An analytical method is developed to calculate the natural frequencies and the corresponding mode shapes of a zigzagstructure proposed for MEMS energy harvesting from ambient vibrations. The high natural frequencies of the existingdesigns of MEMS vibrational energy harvesters are serious drawbacks. A zigzag design is proposed to overcome thisdeficit. The governing partial differential equations are solved using separation of variables for each of the lateral beamsin the structure. The vibration of each beam is related to the vibration of its neighbor beams by continuity andequilibrium conditions. Finally enforcing the boundary conditions results the corresponding eigenvalue problemrevealing the natural frequencies and mode shapes. The usefulness of the design is proved by the relation between thenatural frequencies and number of elements, providing a method of designing a MEMS harvester with low naturalfrequency.
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