The invention is an improved apparatus for damping a wide range of oscillatory or wave motions in a plate, beam, shell or skin. The apparatus includes linearly-extending triangular hinged flexures in the form of spaced apart V-shaped spacer elements with the V substantially normal to the surface of the damped member, each flexure having two substantially rigid legs and a hinge flexure and a body portion adjacent the vertex of the V. An elongated substantially extensionally stiff constraining member is positioned in an offset, substantially parallel relationship to the surface of the damped member. A damping layer of a energy-dissipating viscoelastic material (VEM) connects the body portions of the hinged flexures to the constraining member. One or more of the spacer elements may have a lever attached to its body portion, the lever amplifying motion induced in its flexure toward the distal end of the lever. Multiple laterally-offset assemblies of spacer elements having motion amplifying levers, constraining members and VEM can be placed alongside one another in an offset parallel relationship with the levers being offset longitudinally and/or extending in opposite directions to dampen a wide range of short or long wave vibrations.