A method for reducing vibrations in a drill tubular coupled to a drill bit configured to drill a borehole in a formation includes: constructing a model of a system having the drill tubular, the model having a mass distribution, a stiffness, and/or a damping of the drill tubular; and calculating a plurality of modes using the model. The method also includes increasing an effective damping of the drill tubular for the plurality of modes by modifying at least one of the mass distribution, the stiffness, and the damping of the drill tubular using a predefined damping criterion, wherein the predefined damping criterion includes a ratio, the ratio having a deflection at the drill bit of at least one mode in the plurality and an eigenfrequency of the at least one mode in the plurality, wherein the deflection at the drill bit is raised to a power other than one.