In the underwater sonar or similar devices where the high pressure field is required, the concentrating and black hole like structures have important applications in harvesting energy systems of elastic waves. In this work, a new kind of active elastic metamaterials with cavities and an acoustic concentrator are presented. By the feedback control gain of piezoelectric diaphragms, we can obtain both the controllable effective bulk modulus and density within a wide frequency range. Based on the coordinate transformation method and by the feedback control on the periodic arrangement of acoustic cavities, an acoustic concentrator with multilayered alternative homogeneous materials can be achieved. Numerical results show that the acoustic wave is perfectly limited within the core region of the concentrator, which can enhance the acoustic energy. These characteristics with the tunable effective bulk modulus and density within a very wide frequency range are expected to be helpful for the design of practical acoustic concentrators.