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For an existing design or one that's highly constrained with little scope for modification, a single detailed finite element analysis can help in understanding the different modes of vibration and estimating performance. Price will be quoted based on estimated hours required multiplied by a low hourly rate (currently Au$100 per hour), depending on the complexity of the shape - from about $800 upwards.
For a more comprehensive study of a design, consider generic / parametric sonotrode design using Finite Element Analysis (FEA). This involves reducing any new concept to the simplest form that will accurately represent the finished product and choosing a limited number of parameters to represent the essential features of the design. The values of all these parameters pinpoint a single location in "design space". Then a fully-automated system drives multiple FEA program runs (typically hundreds or thousands of individual analyses) to explore the design space and find optimum designs.
Price will be quoted based on estimated hours required multiplied by a low hourly rate (currently Au$100 per hour). Complete projects start from around Au$3000 (subject to exchange rates, approx. US$2500).
All work is done using the free, open-source FEA program CalculiX and on completion of the work all necessary files will be provided to allow the client to repeat analyses or test future designs themselves. Some computing expertise is required but you don't need to be a FEA specialist to do this...
To request a free quote for your application, please contact me via the Contact Page. I will need full details of the sonotrode you wish to build and all constraints or limitations on the design.