walls, which are on fixed or flexible foundations. This technique is extended to compute the deflection dynamics of coupled shear wall systems that are laterally loaded by an impulse load. The impulse load is the Mach stem of a blast wave generated by an above ground explosion. The Mach stem height is equal to the height of the coupled shear walls. The developed equations of motion and boundary conditions are derived using Hamilton's principle. The Ritz-Galerkin technique is used to develop matrix eigenvalue equations for computing the mode shapes and natural frequencies. A modal analysis, of infinite order, is chosen to solve the dynamic deflection equations. In order to uncouple the equations of motion, which describe the dynamics of the coupled shear wall system, it was necessary to derive two new orthogonality relations. The uncoupled equations are analytically solved using Duhamel's integral. Using the shape functions computed in the free vibration case, a truncated modal solution for the lateral and longitudinal deflections is derived. Using MATLAB, a program was written, which provides all computations and plots of both the shape functions and dynamic solutions. An example was presented to verify the model and to show the application of this technique. |
