MTR/DYNA Vibration Analysis Software

MTR/DYNA analyzes dynamic response of vibratory machine sets supported on rigid foundation at grade or on pile group in layered soil system over rigid base rock or uniform halfspace. The program also outputs foundation dynamic impedance in terms of constant-valued spring-mass-dashpot parameters for use in 3D dynamic response analysis of the superstructure using detailed finite element model.

Analytical Approach

MTR/DYNA is a frequency-domain analysis software. It uses rigorous finite element-based axi-symmetric point load solution with nonreflecting boundaries to calculate the 3n x 3n subgrade dynamic compliance (flexibility) matrix, where n is the number of soil/foundation interaction nodes. The resulting frequency-dependent, fully-coupled, complex-valued compliance matrix is then used to calculate the 6 x 6 foundation dynamic impedance at the center of the rigid, massless foundation by imposing rigid body transformation. In the case of pile group foundations, the dynamic stiffness of the piles at pile/soil interaction nodes are assembled using finite element method and added to the subgrade dynamic impedance matrix and solved for foundation impedance. The 6 x 6 foundation dynamic impedance is then coupled with the inertia of the machine set and support structures to form the final dynamic coefficient matrix, which is then solved for the dynamic loads imposed by the machinery. The system responses calculated at the center of foundation are then transformed to the requested response locations and outputted.

In addition to the system responses, the final transfer functions can be outputted to examine the machine/foundation system resonant frequencies.  The calculated 6 x 6 foundation dynamic impedance functions can be converted to equivalent foundation dynamic stiffness and dashpot (KMC) constants to be used as boundary condition in 3D detailed finite element analysis of superstructure.


The program has been developed specifically for practical applications and has the following characteristics:

  • The soil model consists of semi-infinite, horizontally layered system over rigid base rock or uniform halfspace. Program automatically subdivides the layers into smaller sublayers to ensure that the layer thicknesses satisfy the wave passage criteria for the highest frequency of analysis.
  • Machine foundations may consist of rigid blocks and mat foundation supported at grade or on piles.
  • For surface foundations, the program automatically discretizes the foundation footprint into a uniform grid having grid spacing small enough to satisfy the wave passage criteria for the highest frequency of analysis.
  • For pile foundations, the foundation-soil interaction occurs at all pile/soil interface nodes located at pile tip and along the cylindrical perimeter of the piles at soil layer interfaces. This ensures proper load transfer at pile/soil interface including pile-soil-pile interaction.
  • Piles are modeled using cylindrical pile elements characterized by their material and section properties. All piles are of the same length and properties.
  • Pile group configuration can be generated automatically for rectangular and circular pile group.  For arbitrary pile layout, the pile configuration may be defined by inputting the X and Y coordinates of the individual pile heads at the pile cap level.  Both vertical and batter piles can be modeled with pile cap at the ground surface or elevated above the ground surface.  The piles may have free or restrained head condition.
  • The machine sets, foundation mat and support pedestals are characterized by their translational and rotational lump or block inertia at multiple CGs defined by the coordinates above the foundation level.
  • The dynamic loads imposed by machinery consist of translational forces and rotational moments with out of phase motion applied at multiple points defined by the coordinates above the foundation level.
  • The machine/foundation response can be outputted at multiple points defined by their coordinates above the foundation level.
  • The final transfer functions can be outputted to examine resonant frequencies of the machine/foundation system for different modes of vibration.
  • Foundation dynamic impedance can be outputted in terms of equivalent stiffness, mass and dashpot constants for each frequency of vibration.
  • Restart capabilities allow analysis with new superstructure properties and different load cases to be performed quickly and efficiently by recovering the foundation impedance properties.
  • The machine operational frequencies can be analyzed to frequencies of 100Hz.

Input Data

The input data has been greatly simplified by automating the model generation and post-processing of the results in the program. The input to the program consists of the following.

  • Soil profile and properties
  • Foundation dimensions if surface foundations
  • Pile group configuration and properties if pile foundation
  • Lump or block inertia properties and CGs of machine sets and support structures
  • Amplitude, phase, and point of application of dynamic loads
  • Frequencies of analysis
  • Locations of response outputs


  • Dynamic response of the machine/foundation system subjected to dynamic loads imposed by the machine operations.
  • Foundation dynamic impedance and compliance functions for a specified frequency range to examine foundation system natural frequencies.
  • Foundation spring-mass-dashpot constants distributed over foundation area or per pile for input to detailed finite element analysis of superstructure.


MTR/DYNA is developed to perform rigorous vibration analysis of the foundation/soil system to properly account for soil structure interaction including the effects of:

  • Soil layering
  • Rigid base rock and uniform halfspace
  • Soil material damping
  • Foundation radiation (geometric) damping
  • Ground water table (high Poisson’s ratio)
  • Nonlinear soil behavior
  • Coupled foundation modes
  • Pile/soil interaction and pile group effects
  • Vibration analysis to frequencies of 100Hz

MTR/DYNA facilitates evaluation of the machine/foundation systems by assuming that the machine set and support structure are rigid relative to the soil and the foundation piles are of similar type.  For the final design, where more refined model of the superstructure is used the program provides equivalent foundation dynamic stiffness and damping parameters for vibration analysis.

For sample validation problem, please see Technical Node 01/11/2016.

MTR/DYNA implements rigorous solution for wave propagation in an unbounded soil media for both the ground and pile supported foundations.  This wave propagation scheme is illustrated in the video below that shows proper dissipation of energy in the foundation media from the horizontal harmonic vibration of a rigid foundation supported at the surface of uniform soil halfspace.