A cooling system including a support structure and a cooling element is described. The cooling element has a thickness and includes an anchored region and a cantilevered arm. The anchored region is coupled to and supported by the support structure. The cantilevered arm extends outward from the anchored region. The cantilevered arm includes at least one cavity therein. The at least one cavity has a depth of at least one-third and not more than three-fourths of the thickness of the cooling element. The cooling element is configured to undergo vibrational motion when actuated to drive a fluid for cooling a heat-generating structure.