Geometrical stiffness of loudspeaker cones:
FEA analysis and cone design
The geometry of a loudspeaker cone has a major influence on its mechanical stiffness, break-up behaviour and resulting frequency response.
This technical study examines how different cone geometries affect loudspeaker performance using Finite Element Modelling (FEM) with FINECone. Originally presented by Peter Larsen at the 2003 ALMA World Cone Symposium, the study demonstrates that geometrical stiffness is an important loudspeaker cone design parameter, alongside material properties.
The analysis compares flat, conical and curved cone geometries, including a modified Y-cone, and examines the effects of softer and higher-damping cone materials.
Why geometrical stiffness of loudspeaker cones matters in loudspeaker cone design
Loudspeaker cone behaviour is influenced by both the properties of the cone material and the geometry of the cone itself.Material properties such as stiffness, density and damping are important, but the physical shape of the cone also determines how effectively it resists deformation.
A cone with low geometrical stiffness can begin to break up at relatively low frequencies. Instead of moving as a relatively coherent piston, different areas of the cone begin to move with different amplitudes and phases.These modal movements can produce:
peaks and dips in frequency response
irregular off-axis response
cone break-up modes
changes in directivity
localised flexing of the cone
undesirable response features around the cone edge or neck.
The FINECone FEM study demonstrates these effects by changing the cone geometry while maintaining the other elements of the loudspeaker model.
FEA analysis of loudspeaker cone geometry
The study uses a 6.5-inch woofer model with a rubber surround, spider and voice coil/former. FINECone is used to perform the FEM analysis, based on an axisymmetric Multi Segment Method. The initial analysis uses an aluminium cone because its relatively low damping makes the cone modes particularly visible.
The study then compares several geometries, including:
flat cone
shallow 10-degree cone
deep conical cone
convex curved cone
concave curved cone
concave Y-cone with a modified cone neck.
The analysis also examines talc-filled polypropylene and paper-pulp cone materials to demonstrate the interaction between material stiffness, damping and cone geometry.
Flat loudspeaker cones
The completely flat cone provides a useful starting point because its geometrical stiffness is very low.
Despite using aluminium, the simulated frequency response becomes irregular from around 100 Hz as the cone begins to break up.
The FEM analysis also shows higher-order break-up modes, with multiple node lines developing across the cone surface.
This illustrates an important point in loudspeaker cone design: a stiff material alone does not necessarily produce a sufficiently stiff cone structure. The geometry itself contributes significantly to the mechanical behaviour.
Increasing stiffness with cone angle
Introducing even a relatively small cone angle substantially changes the behaviour.
The study examines a shallow cone with a 10-degree angle from flat. The additional three-dimensional geometry increases stiffness in the vertical direction and significantly improves the simulated frequency response.
In the example, the response remains relatively flat up to approximately 1 kHz, compared with the early irregularities of the completely flat cone.
This demonstrates why cone depth and profile are important variables when designing loudspeaker diaphragms.
Deep conical loudspeaker cones
The deeper conical geometry provides further extended response, although moderate high-frequency peaks remain.
The study notes that this type of response is relatively typical of a deep conical cone and demonstrates that increasing geometrical stiffness does not necessarily eliminate all modal behaviour.
Instead, cone geometry changes where and how the modes occur.
FEA makes these changes visible before physical prototyping, allowing the designer to investigate alternative geometries and identify potentially problematic modes during the design process.
Curved cone geometry and edge break-up
Curving the cone introduces another important change in its mechanical behaviour.
The convex curved cone in the study produces extended high-frequency response, but also develops a peak followed by a step and a response “hole”.
The FEM mode analysis identifies flexing around the outer edge of the cone and surround. Above approximately 1.7 kHz, the outer edge moves out of phase with the main cone structure.
This produces the characteristic edge-hole behaviour associated with insufficient geometrical stiffness around the cone edge.
This is an example of why looking only at the overall frequency response may not reveal the underlying mechanical cause of a response anomaly.
Concave curved cones
The study then examines a concave curved cone with the same overall depth.
The response remains flat to a higher frequency but develops more pronounced peaks.
The FEM mode analysis shows that the problem has effectively moved from the cone edge to the voice coil neck. Flexing at the inside of the cone neck produces significant peaks at higher frequencies.
This illustrates an important principle of cone design:
Increasing stiffness in one part of a diaphragm can move the dominant mechanical problem to another part of the structure.
The complete cone geometry therefore needs to be considered rather than optimising a single section in isolation.
The Y-cone: increasing neck stiffness
The study investigates a modified geometry in which the cone neck is bent to increase its geometrical stiffness.
This Y-cone design retains the basic concave curved geometry while increasing stiffness around the voice coil neck.
The resulting response has a similar overall shape, but the lower major peak is shifted upward to approximately 5 kHz.
The FEM analysis therefore provides a direct illustration of how a relatively small geometric modification can change the frequency at which a structural mode becomes significant.
Cone material, stiffness and damping
Cone geometry cannot be considered independently from material properties.
The study subsequently examines softer materials, including talc-filled polypropylene and medium-stiff paper pulp.
A softer cone material generally has lower structural stiffness. If it is combined with a geometry that also has low geometrical stiffness, break-up problems can become worse.
However, damping changes the resulting frequency response.
The polypropylene Y-cone example shows a well-damped response with an approximately second-order low-pass characteristic above 2 kHz. The lower material stiffness moves the modal behaviour to a lower frequency, while the higher damping reduces the severity of the resulting peak.
The paper cone example similarly produces a smoother response than the aluminium version, with its lower-stiffness modes shifted down in frequency but substantially better damped.
This demonstrates the relationship between three important cone-design variables:
Geometry + material stiffness + material damping
A successful cone design therefore does not necessarily require maximum material stiffness. The objective is to achieve the required modal and acoustic behaviour through an appropriate combination of geometry and material properties.
What loudspeaker cone FEA can reveal
The study demonstrates why FEA is useful in loudspeaker diaphragm development.
A conventional frequency-response measurement can show that a cone has a peak, dip or irregularity. FEA can help identify why that feature occurs. For example, the analysis can reveal:
where a cone is flexing
the frequency at which a mode develops
the location of node lines
whether the cone edge or neck is becoming dominant
how changing cone depth affects stiffness
how curvature changes modal behaviour
how material stiffness changes modal frequency
how damping affects the severity of resonances
how geometric modifications move unwanted modes.
This makes FEA particularly useful during the iterative stages of loudspeaker cone design, before committing to physical prototypes.
FINECone for loudspeaker cone FEA
The original study was carried out using FINECone, LOUDSOFT’s loudspeaker cone FEM software.
FINECone is designed specifically for loudspeaker diaphragm development and allows engineers to investigate the mechanical and acoustic behaviour of cone and dome structures using FEA.
The study demonstrates the value of using a loudspeaker-specific FEM approach: the cone geometry can be modified and its resulting modal behaviour and frequency response examined as part of the loudspeaker development process.
Learn more about FINECone
Key findings from the study
The original study reached several important conclusions about loudspeaker cone design.
Cone geometry directly affects structural stiffness.
Changing the cone profile can substantially change its resistance to deformation, even when the cone material remains unchanged.
Geometrical stiffness strongly affects break-up behaviour.
Low geometrical stiffness can allow break-up modes to develop at relatively low frequencies.
The location of flexing matters.
Increasing stiffness in one region can shift the dominant deformation to another part of the cone, such as the edge or voice coil neck.
Material and geometry must be considered together.
Softer materials can work effectively when combined with appropriate high-stiffness geometries and sufficient damping.
FEA can identify the structural cause of acoustic response features.
Modal analysis provides information that cannot be obtained from a frequency-response curve alo
Original paper:
This page is based on the original technical paper:
Geometrical Stiffness of Loudspeaker Cones — A FINECone FEM Study
Peter Larsen, LOUDSOFT
Presented at the 2003 ALMA World Cone Symposium.
The original paper contains the complete FEM results, cone geometries, mode plots and frequency-response figures discussed on this page.
Download the original Geometrical Stiffness of Loudspeaker Cones PDF:
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Frequently asked questions
What is geometrical stiffness in a loudspeaker cone?
Geometrical stiffness is the structural stiffness contributed by the physical shape and geometry of a loudspeaker cone. Cone depth, angle, curvature and local geometry can all affect how strongly the cone resists deformation and how its structural modes develop.
Why does cone geometry affect loudspeaker frequency response?
Cone geometry determines how the diaphragm deforms as frequency increases. When different parts of the cone begin moving with different amplitudes and phases, break-up modes can produce peaks, dips and other irregularities in the frequency response.
What is loudspeaker cone FEA?
Loudspeaker cone FEA, or Finite Element Analysis, is a numerical method used to analyse the mechanical behaviour of a cone or diaphragm. It can be used to investigate deformation, resonant modes, stiffness and break-up behaviour before physical prototypes are produced.
Does a stiffer cone always produce better sound?
No. Material stiffness is only one part of cone design. Geometry and damping also influence modal behaviour. A suitable combination of geometrical stiffness, material stiffness and damping can produce a more controlled response than simply maximising material stiffness.
How can FEA help with loudspeaker cone design?
FEA allows engineers to examine how changes in cone geometry and material properties affect structural modes and frequency response. This can help identify potential break-up problems and optimise the diaphragm before physical prototyping.
What is FINECone?
FINECone is LOUDSOFT’s FEM software for loudspeaker cone and diaphragm design. It was used for the original geometrical stiffness study described on this page.
