  Motivated by recent advances in the inverse design of electromagnetic
materials, we develop two methods for manipulating flexural waves on thin
elastic plates. Firstly, we derive a technique for determining plate pinning or
mass-loading of a thin plate, designing structures that focus elastic energy,
or isolate a region of space from vibrations. Taking inspiration from the
adjoint method in electromagnetism, we show how to design graded plates to act
as lenses or perform mode shaping. Both of the methods presented are simple,
versatile and straightforward to implement, making them useful for designing a
wide range of devices for sensing, energy harvesting and vibration isolation.
