Spring and Gravity Laws of Vibration Energy Harvesting: Duality of Mass and Anomalously Nonmonotonic Nonlinear Power

Usual theory has it that large power is only attained by using large mass in harvesting of vibration energy. But can a heavy harvester be displaced at all or meaningfully under small vibration sources? Large mass means large materials with high costs, less ease of transportation and high difficulty of integration into portable technologies. Herein, it is derived and proved that power is inversely proportional to mass, and directly proportional to the stiffness of spring and to the gravity of the local environment where vibration energy is harvested. Systematic studies of several commercial and proof-of-concept piezoelectric, magnetic and mechanical vibration energy harvesters supported and established these mathematical findings. This paper further clarified the theory of maximizing power by mass increment and revealed that it only holds provided the displacement amplitude of vibration source is sufficient, otherwise power regresses to inverse of mass. Nonmonotonic nonlinear power which is common in reality is in accordance with expectations of dual mass and power relationships of both inverse and direct proportionalities, mediated by differing structural arrangements and properties of spring, fluctuation or permanence of displacement amplitude of vibration source, and characteristic scavenging of surface gravitational power